Emotional Patterns Over Time

Mastery Evidence

Identify a recurring emotional trigger and their typical response to it
Describe how their emotional understanding has changed compared to when they were younger
Set a personal goal related to emotional awareness, such as noticing when stress is building

Assessment Prompt

“Can [child] tell you something like 'I always get stressed before tests but I've learned that's normal for me' — showing they understand their own emotional patterns?”

Curriculum Standards1 alignment

PSPE-ID-CU-P3-5IB PYP Personal, Social and Physical Education (PSPE) Scope and Sequencecodes only

Standard code — full text not included in this dataset.

Prerequisites5

Personal Growth Over Time
softAges 10—11
Patterns in Your Own Reactions
softAges 7—9
Personal Coping Toolkit
softAges 9—11
Emotions and Decision-Making
hardAges 9—11
Culture and Experience Shape Emotions
softAges 9—11

Show full prerequisite tree

Personal Growth Over Time soft
Recognising how emotional awareness has grown over time is the Emotional Literacy domain-specific form of the foundational growth-reflection habit
- Patterns in Your Own Reactions soft
  Recognising that your patterns have changed over time requires first having noticed those patterns in the present
  - Vocabulary: self hard
    Noticing own patterns requires vocabulary of 'pattern', 'trigger', and 'reflect'
  - Feelings Versus Actions hard
    Noticing patterns in your reactions requires first understanding that feelings and responses are separable — you can only track a pattern once you're aware of the gap between feeling and action
    - Naming Your Feelings hard
      Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
      - Vocabulary: self hard
        Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
      - Feeling of not understanding soft
        Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
    - Vocabulary: self hard
      Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
  - Spotting Patterns soft
    Noticing recurring patterns in your own reactions is the PSD form of the universal pattern-recognition habit
    - Connecting New & Old Ideas soft
      Spotting patterns across domains is an extension of the habit of connecting new ideas to existing ones
      - Thinking Before Starting hard
        Making connections between new and old ideas requires the habit of activating prior knowledge first
        
        Persisting When It's Hard hard
        Activating prior knowledge requires the foundational habit of persistent engagement with new material
- Questioning First Impressions hard
  Reflecting on your own growth requires first having developed honest self-awareness of your assumptions and reactions — growth reflection is hollow without prior self-scrutiny
  - Vocabulary: self hard
    Questioning own assumptions requires precise vocabulary of 'assumption', 'bias', and 'perspective'
  - Patterns in Your Own Reactions soft
    Noticing that your first read of a situation might be wrong requires awareness of your own patterns of assumption and reaction
    - Vocabulary: self hard
      Noticing own patterns requires vocabulary of 'pattern', 'trigger', and 'reflect'
    - Feelings Versus Actions hard
      Noticing patterns in your reactions requires first understanding that feelings and responses are separable — you can only track a pattern once you're aware of the gap between feeling and action
      - Naming Your Feelings hard
        Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
        
        Vocabulary: self hard
        Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
        
        Feeling of not understanding soft
        Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
      - Vocabulary: self hard
        Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
    - Spotting Patterns soft
      Noticing recurring patterns in your own reactions is the PSD form of the universal pattern-recognition habit
      - Connecting New & Old Ideas soft
        Spotting patterns across domains is an extension of the habit of connecting new ideas to existing ones
        
        Thinking Before Starting hard
        Making connections between new and old ideas requires the habit of activating prior knowledge first
        
        Persisting When It's Hard hard
        Activating prior knowledge requires the foundational habit of persistent engagement with new material
  - Your Impact on Others hard
    Questioning your assumptions about social situations requires first having practised the harder skill of seeing yourself from another person's perspective
    - Teaching It Back soft
      Reflecting on how your behaviour landed on others requires being able to articulate your own thinking and intentions clearly — the self-explanation habit applied to social experience
      - Explaining Mathematical Reasoning soft
        The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
        
        Showing Your Working hard
        Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
        
        Numbers up to 10 into pairs soft
        Explaining part-part-whole decompositions exercises showing and telling
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Number bonds to 9 soft
        Explaining how to find number bonds to 10 exercises showing thinking with objects
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening and responding soft
        Explaining mathematical reasoning orally requires basic listening and responding skills
        
        What the equals sign means soft
        Determining whether equations are true/false exercises evaluating and justifying
        
        Reading +, −, and = symbols hard
        Deep understanding of = requires already being able to read and write number sentences
        
        Reading and writing numbers to 20 hard
        Writing number sentences requires reading and writing numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
        
        Addition as combining or putting together two hard
        Reading/writing the + symbol requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Reading/writing the − symbol requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Addition in any order soft
        Justifying why a+b=b+a exercises logical mathematical argument
        
        Addition as combining or putting together two hard
        Understanding commutativity of addition requires understanding addition
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Thinking Before Starting hard
        Explaining in your own words requires connecting new learning to existing knowledge already held in mind
        
