Risk, Uncertainty, and Cognitive Bias
CONCEPTUALDistinguish between risk (decisions with known probabilities) and uncertainty (decisions with unknown outcomes); identify cognitive biases that distort risk assessment: availability heuristic (judging likelihood by how easily examples come to mind), present bias (overvaluing the immediate over the future), optimism bias (underestimating personal risk), and groupthink; understand why adolescent brains are biologically calibrated toward higher risk tolerance; apply a structured decision-making framework to real choices; understand the role of personal values in decisions where facts alone cannot determine the answer
Mastery Evidence
Assessment Prompt
“Can [child] explain why taking a risk isn't always irrational — and describe one cognitive bias that causes people to misjudge risk in their everyday decisions, such as why teenagers tend to underestimate certain dangers?”
Prerequisites2
- Difficult Ethical ChoiceshardAges 9—11
- Ethics in Real-World IssueshardAges 9—11
Show full prerequisite tree
- Using evidence to answer questions soft
The SEL skill of navigating ethical grey areas benefits from scientific thinking: using evidence to identify differences, similarities, and changes before drawing conclusions
- Drawing conclusions from evidence hard
Must draw conclusions before identifying patterns and using evidence to support findings
- Teaching It Back soft
Reporting scientific findings in your own words draws directly on the universal self-explanation habit
- Explaining Mathematical Reasoning soft
The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
- Showing Your Working hard
Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
- Numbers up to 10 into pairs soft
Explaining part-part-whole decompositions exercises showing and telling
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Number bonds to 9 soft
Explaining how to find number bonds to 10 exercises showing thinking with objects
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Listening and responding soft
Explaining mathematical reasoning orally requires basic listening and responding skills
- What the equals sign means soft
Determining whether equations are true/false exercises evaluating and justifying
- Reading +, −, and = symbols hard
Deep understanding of = requires already being able to read and write number sentences
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- 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
- Classifying living things hard
Must present data before reporting conclusions and making predictions
- Pictograms and tally charts soft
Science data presentation (tables, bar charts) builds on maths pictogram/table skills
- Pictograms and tally charts (age 6+) hard
Constructing pictograms, tally charts, and bar charts requires these display vocabulary terms
- Sorting into categories hard
Constructing pictograms and tally charts requires classifying and counting objects first
- Comparing groups: more or fewer soft
Sorting categories by count benefits from ability to compare quantities
- Counting objects to 20 soft
Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20
- 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'
- Counting objects to 20 hard
Counting objects in each category requires being able to count sets of objects
- 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'
- Sorting Data into Categories soft
Data representation formats (pictograms, tally charts) support organising data
- 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'
- Pictograms and tally charts (age 6+) hard
Organising and representing data requires data, tally, frequency, and category vocabulary
- Sorting into categories hard
Organising data in categories builds on classifying and counting objects in categories
- Comparing groups: more or fewer soft
Sorting categories by count benefits from ability to compare quantities
- Counting objects to 20 soft
Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20
- 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'
- Counting objects to 20 hard
Counting objects in each category requires being able to count sets of objects
- 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'
- Measurable Attributes of Objects soft
Systematic scientific measurement builds on understanding measurable attributes from maths
- Asking Questions soft
Formulating scientific questions builds on the general skill of asking relevant questions to extend understanding, developed in English speaking and listening
- Question Words hard
Generating effective questions requires knowledge of question words (who, what, where, when, why, how)
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Observation vs Interpretation soft
Asking good scientific questions requires noticing the distinction between observation and interpretation — a question like 'why did this happen?' only makes sense once you've separated what you saw from what you inferred
- Feeling of not understanding soft
Noticing the observation/interpretation distinction requires monitoring your own thinking — the universal comprehension-monitoring habit applied to scientific reasoning
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Feeling of not understanding soft
Asking scientific questions is the science-domain expression of the universal comprehension-monitoring habit: noticing what you don't yet understand
