Habits and Motivation
CONCEPTUALUnderstand habit formation through the cue-routine-reward loop and how to design new habits intentionally; distinguish intrinsic motivation (doing something for its own value) from extrinsic motivation (rewards/punishments) and understand when each is more effective; understand procrastination as primarily an emotion regulation problem (avoiding discomfort) rather than a time management failure; apply self-determination theory (autonomy, competence, relatedness) to boost intrinsic motivation; design environments that reduce friction for desired behaviours
Mastery Evidence
Assessment Prompt
“If [child] keeps meaning to do something important but finds themselves putting it off, can they explain the real reason people procrastinate — it's not laziness — and describe one practical change they could make to their environment to make starting easier?”
Prerequisites2
- Good Stress and Bad StresshardAges 11—12
- Personal Goal-SettinghardAges 9—11
Show full prerequisite tree
- Good Stress and Bad Stress hard
Advanced resilience skills depends on foundational advanced self-regulation
- 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
- 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
- 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
- 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
- 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
- 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
- Adding and subtracting hard
Word problems to 20 require the procedural ability to add/subtract to 20
- 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
Fluency with addition within 5 requires understanding addition as combining
- Subtraction as taking away or separating hard
Fluency with subtraction within 5 requires understanding subtraction as taking away
- Addition and subtraction word problems soft
Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
- Representing Addition and Subtraction hard
Solving word problems within 10 requires ability to represent the operations with objects/drawings
- Addition as combining or putting together two hard
Representing addition with objects/drawings requires understanding what addition means
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Representing subtraction with objects/drawings requires understanding what subtraction means
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Making Sense of Problems hard
Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
- Checking Your Own Work soft
Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
- How Many in Total? soft
Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Listening to Texts Read Aloud soft
Making sense of word problems requires listening comprehension skills
- Addition as combining or putting together two soft
Making sense of addition problems requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Persisting When It's Hard soft
Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
- Multi-Step Problem Solving soft
The LtL strategy evaluation skill (9-10) builds on the maths-specific checking habit developed with teacher support at 7-8
- Trying a New Approach soft
Trying a different mathematical strategy when stuck is the maths-specific application of the universal strategy-switching habit
- Feeling of not understanding hard
Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Planning a Task hard
Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
- Checking Your Own Work hard
Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
- Building sentences soft
Cross-subject: making sense of multi-step word problems requires understanding that sentences express complete thoughts (reading comprehension foundation)
- 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
- 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
- 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
Fluency with addition within 5 requires understanding addition as combining
- Subtraction as taking away or separating hard
Fluency with subtraction within 5 requires understanding subtraction as taking away
- Planning a Task soft
Planning a mathematical approach is the domain-specific application of the universal task-planning habit
- Checking Your Own Work hard
Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
- Adding and subtracting hard
Word problems to 20 require the procedural ability to add/subtract to 20
- Addition and subtraction word problems soft
Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
- Representing Addition and Subtraction hard
Solving word problems within 10 requires ability to represent the operations with objects/drawings
- Addition as combining or putting together two hard
Representing addition with objects/drawings requires understanding what addition means
- Subtraction as taking away or separating hard
Representing subtraction with objects/drawings requires understanding what subtraction means
- Making Sense of Problems hard
Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making
- Checking Your Own Work soft
Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context
- How Many in Total? soft
Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Listening to Texts Read Aloud soft
Making sense of word problems requires listening comprehension skills
- Addition as combining or putting together two soft
Making sense of addition problems requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Persisting When It's Hard soft
Mathematical perseverance with problems is the domain-specific application of the universal persistence habit
- Inverse: addition undoes subtraction hard
Using inverse to check answers requires understanding the inverse relationship
- Finding a missing number in addition hard
Inverse relationship builds on understanding subtraction as unknown-addend
- Addition as combining or putting together two hard
Unknown-addend requires understanding both addition and subtraction
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Subtraction as unknown-addend reframes subtraction conceptually
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Addition and subtraction within 1000 soft
Estimating and checking applies to three-digit calculations
- The three digits of a three-digit number hard
Three-digit operations require three-digit place-value understanding
- 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
- Fluent adding and subtracting within 100 hard
Adding/subtracting within 1000 extends within-100 skills
- 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
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Fluent adding and subtracting within 100 hard
Columnar methods require fluent within-100 addition/subtraction
- 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
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- 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
- Fluent adding and subtracting within 100 hard
Adding/subtracting within 1000 extends within-100 skills
- Fluent adding and subtracting within 100 hard
Solving word problems within 100 requires fluent computation 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
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Adding and subtracting hard
Word problems to 20 require the procedural ability to add/subtract to 20
- Addition and subtraction word problems soft
Word problems to 20 extend from word problems within 10 — same problem structures at a higher range
- Representing Addition and Subtraction hard
Solving word problems within 10 requires ability to represent the operations with objects/drawings
- Learning from Mistakes hard
Evaluating whether a strategy helped requires being able to analyse what went wrong when it didn't
- Checking Your Own Work soft
Investigating why something was wrong grows from the earlier habit of checking whether an answer seems right
- Trying a New Approach hard
Error analysis requires the habit of trying different approaches — you need to have tried something before you can analyse what went wrong
- Feeling of not understanding hard
Strategy switching is triggered by noticing the current approach isn't working — requires comprehension monitoring
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Planning a Task hard
Switching strategy requires first having made a plan — you can only switch away from something you chose deliberately
- Checking Your Own Work hard
Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
- Planning a Task soft
PSD decision-making processes transfer directly to Learning-to-Learn planning frameworks
- Checking Your Own Work hard
Planning before a task grows from the habit of checking back after finishing — both are self-regulatory bookends
- Vocabulary: making decisions and keeping safe hard
Understanding that actions have consequences requires the vocabulary word 'consequence' as a named concept
- Triggers and Causes of Feelings hard
Body-emotion connection builds on understanding emotional triggers
- Choosing the Right Coping Strategy hard
Advanced self-regulation depends on earlier foundational self-regulation
- 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
- 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
- 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
- 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)
- 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
- Adding and subtracting hard
Word problems to 20 require the procedural ability to add/subtract to 20
- 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
- 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)
- 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
- 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
- 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
- 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
- Adding and subtracting hard
Word problems to 20 require the procedural ability to add/subtract to 20
- 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
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
- 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
- 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
- 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
- Addition and subtraction within 20 hard
Adding within 100 extends within-20 strategies to larger numbers
- 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
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- Fluent adding and subtracting within 100 hard
Columnar methods require fluent within-100 addition/subtraction
- Addition and subtraction within 20 hard
Adding within 100 extends within-20 strategies to larger numbers
- 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
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- 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
- 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
- Fluent adding and subtracting within 100 hard
Adding/subtracting within 1000 extends within-100 skills
- 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
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Fluent adding and subtracting within 100 hard
Solving word problems within 100 requires fluent computation within 100
- Addition and subtraction within 20 hard
Adding within 100 extends within-20 strategies to larger numbers
- 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
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- Adding and subtracting hard
Word problems to 20 require the procedural ability to add/subtract to 20
- 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)
- 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 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
- 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
- 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
- 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'
- 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
- Adding and subtracting hard
Word problems to 20 require the procedural ability to add/subtract to 20
- 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'
- 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
- 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
Unlocks1
- Growth Through AdversityhardAges 13—14