        Persisting When It's Hard hard
        Activating prior knowledge requires the foundational habit of persistent engagement with new material
    - Vocabulary: self hard
      Reflecting on impact on others requires vocabulary of 'impact', 'perspective', and 'reflect'
    - Patterns in Your Own Reactions hard
      Reflecting on the impact of your behaviour on others requires first having noticed patterns in your own reactions — you need self-knowledge before you can examine your social footprint
      - Vocabulary: self hard
        Noticing own patterns requires vocabulary of 'pattern', 'trigger', and 'reflect'
      - Feelings Versus Actions hard
        Noticing patterns in your reactions requires first understanding that feelings and responses are separable — you can only track a pattern once you're aware of the gap between feeling and action
        
        Naming Your Feelings hard
        Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
        
        Vocabulary: self hard
        Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
        
        Feeling of not understanding soft
        Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Vocabulary: self hard
        Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
      - Spotting Patterns soft
        Noticing recurring patterns in your own reactions is the PSD form of the universal pattern-recognition habit
        
        Connecting New & Old Ideas soft
        Spotting patterns across domains is an extension of the habit of connecting new ideas to existing ones
        
        Thinking Before Starting hard
        Making connections between new and old ideas requires the habit of activating prior knowledge first
        
        Persisting When It's Hard hard
        Activating prior knowledge requires the foundational habit of persistent engagement with new material
    - Feelings Versus Actions soft
      Reflecting on impact requires understanding that your actions were choices, not automatic responses to feelings — the feelings/actions distinction underpins social accountability
      - Naming Your Feelings hard
        Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
        
        Vocabulary: self hard
        Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
        
        Feeling of not understanding soft
        Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
      - Vocabulary: self hard
        Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
  - Understanding Why soft
    Questioning your assumptions about why someone acted a certain way is elaborative interrogation applied to social cognition — asking 'why do I think this?' rather than accepting the first explanation
    - Teaching It Back hard
      Asking 'why does this work?' requires first being able to explain what you know — interrogation builds on explanation
      - Explaining Mathematical Reasoning soft
        The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
        
        Showing Your Working hard
        Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
        
        Numbers up to 10 into pairs soft
        Explaining part-part-whole decompositions exercises showing and telling
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Number bonds to 9 soft
        Explaining how to find number bonds to 10 exercises showing thinking with objects
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening and responding soft
        Explaining mathematical reasoning orally requires basic listening and responding skills
        
        What the equals sign means soft
        Determining whether equations are true/false exercises evaluating and justifying
        
        Reading +, −, and = symbols hard
        Deep understanding of = requires already being able to read and write number sentences
        
        Reading and writing numbers to 20 hard
        Writing number sentences requires reading and writing numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
        
        Addition as combining or putting together two hard
        Reading/writing the + symbol requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Reading/writing the − symbol requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Addition in any order soft
        Justifying why a+b=b+a exercises logical mathematical argument
        
        Addition as combining or putting together two hard
        Understanding commutativity of addition requires understanding addition
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Thinking Before Starting hard
        Explaining in your own words requires connecting new learning to existing knowledge already held in mind
        
        Persisting When It's Hard hard
        Activating prior knowledge requires the foundational habit of persistent engagement with new material
- Reflecting After Learning soft
  Reflecting on your own personal growth is the PSD form of the universal learning-reflection habit
  - Teaching It Back soft
    Articulating what helped in the learning process requires the self-explanation habit
    - Explaining Mathematical Reasoning soft
      The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
      - Showing Your Working hard
        Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
        
        Numbers up to 10 into pairs soft
        Explaining part-part-whole decompositions exercises showing and telling
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Number bonds to 9 soft
        Explaining how to find number bonds to 10 exercises showing thinking with objects
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening and responding soft
        Explaining mathematical reasoning orally requires basic listening and responding skills
      - What the equals sign means soft
        Determining whether equations are true/false exercises evaluating and justifying
        
        Reading +, −, and = symbols hard
        Deep understanding of = requires already being able to read and write number sentences
        
        Reading and writing numbers to 20 hard
        Writing number sentences requires reading and writing numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
        
        Addition as combining or putting together two hard
        Reading/writing the + symbol requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Reading/writing the − symbol requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Addition in any order soft
        Justifying why a+b=b+a exercises logical mathematical argument
        