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Persisting When It's Hard soft
Scientific enquiry requires persistence through uncertainty — the universal persistence habit underpins willingness to keep investigating
- Asking Questions soft
Formulating scientific questions builds on the general skill of asking relevant questions to extend understanding, developed in English speaking and listening
- Question Words hard
Generating effective questions requires knowledge of question words (who, what, where, when, why, how)
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Observation vs Interpretation soft
Asking good scientific questions requires noticing the distinction between observation and interpretation — a question like 'why did this happen?' only makes sense once you've separated what you saw from what you inferred
- Feeling of not understanding soft
Noticing the observation/interpretation distinction requires monitoring your own thinking — the universal comprehension-monitoring habit applied to scientific reasoning
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Feeling of not understanding soft
Asking scientific questions is the science-domain expression of the universal comprehension-monitoring habit: noticing what you don't yet understand
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Persisting When It's Hard soft
Scientific enquiry requires persistence through uncertainty — the universal persistence habit underpins willingness to keep investigating
- Building Writing Stamina soft
Reporting science findings orally and in writing draws on the non-fiction writing skills (recounts, explanations) established in English
- Expressing Feelings with Words soft
Writing about real events draws on the ability to put feelings into words — the SEL skill of expressing emotions verbally before encoding them in written form
- Triggers and Causes of Feelings soft
Expressing feelings in words benefits from understanding triggers
- 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
- Writing Process Vocabulary hard
Informative writing requires knowing 'genre', 'audience', 'purpose', and 'detail' as concepts
- Expressing & Justifying Opinions soft
Oral expression skills support understanding formality in speech
- Exploring Ideas Through Talk soft
Conversational skills provide foundation for evaluating viewpoints
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Writing Process Vocabulary hard
Oral composition requires vocabulary like 'compose', 'sentence', and 'sequence' to participate meaningfully in the exercise
- Simple Stories with Beginning and Ending hard
Writing about real events builds on narrative writing skills
- Rote counting to 100 soft
Sequencing events in narrative writing draws on the ordinal/sequential thinking developed through counting
- Writing Process Vocabulary hard
Writing simple narratives requires 'narrative', 'sequence', 'beginning', 'middle', 'ending' as shared vocabulary
- Expressing & Justifying Opinions soft
Oral expression skills support understanding formality in speech
- Exploring Ideas Through Talk soft
Conversational skills provide foundation for evaluating viewpoints
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Writing Process Vocabulary hard
Oral composition requires vocabulary like 'compose', 'sentence', and 'sequence' to participate meaningfully in the exercise
- Writing Process Vocabulary hard
Writing for different purposes requires the vocabulary of purpose, genre, recount, and instruction
- Simple tests and experiments hard
Must do simple tests before setting up formal fair tests with controlled variables
- Asking Questions soft
Formulating scientific questions builds on the general skill of asking relevant questions to extend understanding, developed in English speaking and listening
- Question Words hard
Generating effective questions requires knowledge of question words (who, what, where, when, why, how)
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Observation vs Interpretation soft
Asking good scientific questions requires noticing the distinction between observation and interpretation — a question like 'why did this happen?' only makes sense once you've separated what you saw from what you inferred
- Feeling of not understanding soft
Noticing the observation/interpretation distinction requires monitoring your own thinking — the universal comprehension-monitoring habit applied to scientific reasoning
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Feeling of not understanding soft
Asking scientific questions is the science-domain expression of the universal comprehension-monitoring habit: noticing what you don't yet understand
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Persisting When It's Hard soft
Scientific enquiry requires persistence through uncertainty — the universal persistence habit underpins willingness to keep investigating
- Reading between the lines soft
Using evidence to answer scientific questions mirrors the skill of asking and answering questions about key details in informational texts in English
- Could there be another explanation? soft
Identifying similarities and differences in evidence opens up space for alternative explanations — patterns that differ from expectations prompt the habit of seeking alternatives
- Changing Your Mind with Evidence hard
Actively seeking alternative explanations requires first having the habit of not defending your original interpretation against the evidence
