Personal Coping Toolkit

Mastery Evidence

Describe at least three personal coping strategies and when each is most effective
Recommend a strategy to a friend based on the friend's specific situation
Evaluate whether a strategy they tried worked well and explain their reasoning

Assessment Prompt

“Can [child] tell you 'When I'm stressed about exams I go for a walk and that helps, but when I'm sad I need to talk to someone' — showing they know their own coping toolkit?”

Curriculum Standards2 alignments

PSPE-ID-CU-P3-6IB PYP Personal, Social and Physical Education (PSPE) Scope and Sequencecodes only

Standard code — full text not included in this dataset.

PSPE-ID-CU-P4-7IB PYP Personal, Social and Physical Education (PSPE) Scope and Sequencecodes only

Standard code — full text not included in this dataset.

Prerequisites4

Resilience and Bouncing Back
hardAges 9—11
Personal Goal-Setting
softAges 9—11
Patterns in Your Own Reactions
softAges 7—9
Choosing a Strategy
softAges 9—10

Show full prerequisite tree

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)
        
        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
      - 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)
        
        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
        
        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'
        
        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
        
        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
        
        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
        
        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 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
        
        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
        
        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
        
        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
        
        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
      - 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)
        
        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
      - 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)
        
        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
        
        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'
        
        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
        
        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
        
        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
        
        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 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
        
        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
        
        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
        
        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
        
        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
      - 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)
        
        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)
        
        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
  - 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)
        
        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
  - 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)
        
        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
  - 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)
        
        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
        
        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
        
        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
        
        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)
        
        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
        
        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
        
        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)
        
        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
        
        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 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
        
        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)
        
        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
        
        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'
  - 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
        
        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)
        
        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
        
        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 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
        
        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)
        
        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
        
        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'
      - 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
        
        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)
    - 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
        
        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)
        
        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
        
        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 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
        
        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)
        
        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
        
        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'
      - 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
        
        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'
- 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

Unlocks2

Emotional Patterns Over Time
softAges 9—11
Growth Through Adversity
hardAges 13—14