        Addition as combining or putting together two hard
        Understanding commutativity of addition requires understanding addition
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
    - Thinking Before Starting hard
      Explaining in your own words requires connecting new learning to existing knowledge already held in mind
      - Persisting When It's Hard hard
        Activating prior knowledge requires the foundational habit of persistent engagement with new material
  - Learning from Mistakes hard
    Reflecting on the learning process requires the ability to analyse errors — reflection without error analysis stays superficial
    - Checking Your Own Work soft
      Investigating why something was wrong grows from the earlier habit of checking whether an answer seems right
    - Trying a New Approach hard
      Error analysis requires the habit of trying different approaches — you need to have tried something before you can analyse what went wrong
      - Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
      - Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
Patterns in Your Own Reactions soft
Reflecting on emotional patterns over time and recognising recurring triggers builds on the foundational habit of noticing patterns in your reactions
- Vocabulary: self hard
  Noticing own patterns requires vocabulary of 'pattern', 'trigger', and 'reflect'
- Feelings Versus Actions hard
  Noticing patterns in your reactions requires first understanding that feelings and responses are separable — you can only track a pattern once you're aware of the gap between feeling and action
  - Naming Your Feelings hard
    Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
    - Vocabulary: self hard
      Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
    - Feeling of not understanding soft
      Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
      - Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
  - Vocabulary: self hard
    Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
- Spotting Patterns soft
  Noticing recurring patterns in your own reactions is the PSD form of the universal pattern-recognition habit
  - Connecting New & Old Ideas soft
    Spotting patterns across domains is an extension of the habit of connecting new ideas to existing ones
    - Thinking Before Starting hard
      Making connections between new and old ideas requires the habit of activating prior knowledge first
      - Persisting When It's Hard hard
        Activating prior knowledge requires the foundational habit of persistent engagement with new material
Personal Coping Toolkit soft
Emotional pattern reflection connects to coping toolkit reflection
- Resilience and Bouncing Back hard
  Coping toolkit reflection builds on understanding resilience
  - Coping with Life Changes hard
    Resilience concept builds on coping with change
    - Words for Big Feelings soft
      Coping with change draws on vocabulary like 'cope', 'strategy', and 'settle'
  - Vocabulary: resilience and self hard
    Resilience as a concept requires understanding 'resilience', 'setback', 'persevere', and 'regulate' as precise terms
  - Choosing the Right Coping Strategy hard
    Resilience builds on having multiple coping strategies
    - Vocabulary: resilience and self hard
      Distinguishing different coping strategies requires the vocabulary of regulation, triggers, and distress
    - Simple Calming Strategies hard
      Different coping strategies builds on knowing basic calming strategies
      - Naming Basic Emotions soft
        Calming strategies benefit from naming the emotion you're trying to manage
      - Words for Big Feelings hard
        Calming strategies (calm, breathe, settle) rely on knowing this vocabulary to name and apply the techniques
    - How Emotions Feel in Your Body soft
      Choosing coping strategies benefits from reading body-emotion signals
      - Triggers and Causes of Feelings hard
        Body-emotion connection builds on understanding emotional triggers
        
        Feelings Change and Differ soft
        Identifying triggers benefits from knowing feelings change
        
        Naming Basic Emotions soft
        Understanding feelings change benefits from naming basic emotions
  - Emotions and Decision-Making soft
    Resilience benefits from understanding emotions influence decisions
    - Stop, Think, Then Choose soft
      Understanding emotions affect decisions connects to the decision-making process
      - Vocabulary: ethics and citizenship soft
        Decision-making process applies vocabulary of 'ethical', 'consequence', and 'responsibility'
      - Choosing a Strategy soft
        PSD decision-making skills underpin strategy selection in Learning-to-Learn
        
        Trying a New Approach hard
        Evaluating a strategy requires having deliberately chosen and tried different strategies — you need the switching habit first
        
        Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
        
        Guided Multi-Step Problem Solving soft
        The LtL strategy evaluation skill (9-10) builds on the early scaffolded habit of checking reasonableness in maths introduced at 6-7
        
        Feeling of not understanding soft
        Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Addition and subtraction within 20 soft
        Choosing strategies for adding within 20 requires planning and evaluating approaches
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Planning a Task soft
        Planning a mathematical approach is the domain-specific application of the universal task-planning habit
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
        
        Early Word Problems soft
        Planning approaches to word problems within 20 exercises this skill
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Making Sense of Problems hard
        Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
        
        Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
        
        How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
        
        Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
        
        Multi-Step Problem Solving soft
        The LtL strategy evaluation skill (9-10) builds on the maths-specific checking habit developed with teacher support at 7-8
        
        Trying a New Approach soft
        Trying a different mathematical strategy when stuck is the maths-specific application of the universal strategy-switching habit
        
        Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
        
        Building sentences soft
        Cross-subject: making sense of multi-step word problems requires understanding that sentences express complete thoughts (reading comprehension foundation)
        
        Guided Multi-Step Problem Solving hard
        Age 7-8 problem-solving builds on age 6-7 problem-solving
        
        Feeling of not understanding soft
        Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Addition and subtraction within 20 soft
        Choosing strategies for adding within 20 requires planning and evaluating approaches
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Planning a Task soft
        Planning a mathematical approach is the domain-specific application of the universal task-planning habit
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
        
        Early Word Problems soft
        Planning approaches to word problems within 20 exercises this skill
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        Making Sense of Problems hard
        Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
        
        Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
        
        How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
        
        Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
        
        Estimating by rounding soft
        Estimating and checking answers exercises problem-solving at this age
        
        Inverse: addition undoes subtraction hard
        Using inverse to check answers requires understanding the inverse relationship
        
        Finding a missing number in addition hard
        Inverse relationship builds on understanding subtraction as unknown-addend
        