- Observation vs Interpretation hard
Being willing to revise a hypothesis requires first distinguishing observation from interpretation — you can only update your interpretation if you recognise it as separate from the data
- Feeling of not understanding soft
Noticing the observation/interpretation distinction requires monitoring your own thinking — the universal comprehension-monitoring habit applied to scientific reasoning
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Learning from Mistakes soft
Changing your mind when evidence contradicts your prediction is the science form of the universal error-analysis habit — treating surprises as information rather than failures
- 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
- Understanding Why soft
Asking 'is there another explanation?' is the scientific form of the universal elaborative-interrogation habit
- Teaching It Back hard
Asking 'why does this work?' requires first being able to explain what you know — interrogation builds on explanation
- Explaining Mathematical Reasoning soft
The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
- Showing Your Working hard
Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
- Numbers up to 10 into pairs soft
Explaining part-part-whole decompositions exercises showing and telling
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Number bonds to 9 soft
Explaining how to find number bonds to 10 exercises showing thinking with objects
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- 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
- Spotting Patterns soft
Identifying similarities, differences, and changes in scientific data is the science form of the universal pattern-and-structure 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
- Mixed and Conflicting Emotions soft
Ethical grey areas benefit from understanding mixed/conflicting emotions
- Community Rights and Responsibilities soft
Ethical grey areas benefit from understanding rights/responsibilities
- Vocabulary: ethics and citizenship hard
Rights and responsibilities as a framework requires precise vocabulary distinguishing these two related concepts
- Vocabulary: making decisions and keeping safe hard
Understanding why rules exist requires vocabulary of 'rule', 'safe', and 'fair'
- Vocabulary: making decisions and keeping safe hard
Understanding that actions have consequences requires the vocabulary word 'consequence' as a named concept
- Vocabulary: making decisions and keeping safe hard
Distinguishing right from wrong requires vocabulary including 'honest', 'fair', 'trust', and 'right and wrong'
- 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)
- 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)
- 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)
- 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
- 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'
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- Fluent adding and subtracting within 100 hard
Adding/subtracting within 1000 extends within-100 skills
- Addition and subtraction within 20 hard
Adding within 100 extends within-20 strategies to larger numbers
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- The two digits of a two-digit number hard
Adding within 100 using PV requires understanding tens and ones
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- 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
- 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
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- The two digits of a two-digit number hard
Adding within 100 using PV requires understanding tens and ones
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- 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 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 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
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
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- The two digits of a two-digit number hard
Adding within 100 using PV requires understanding tens and ones
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- 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
- 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)
- 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
- Using evidence to answer questions soft
The SEL skill of navigating ethical grey areas benefits from scientific thinking: using evidence to identify differences, similarities, and changes before drawing conclusions
- Drawing conclusions from evidence hard
Must draw conclusions before identifying patterns and using evidence to support findings
- Teaching It Back soft
Reporting scientific findings in your own words draws directly on the universal 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
- Classifying living things hard
Must present data before reporting conclusions and making predictions
- Pictograms and tally charts soft
Science data presentation (tables, bar charts) builds on maths pictogram/table skills
- Pictograms and tally charts (age 6+) hard
Constructing pictograms, tally charts, and bar charts requires these display vocabulary terms
- Sorting into categories hard
Constructing pictograms and tally charts requires classifying and counting objects first
- Comparing groups: more or fewer soft
Sorting categories by count benefits from ability to compare quantities
- Counting objects to 20 soft
Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20
- 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'
- Counting objects to 20 hard
Counting objects in each category requires being able to count sets of objects
- 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'
- Sorting Data into Categories soft
Data representation formats (pictograms, tally charts) support organising data
- 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'
- Pictograms and tally charts (age 6+) hard
Organising and representing data requires data, tally, frequency, and category vocabulary
- Sorting into categories hard
Organising data in categories builds on classifying and counting objects in categories
- Comparing groups: more or fewer soft
Sorting categories by count benefits from ability to compare quantities
- Counting objects to 20 soft
Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20
- Counting objects to 20 hard
Counting objects in each category requires being able to count sets of objects
- 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'
- Measurable Attributes of Objects soft
Systematic scientific measurement builds on understanding measurable attributes from maths
- Asking Questions soft
Formulating scientific questions builds on the general skill of asking relevant questions to extend understanding, developed in English speaking and listening
- Question Words hard
Generating effective questions requires knowledge of question words (who, what, where, when, why, how)
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Observation vs Interpretation soft
Asking good scientific questions requires noticing the distinction between observation and interpretation — a question like 'why did this happen?' only makes sense once you've separated what you saw from what you inferred
- Feeling of not understanding soft
Noticing the observation/interpretation distinction requires monitoring your own thinking — the universal comprehension-monitoring habit applied to scientific reasoning
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Feeling of not understanding soft
Asking scientific questions is the science-domain expression of the universal comprehension-monitoring habit: noticing what you don't yet understand
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Persisting When It's Hard soft
Scientific enquiry requires persistence through uncertainty — the universal persistence habit underpins willingness to keep investigating
- Asking Questions soft
Formulating scientific questions builds on the general skill of asking relevant questions to extend understanding, developed in English speaking and listening
- Question Words hard
Generating effective questions requires knowledge of question words (who, what, where, when, why, how)
- Observation vs Interpretation soft
Asking good scientific questions requires noticing the distinction between observation and interpretation — a question like 'why did this happen?' only makes sense once you've separated what you saw from what you inferred
- Feeling of not understanding soft
Noticing the observation/interpretation distinction requires monitoring your own thinking — the universal comprehension-monitoring habit applied to scientific reasoning
- Feeling of not understanding soft
Asking scientific questions is the science-domain expression of the universal comprehension-monitoring habit: noticing what you don't yet understand
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Persisting When It's Hard soft
Scientific enquiry requires persistence through uncertainty — the universal persistence habit underpins willingness to keep investigating
- Building Writing Stamina soft
Reporting science findings orally and in writing draws on the non-fiction writing skills (recounts, explanations) established in English
- Expressing Feelings with Words soft
Writing about real events draws on the ability to put feelings into words — the SEL skill of expressing emotions verbally before encoding them in written form
- Triggers and Causes of Feelings soft
Expressing feelings in words benefits from understanding triggers
- 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
- Writing Process Vocabulary hard
Informative writing requires knowing 'genre', 'audience', 'purpose', and 'detail' as concepts
- Expressing & Justifying Opinions soft
Oral expression skills support understanding formality in speech
- Exploring Ideas Through Talk soft
Conversational skills provide foundation for evaluating viewpoints
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Writing Process Vocabulary hard
Oral composition requires vocabulary like 'compose', 'sentence', and 'sequence' to participate meaningfully in the exercise
- Simple Stories with Beginning and Ending hard
Writing about real events builds on narrative writing skills
- Rote counting to 100 soft
Sequencing events in narrative writing draws on the ordinal/sequential thinking developed through counting
- Writing Process Vocabulary hard
Writing simple narratives requires 'narrative', 'sequence', 'beginning', 'middle', 'ending' as shared vocabulary
- Expressing & Justifying Opinions soft
Oral expression skills support understanding formality in speech
- Exploring Ideas Through Talk soft
Conversational skills provide foundation for evaluating viewpoints
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Writing Process Vocabulary hard