        Addition as combining or putting together two hard
        Unknown-addend requires understanding both addition and subtraction
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Subtraction as unknown-addend reframes subtraction conceptually
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Addition and subtraction within 1000 soft
        Estimating and checking applies to three-digit calculations
        
        The three digits of a three-digit number hard
        Three-digit operations require three-digit place-value understanding
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        A Ten Is Ten Ones hard
        100 as ten tens extends understanding of 10 as ten ones
        
        The two digits of a two-digit number hard
        Must understand two-digit place value before extending to hundreds
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        Fluent adding and subtracting within 100 hard
        Adding/subtracting within 1000 extends within-100 skills
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Missing number problems (age 7+) soft
        Multi-step A+S problems exercise breaking problems into parts
        
        Adding and subtracting (age 7+) soft
        Formal written methods support solving more complex problems
        
        Fluent adding and subtracting within 100 hard
        Columnar methods require fluent within-100 addition/subtraction
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Addition and subtraction within 1000 hard
        Formal columnar methods build on conceptual understanding of composing/decomposing
        
        The three digits of a three-digit number hard
        Three-digit operations require three-digit place-value understanding
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        Fluent adding and subtracting within 100 hard
        Adding/subtracting within 1000 extends within-100 skills
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Two-Step Word Problems hard
        Complex missing-number problems extend simpler word problems
        
        Fluent adding and subtracting within 100 hard
        Solving word problems within 100 requires fluent computation within 100
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Early Word Problems hard
        Word problems within 100 extend word problems within 20
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Learning from Mistakes hard
        Evaluating whether a strategy helped requires being able to analyse what went wrong when it didn't
        
        Checking Your Own Work soft
        Investigating why something was wrong grows from the earlier habit of checking whether an answer seems right
        
        Trying a New Approach hard
        Error analysis requires the habit of trying different approaches — you need to have tried something before you can analyse what went wrong
        
        Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
      - Planning a Task soft
        PSD decision-making processes transfer directly to Learning-to-Learn planning frameworks
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
      - Actions and Their Consequences hard
        Decision-making process builds on understanding consequences
        
        Vocabulary: making decisions and keeping safe hard
        Understanding that actions have consequences requires the vocabulary word 'consequence' as a named concept
    - How Emotions Feel in Your Body hard
      Emotions influencing decisions builds on body-emotion awareness
      - Triggers and Causes of Feelings hard
        Body-emotion connection builds on understanding emotional triggers
        
        Feelings Change and Differ soft
        Identifying triggers benefits from knowing feelings change
        
        Naming Basic Emotions soft
        Understanding feelings change benefits from naming basic emotions
- Personal Goal-Setting soft
  Reflecting on strategies benefits from goal-setting experience
  - Vocabulary: resilience and self soft
    Goal-setting and progress monitoring uses vocabulary of self-regulation and managing distress when things go wrong
  - Setting Learning Goals soft
    PSD goal-setting scaffolds the learning goal practices taught in Learning-to-Learn
    - Finding Knowledge Gaps hard
      The plan-do-review cycle requires metacognitive monitoring — you cannot honestly review without being able to survey your own understanding
      - Choosing a Strategy hard
        Surveying understanding across a whole topic requires the strategy-evaluation habit applied at a wider scale
        
        Trying a New Approach hard
        Evaluating a strategy requires having deliberately chosen and tried different strategies — you need the switching habit first
        
        Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
        
        Guided Multi-Step Problem Solving soft
        The LtL strategy evaluation skill (9-10) builds on the early scaffolded habit of checking reasonableness in maths introduced at 6-7
        
        Feeling of not understanding soft
        Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Addition and subtraction within 20 soft
        Choosing strategies for adding within 20 requires planning and evaluating approaches
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Planning a Task soft
        Planning a mathematical approach is the domain-specific application of the universal task-planning habit
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
        
        Early Word Problems soft
        Planning approaches to word problems within 20 exercises this skill
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Making Sense of Problems hard
        Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
        
        Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
        
        How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
        
        Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
        
        Multi-Step Problem Solving soft
        The LtL strategy evaluation skill (9-10) builds on the maths-specific checking habit developed with teacher support at 7-8
        
        Trying a New Approach soft
        Trying a different mathematical strategy when stuck is the maths-specific application of the universal strategy-switching habit
        
        Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
        
        Building sentences soft
        Cross-subject: making sense of multi-step word problems requires understanding that sentences express complete thoughts (reading comprehension foundation)
        
        Guided Multi-Step Problem Solving hard
        Age 7-8 problem-solving builds on age 6-7 problem-solving
        
        Feeling of not understanding soft
        Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Addition and subtraction within 20 soft
        Choosing strategies for adding within 20 requires planning and evaluating approaches
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Planning a Task soft
        Planning a mathematical approach is the domain-specific application of the universal task-planning habit
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
        
        Early Word Problems soft
        Planning approaches to word problems within 20 exercises this skill
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        Making Sense of Problems hard
        Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
        
        Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
        
        How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
        
        Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
        
        Estimating by rounding soft
        Estimating and checking answers exercises problem-solving at this age
        