Oral composition requires vocabulary like 'compose', 'sentence', and 'sequence' to participate meaningfully in the exercise
- Writing Process Vocabulary hard
Writing for different purposes requires the vocabulary of purpose, genre, recount, and instruction
- Simple tests and experiments hard
Must do simple tests before setting up formal fair tests with controlled variables
- Asking Questions soft
Formulating scientific questions builds on the general skill of asking relevant questions to extend understanding, developed in English speaking and listening
- Question Words hard
Generating effective questions requires knowledge of question words (who, what, where, when, why, how)
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Observation vs Interpretation soft
Asking good scientific questions requires noticing the distinction between observation and interpretation — a question like 'why did this happen?' only makes sense once you've separated what you saw from what you inferred
- Feeling of not understanding soft
Noticing the observation/interpretation distinction requires monitoring your own thinking — the universal comprehension-monitoring habit applied to scientific reasoning
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Feeling of not understanding soft
Asking scientific questions is the science-domain expression of the universal comprehension-monitoring habit: noticing what you don't yet understand
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Persisting When It's Hard soft
Scientific enquiry requires persistence through uncertainty — the universal persistence habit underpins willingness to keep investigating
- Reading between the lines soft
Using evidence to answer scientific questions mirrors the skill of asking and answering questions about key details in informational texts in English
- Could there be another explanation? soft
Identifying similarities and differences in evidence opens up space for alternative explanations — patterns that differ from expectations prompt the habit of seeking alternatives
- Changing Your Mind with Evidence hard
Actively seeking alternative explanations requires first having the habit of not defending your original interpretation against the evidence
- Observation vs Interpretation hard
Being willing to revise a hypothesis requires first distinguishing observation from interpretation — you can only update your interpretation if you recognise it as separate from the data
- Feeling of not understanding soft
Noticing the observation/interpretation distinction requires monitoring your own thinking — the universal comprehension-monitoring habit applied to scientific reasoning
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Learning from Mistakes soft
Changing your mind when evidence contradicts your prediction is the science form of the universal error-analysis habit — treating surprises as information rather than failures
- 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
- Understanding Why soft
Asking 'is there another explanation?' is the scientific form of the universal elaborative-interrogation habit
- Teaching It Back hard
Asking 'why does this work?' requires first being able to explain what you know — interrogation builds on explanation
- Explaining Mathematical Reasoning soft
The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
- Showing Your Working hard
Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
- Numbers up to 10 into pairs soft
Explaining part-part-whole decompositions exercises showing and telling
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Number bonds to 9 soft
Explaining how to find number bonds to 10 exercises showing thinking with objects
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- Listening and responding soft
Explaining mathematical reasoning orally requires basic listening and responding skills
- What the equals sign means soft
Determining whether equations are true/false exercises evaluating and justifying
- Reading +, −, and = symbols hard
Deep understanding of = requires already being able to read and write number sentences
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Addition 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
- Spotting Patterns soft
Identifying similarities, differences, and changes in scientific data is the science form of the universal pattern-and-structure 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
- Mixed and Conflicting Emotions soft
Ethical grey areas benefit from understanding mixed/conflicting emotions
- Community Rights and Responsibilities soft
Ethical grey areas benefit from understanding rights/responsibilities
- Vocabulary: ethics and citizenship hard
Rights and responsibilities as a framework requires precise vocabulary distinguishing these two related concepts
- Vocabulary: making decisions and keeping safe hard
Understanding why rules exist requires vocabulary of 'rule', 'safe', and 'fair'
- Vocabulary: making decisions and keeping safe hard
Understanding that actions have consequences requires the vocabulary word 'consequence' as a named concept
- Vocabulary: making decisions and keeping safe hard
Distinguishing right from wrong requires vocabulary including 'honest', 'fair', 'trust', and 'right and wrong'
- 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)
- 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
- 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
- Stereotypes and Individual Differences hard
Examining own biases builds on understanding stereotypes
- Vocabulary: social awareness hard
Understanding stereotypes requires knowing 'stereotype', 'prejudice', 'discrimination', and 'bias' as distinct terms
- Different Lives and Experiences hard
Recognising stereotypes builds on understanding diverse life experiences
- Seeing Someone Else's Point of View soft
Understanding different lives benefits from perspective-taking skills
- Vocabulary: social awareness soft
Perspective-taking practice is enriched by precise vocabulary including 'perspective', 'bias', and 'compassion'
- Vocabulary: understanding others hard
Understanding that others have perspectives and feelings requires the vocabulary of empathy and perspective
- Vocabulary: social awareness soft
Understanding diverse lives requires vocabulary for compassion, fairness, and community
- Similarities & Differences hard
Understanding different lives builds on noticing similarities/differences
- Vocabulary: understanding others soft
Noticing similarities and differences among people draws on vocabulary of community, fair, and care
- Stereotypes and Individual Differences hard
Understanding prejudice builds on recognising stereotypes
- Vocabulary: social awareness hard
Understanding stereotypes requires knowing 'stereotype', 'prejudice', 'discrimination', and 'bias' as distinct terms
- Different Lives and Experiences hard
Recognising stereotypes builds on understanding diverse life experiences
- Seeing Someone Else's Point of View soft
Understanding different lives benefits from perspective-taking skills
- Vocabulary: social awareness soft
Perspective-taking practice is enriched by precise vocabulary including 'perspective', 'bias', and 'compassion'
- Vocabulary: understanding others hard
Understanding that others have perspectives and feelings requires the vocabulary of empathy and perspective
- Vocabulary: social awareness soft
Understanding diverse lives requires vocabulary for compassion, fairness, and community
- Similarities & Differences hard
Understanding different lives builds on noticing similarities/differences
- Vocabulary: understanding others soft
Noticing similarities and differences among people draws on vocabulary of community, fair, and care
- Vocabulary: social awareness hard
Discussing prejudice and discrimination requires precise vocabulary to distinguish individual bias from systemic discrimination
- Vocabulary: ethics and citizenship hard
The bystander/upstander distinction is entirely vocabulary-dependent — these specific terms must be taught first
- Seeing Someone Else's Point of View soft
Understanding bullying impact benefits from perspective-taking
- Vocabulary: social awareness soft
Perspective-taking practice is enriched by precise vocabulary including 'perspective', 'bias', and 'compassion'
- Vocabulary: understanding others hard
Understanding that others have perspectives and feelings requires the vocabulary of empathy and perspective
- Vocabulary: ethics and citizenship hard
Understanding bullying requires precise vocabulary distinguishing bullying types including 'cyberbullying'
- Vocabulary: making decisions and keeping safe hard
Understanding that actions have consequences requires the vocabulary word 'consequence' as a named concept
- Vocabulary: making decisions and keeping safe hard
Distinguishing right from wrong requires vocabulary including 'honest', 'fair', 'trust', and 'right and wrong'
- Vocabulary: understanding others hard
Showing kindness meaningfully requires vocabulary for empathy, care, and community
- Other People's Feelings and Thoughts soft
Showing kindness benefits from knowing others have feelings
- Vocabulary: understanding others hard
Understanding that others have perspectives and feelings requires the vocabulary of empathy and perspective
- Questioning First Impressions soft
Reflecting on unconscious assumptions and biases towards others builds on the foundational habit of questioning your first reading of social situations
- Vocabulary: self hard
Questioning own assumptions requires precise vocabulary of 'assumption', 'bias', and 'perspective'
- Patterns in Your Own Reactions soft
Noticing that your first read of a situation might be wrong requires awareness of your own patterns of assumption and reaction
- Vocabulary: self hard
Noticing own patterns requires vocabulary of 'pattern', 'trigger', and 'reflect'
- Feelings Versus Actions hard
Noticing patterns in your reactions requires first understanding that feelings and responses are separable — you can only track a pattern once you're aware of the gap between feeling and action
- Naming Your Feelings hard
Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
- Vocabulary: self hard
Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
- Feeling of not understanding soft
Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Vocabulary: self hard
Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
- Spotting Patterns soft
Noticing recurring patterns in your own reactions is the PSD form of the universal pattern-recognition habit
- Connecting New & Old Ideas soft
Spotting patterns across domains is an extension of the habit of connecting new ideas to existing ones
- Thinking Before Starting hard
Making connections between new and old ideas requires the habit of activating prior knowledge first