        Inverse: addition undoes subtraction hard
        Using inverse to check answers requires understanding the inverse relationship
        
        Finding a missing number in addition hard
        Inverse relationship builds on understanding subtraction as unknown-addend
        
        Addition as combining or putting together two hard
        Unknown-addend requires understanding both addition and subtraction
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Subtraction as unknown-addend reframes subtraction conceptually
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Addition and subtraction within 1000 soft
        Estimating and checking applies to three-digit calculations
        
        The three digits of a three-digit number hard
        Three-digit operations require three-digit place-value understanding
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        A Ten Is Ten Ones hard
        100 as ten tens extends understanding of 10 as ten ones
        
        The two digits of a two-digit number hard
        Must understand two-digit place value before extending to hundreds
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        Fluent adding and subtracting within 100 hard
        Adding/subtracting within 1000 extends within-100 skills
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Missing number problems (age 7+) soft
        Multi-step A+S problems exercise breaking problems into parts
        
        Adding and subtracting (age 7+) soft
        Formal written methods support solving more complex problems
        
        Fluent adding and subtracting within 100 hard
        Columnar methods require fluent within-100 addition/subtraction
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Addition and subtraction within 1000 hard
        Formal columnar methods build on conceptual understanding of composing/decomposing
        
        The three digits of a three-digit number hard
        Three-digit operations require three-digit place-value understanding
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        Fluent adding and subtracting within 100 hard
        Adding/subtracting within 1000 extends within-100 skills
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Two-Step Word Problems hard
        Complex missing-number problems extend simpler word problems
        
        Fluent adding and subtracting within 100 hard
        Solving word problems within 100 requires fluent computation within 100
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Early Word Problems hard
        Word problems within 100 extend word problems within 20
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Learning from Mistakes hard
        Evaluating whether a strategy helped requires being able to analyse what went wrong when it didn't
        
        Checking Your Own Work soft
        Investigating why something was wrong grows from the earlier habit of checking whether an answer seems right
        
        Trying a New Approach hard
        Error analysis requires the habit of trying different approaches — you need to have tried something before you can analyse what went wrong
        
        Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
      - Reflecting After Learning hard
        Metacognitive monitoring of a topic requires the reflective habits built in individual learning episodes
        
        Teaching It Back soft
        Articulating what helped in the learning process requires the self-explanation habit
        
        Explaining Mathematical Reasoning soft
        The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
        
        Showing Your Working hard
        Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
        
        Numbers up to 10 into pairs soft
        Explaining part-part-whole decompositions exercises showing and telling
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Number bonds to 9 soft
        Explaining how to find number bonds to 10 exercises showing thinking with objects
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Listening and responding soft
        Explaining mathematical reasoning orally requires basic listening and responding skills
        
        What the equals sign means soft
        Determining whether equations are true/false exercises evaluating and justifying
        
        Reading +, −, and = symbols hard
        Deep understanding of = requires already being able to read and write number sentences
        
        Reading and writing numbers to 20 hard
        Writing number sentences requires reading and writing numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Addition as combining or putting together two hard
        Reading/writing the + symbol requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Reading/writing the − symbol requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Addition in any order soft
        Justifying why a+b=b+a exercises logical mathematical argument
        
        Addition as combining or putting together two hard
        Understanding commutativity of addition requires understanding addition
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Thinking Before Starting hard
        Explaining in your own words requires connecting new learning to existing knowledge already held in mind
        
        Persisting When It's Hard hard
        Activating prior knowledge requires the foundational habit of persistent engagement with new material
        
        Learning from Mistakes hard
        Reflecting on the learning process requires the ability to analyse errors — reflection without error analysis stays superficial
        
        Checking Your Own Work soft
        Investigating why something was wrong grows from the earlier habit of checking whether an answer seems right
        
        Trying a New Approach hard
        Error analysis requires the habit of trying different approaches — you need to have tried something before you can analyse what went wrong
        
        Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
    - Planning a Task hard
      The plan-do-review cycle is the mature form of the basic planning habit established at age 6-7
      - Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
  - Breaking Tasks into Steps hard
    Goal-setting builds on ability to break tasks into steps
    - Vocabulary: resilience and self soft
      Breaking tasks into steps is a self-regulation strategy; vocabulary of being overwhelmed and managing setbacks is helpful
    - Guided Multi-Step Problem Solving soft
      The SEL skill of breaking a big task into manageable steps parallels and builds on the mathematical practice of planning a step-by-step approach to complex problems
      - Feeling of not understanding soft
        Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
      - Addition and subtraction within 20 soft
        Choosing strategies for adding within 20 requires planning and evaluating approaches
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Planning a Task soft
        Planning a mathematical approach is the domain-specific application of the universal task-planning habit
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
      - Early Word Problems soft
        Planning approaches to word problems within 20 exercises this skill
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Making Sense of Problems hard
        Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
        
        Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
        
        How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
        
        Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
    - Growth Mindset hard
      Breaking tasks into steps builds on growth mindset perseverance
      - Vocabulary: resilience and self hard
        The growth mindset concept requires understanding the vocabulary pair 'growth mindset' vs 'fixed mindset'
      - Learning from Mistakes hard
        Growth mindset builds on understanding mistakes as learning opportunities
        
        Words for Big Feelings soft
        Framing mistakes as learning uses the vocabulary of feelings management and coping with setback
      - Making Sense of Problems soft
        Growth mindset understanding (SEL) is grounded in the concrete experience of persevering through mathematical problems — the abstract principle is made real through mathematics
        
        Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
        
        How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
        
        Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
- Patterns in Your Own Reactions soft
  Building a personal toolkit of self-regulation strategies requires first having noticed the patterns of situations that trigger you and the reactions you typically have
  - Vocabulary: self hard
    Noticing own patterns requires vocabulary of 'pattern', 'trigger', and 'reflect'
  - Feelings Versus Actions hard
    Noticing patterns in your reactions requires first understanding that feelings and responses are separable — you can only track a pattern once you're aware of the gap between feeling and action
    - Naming Your Feelings hard
      Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
      - Vocabulary: self hard
        Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
      - Feeling of not understanding soft
        Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
    - Vocabulary: self hard
      Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
  - Spotting Patterns soft
    Noticing recurring patterns in your own reactions is the PSD form of the universal pattern-recognition habit
    - Connecting New & Old Ideas soft
      Spotting patterns across domains is an extension of the habit of connecting new ideas to existing ones
      - Thinking Before Starting hard
        Making connections between new and old ideas requires the habit of activating prior knowledge first
        
        Persisting When It's Hard hard
        Activating prior knowledge requires the foundational habit of persistent engagement with new material
- Choosing a Strategy soft
  Building a personal toolkit of self-regulation strategies and evaluating which work best is the PSD form of the universal strategy-evaluation habit
  - Trying a New Approach hard
    Evaluating a strategy requires having deliberately chosen and tried different strategies — you need the switching habit first
    - Feeling of not understanding hard
      Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
      - Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
    - Planning a Task hard
      Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
      - Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
  - Guided Multi-Step Problem Solving soft
    The LtL strategy evaluation skill (9-10) builds on the early scaffolded habit of checking reasonableness in maths introduced at 6-7
    - Feeling of not understanding soft
      Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit
      - Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
    - Addition and subtraction within 20 soft
      Choosing strategies for adding within 20 requires planning and evaluating approaches
      - Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
    - Planning a Task soft
      Planning a mathematical approach is the domain-specific application of the universal task-planning habit
      - Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
    - Early Word Problems soft
      Planning approaches to word problems within 20 exercises this skill
      - Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
    - Making Sense of Problems hard
      Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
      - Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
      - How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
      - Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
  - Multi-Step Problem Solving soft
    The LtL strategy evaluation skill (9-10) builds on the maths-specific checking habit developed with teacher support at 7-8
    - Trying a New Approach soft
      Trying a different mathematical strategy when stuck is the maths-specific application of the universal strategy-switching habit
      - Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
      - Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
    - Building sentences soft
      Cross-subject: making sense of multi-step word problems requires understanding that sentences express complete thoughts (reading comprehension foundation)
    - Guided Multi-Step Problem Solving hard
      Age 7-8 problem-solving builds on age 6-7 problem-solving
      - Feeling of not understanding soft
        Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
      - Addition and subtraction within 20 soft
        Choosing strategies for adding within 20 requires planning and evaluating approaches
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Planning a Task soft
        Planning a mathematical approach is the domain-specific application of the universal task-planning habit
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
      - Early Word Problems soft
        Planning approaches to word problems within 20 exercises this skill
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Making Sense of Problems hard
        Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
        
        Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
        
        How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
        
        Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
    - Estimating by rounding soft
      Estimating and checking answers exercises problem-solving at this age
      - Inverse: addition undoes subtraction hard
        Using inverse to check answers requires understanding the inverse relationship
        
        Finding a missing number in addition hard
        Inverse relationship builds on understanding subtraction as unknown-addend
        
        Addition as combining or putting together two hard
        Unknown-addend requires understanding both addition and subtraction
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Subtraction as unknown-addend reframes subtraction conceptually
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Addition and subtraction within 1000 soft
        Estimating and checking applies to three-digit calculations
        
        The three digits of a three-digit number hard
        Three-digit operations require three-digit place-value understanding
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        A Ten Is Ten Ones hard
        100 as ten tens extends understanding of 10 as ten ones
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        The two digits of a two-digit number hard
        Must understand two-digit place value before extending to hundreds
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
        
        Fluent adding and subtracting within 100 hard
        Adding/subtracting within 1000 extends within-100 skills
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
    - Missing number problems (age 7+) soft
      Multi-step A+S problems exercise breaking problems into parts
      - Adding and subtracting (age 7+) soft
        Formal written methods support solving more complex problems
        
        Fluent adding and subtracting within 100 hard
        Columnar methods require fluent within-100 addition/subtraction
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Addition and subtraction within 1000 hard
        Formal columnar methods build on conceptual understanding of composing/decomposing
        
        The three digits of a three-digit number hard
        Three-digit operations require three-digit place-value understanding
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        A Ten Is Ten Ones hard
        100 as ten tens extends understanding of 10 as ten ones
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The two digits of a two-digit number hard
        Must understand two-digit place value before extending to hundreds
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Fluent adding and subtracting within 100 hard
        Adding/subtracting within 1000 extends within-100 skills
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
      - Two-Step Word Problems hard
        Complex missing-number problems extend simpler word problems
        
        Fluent adding and subtracting within 100 hard
        Solving word problems within 100 requires fluent computation within 100
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Early Word Problems hard
        Word problems within 100 extend word problems within 20
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
  - Learning from Mistakes hard
    Evaluating whether a strategy helped requires being able to analyse what went wrong when it didn't
    - Checking Your Own Work soft
      Investigating why something was wrong grows from the earlier habit of checking whether an answer seems right
    - Trying a New Approach hard
      Error analysis requires the habit of trying different approaches — you need to have tried something before you can analyse what went wrong
      - Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
      - Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
Emotions and Decision-Making hard
Reflecting on emotional patterns builds on understanding emotions influence decisions
- Stop, Think, Then Choose soft
  Understanding emotions affect decisions connects to the decision-making process
  - Vocabulary: ethics and citizenship soft
    Decision-making process applies vocabulary of 'ethical', 'consequence', and 'responsibility'
  - Choosing a Strategy soft
    PSD decision-making skills underpin strategy selection in Learning-to-Learn
    - Trying a New Approach hard
      Evaluating a strategy requires having deliberately chosen and tried different strategies — you need the switching habit first
      - Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
      - Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
    - Guided Multi-Step Problem Solving soft
      The LtL strategy evaluation skill (9-10) builds on the early scaffolded habit of checking reasonableness in maths introduced at 6-7
      - Feeling of not understanding soft
        Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
      - Addition and subtraction within 20 soft
        Choosing strategies for adding within 20 requires planning and evaluating approaches
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Planning a Task soft
        Planning a mathematical approach is the domain-specific application of the universal task-planning habit
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
      - Early Word Problems soft
        Planning approaches to word problems within 20 exercises this skill
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
      - Making Sense of Problems hard
        Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
        
        Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
        
        How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
        
        Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
    - Multi-Step Problem Solving soft
      The LtL strategy evaluation skill (9-10) builds on the maths-specific checking habit developed with teacher support at 7-8
      - Trying a New Approach soft
        Trying a different mathematical strategy when stuck is the maths-specific application of the universal strategy-switching habit
        
        Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
      - Building sentences soft
        Cross-subject: making sense of multi-step word problems requires understanding that sentences express complete thoughts (reading comprehension foundation)
      - Guided Multi-Step Problem Solving hard
        Age 7-8 problem-solving builds on age 6-7 problem-solving
        
        Feeling of not understanding soft
        Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Addition and subtraction within 20 soft
        Choosing strategies for adding within 20 requires planning and evaluating approaches
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Planning a Task soft
        Planning a mathematical approach is the domain-specific application of the universal task-planning habit
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
        
        Early Word Problems soft
        Planning approaches to word problems within 20 exercises this skill
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Making Sense of Problems hard
        Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
        
        Checking Your Own Work soft
        Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
        
        How Many in Total? soft
        Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Listening to Texts Read Aloud soft
        Making sense of word problems requires listening comprehension skills
        
        Addition as combining or putting together two soft
        Making sense of addition problems requires understanding addition as combining
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Persisting When It's Hard soft
        Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
      - Estimating by rounding soft
        Estimating and checking answers exercises problem-solving at this age
        
        Inverse: addition undoes subtraction hard
        Using inverse to check answers requires understanding the inverse relationship
        
        Finding a missing number in addition hard
        Inverse relationship builds on understanding subtraction as unknown-addend
        
        Addition as combining or putting together two hard
        Unknown-addend requires understanding both addition and subtraction
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Subtraction as taking away or separating hard
        Subtraction as unknown-addend reframes subtraction conceptually
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Addition and subtraction within 1000 soft
        Estimating and checking applies to three-digit calculations
        
        The three digits of a three-digit number hard
        Three-digit operations require three-digit place-value understanding
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        A Ten Is Ten Ones hard
        100 as ten tens extends understanding of 10 as ten ones
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The two digits of a two-digit number hard
        Must understand two-digit place value before extending to hundreds
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Fluent adding and subtracting within 100 hard
        Adding/subtracting within 1000 extends within-100 skills
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
      - Missing number problems (age 7+) soft
        Multi-step A+S problems exercise breaking problems into parts
        
        Adding and subtracting (age 7+) soft
        Formal written methods support solving more complex problems
        
        Fluent adding and subtracting within 100 hard
        Columnar methods require fluent within-100 addition/subtraction
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Addition and subtraction within 1000 hard
        Formal columnar methods build on conceptual understanding of composing/decomposing
        
        The three digits of a three-digit number hard
        Three-digit operations require three-digit place-value understanding
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        A Ten Is Ten Ones hard
        100 as ten tens extends understanding of 10 as ten ones
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        The two digits of a two-digit number hard
        Must understand two-digit place value before extending to hundreds
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (tens and ones)
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        Fluent adding and subtracting within 100 hard
        Adding/subtracting within 1000 extends within-100 skills
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Two-Step Word Problems hard
        Complex missing-number problems extend simpler word problems
        
        Fluent adding and subtracting within 100 hard
        Solving word problems within 100 requires fluent computation within 100
        
        Adding within 100 hard
        Fluency within 100 builds on strategy-based adding within 100
        
        Addition and subtraction within 20 hard
        Adding within 100 extends within-20 strategies to larger numbers
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        The two digits of a two-digit number hard
        Adding within 100 using PV requires understanding tens and ones
        
        A Ten Is Ten Ones hard
        Understanding tens and ones place value requires the concept of 10 as a bundle
        
        The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        The teen numbers hard
        General two-digit place value extends from understanding teen number composition
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        Fluent adding and subtracting within 20 hard
        Fluency within 100 requires fluent single-digit facts
        
        Addition and subtraction within 20 hard
        Fluency within 20 requires prior strategy-based adding/subtracting within 20
        
        Number bonds to 9 hard
        Making-ten strategy requires knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 10 hard
        Strategies for within-20 calculation build on fluent within-10 knowledge
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Fluent adding and subtracting within 10 hard
        Fluency within 20 builds on fluency within 10
        
        Number bonds to 9 hard
        Fluency within 10 requires knowing number bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Fluency within 10 extends from fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Early Word Problems hard
        Word problems within 100 extend word problems within 20
        
        Adding and subtracting hard
        Word problems to 20 require the procedural ability to add/subtract to 20
        
        Number bonds hard
        Adding/subtracting to 20 procedurally requires knowing the number bonds
        
        Number bonds to 9 hard
        Number bonds within 20 builds on knowing bonds to 10
        
        Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Fluent adding and subtracting within 5 hard
        Recalling bonds within 20 builds on fluency within 5
        
        Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        Subtraction as taking away or separating hard
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        Addition and subtraction word problems soft
        Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
        
        Representing Addition and Subtraction hard
        Solving word problems within 10 requires ability to represent the operations with objects/drawings
        
        Addition as combining or putting together two hard
        Representing addition with objects/drawings requires understanding what addition means
        
        How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        Subtraction as taking away or separating hard
        Representing subtraction with objects/drawings requires understanding what subtraction means
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
    - Learning from Mistakes hard
      Evaluating whether a strategy helped requires being able to analyse what went wrong when it didn't
      - Checking Your Own Work soft
        Investigating why something was wrong grows from the earlier habit of checking whether an answer seems right
      - Trying a New Approach hard
        Error analysis requires the habit of trying different approaches — you need to have tried something before you can analyse what went wrong
        
        Feeling of not understanding hard
        Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
        
        Asking for Help hard
        Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
        
        Planning a Task hard
        Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
        
        Checking Your Own Work hard
        Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
  - Planning a Task soft
    PSD decision-making processes transfer directly to Learning-to-Learn planning frameworks
    - Checking Your Own Work hard
      Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
  - Actions and Their Consequences hard
    Decision-making process builds on understanding consequences
    - Vocabulary: making decisions and keeping safe hard
      Understanding that actions have consequences requires the vocabulary word 'consequence' as a named concept
- How Emotions Feel in Your Body hard
  Emotions influencing decisions builds on body-emotion awareness
  - Triggers and Causes of Feelings hard
    Body-emotion connection builds on understanding emotional triggers
    - Feelings Change and Differ soft
      Identifying triggers benefits from knowing feelings change
      - Naming Basic Emotions soft
        Understanding feelings change benefits from naming basic emotions
Culture and Experience Shape Emotions soft
Reflection on patterns benefits from understanding cultural context
- Hidden and Masked Feelings hard
  Cultural shaping of emotions builds on knowing people mask/hide feelings
  - Expressing Feelings with Words hard
    Recognising masked feelings builds on expressing own feelings appropriately
    - Triggers and Causes of Feelings soft
      Expressing feelings in words benefits from understanding triggers
      - Feelings Change and Differ soft
        Identifying triggers benefits from knowing feelings change
        
        Naming Basic Emotions soft
        Understanding feelings change benefits from naming basic emotions
    - Simple Calming Strategies soft
      Expressing feelings in words benefits from calming down first
      - Naming Basic Emotions soft
        Calming strategies benefit from naming the emotion you're trying to manage
      - Words for Big Feelings hard
        Calming strategies (calm, breathe, settle) rely on knowing this vocabulary to name and apply the techniques
  - Mild to Strong Emotions soft
    Recognising masked feelings benefits from understanding emotion intensity
    - Naming Basic Emotions hard
      Emotion intensity builds on knowing basic emotion categories

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Emotional Intelligence
hardAges 13—14