- Persisting When It's Hard hard
Activating prior knowledge requires the foundational habit of persistent engagement with new material
- Your Impact on Others hard
Questioning your assumptions about social situations requires first having practised the harder skill of seeing yourself from another person's perspective
- Teaching It Back soft
Reflecting on how your behaviour landed on others requires being able to articulate your own thinking and intentions clearly — the self-explanation habit applied to social experience
- Explaining Mathematical Reasoning soft
The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
- Showing Your Working hard
Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
- Numbers up to 10 into pairs soft
Explaining part-part-whole decompositions exercises showing and telling
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Number bonds to 9 soft
Explaining how to find number bonds to 10 exercises showing thinking with objects
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- 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
- Vocabulary: self hard
Reflecting on impact on others requires vocabulary of 'impact', 'perspective', and 'reflect'
- Patterns in Your Own Reactions hard
Reflecting on the impact of your behaviour on others requires first having noticed patterns in your own reactions — you need self-knowledge before you can examine your social footprint
- Vocabulary: self hard
Noticing own patterns requires vocabulary of 'pattern', 'trigger', and 'reflect'
- Feelings Versus Actions hard
Noticing patterns in your reactions requires first understanding that feelings and responses are separable — you can only track a pattern once you're aware of the gap between feeling and action
- Naming Your Feelings hard
Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
- Vocabulary: self hard
Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
- Feeling of not understanding soft
Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Vocabulary: self hard
Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
- Spotting Patterns soft
Noticing recurring patterns in your own reactions is the PSD form of the universal pattern-recognition habit
- Connecting New & Old Ideas soft
Spotting patterns across domains is an extension of the habit of connecting new ideas to existing ones
- Thinking Before Starting hard
Making connections between new and old ideas requires the habit of activating prior knowledge first
- Persisting When It's Hard hard
Activating prior knowledge requires the foundational habit of persistent engagement with new material
- Feelings Versus Actions soft
Reflecting on impact requires understanding that your actions were choices, not automatic responses to feelings — the feelings/actions distinction underpins social accountability
- Naming Your Feelings hard
Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
- Vocabulary: self hard
Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
- Feeling of not understanding soft
Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Vocabulary: self hard
Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
- Understanding Why soft
Questioning your assumptions about why someone acted a certain way is elaborative interrogation applied to social cognition — asking 'why do I think this?' rather than accepting the first explanation
- Teaching It Back hard
Asking 'why does this work?' requires first being able to explain what you know — interrogation builds on explanation
- Explaining Mathematical Reasoning soft
The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
- Showing Your Working hard
Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
- Numbers up to 10 into pairs soft
Explaining part-part-whole decompositions exercises showing and telling
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Number bonds to 9 soft
Explaining how to find number bonds to 10 exercises showing thinking with objects
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- 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
- Community Rights and Responsibilities soft
Ethical evaluation benefits from understanding rights/responsibilities
- Vocabulary: ethics and citizenship hard
Rights and responsibilities as a framework requires precise vocabulary distinguishing these two related concepts
- Vocabulary: making decisions and keeping safe hard
Understanding why rules exist requires vocabulary of 'rule', 'safe', and 'fair'
- Vocabulary: making decisions and keeping safe hard
Understanding that actions have consequences requires the vocabulary word 'consequence' as a named concept
- Vocabulary: making decisions and keeping safe hard
Distinguishing right from wrong requires vocabulary including 'honest', 'fair', 'trust', and 'right and wrong'
- Identifying Reasons Behind a Speaker's Points soft
Ethical evaluation benefits from evaluating reasoning and evidence in speech
- Why the author wrote it soft
Evaluating a speaker's reasoning parallels evaluating an author's purpose and point of view in reading
- Book Features and Author's Reasons hard
Distinguishing own POV from author's extends identifying author's reasons/supporting points
- Engaging Listeners and Valuing Viewpoints hard
Identifying a speaker's reasons and evidence builds on evaluating viewpoints and building on others' contributions in discussion
- Teaching It Back soft
Building on others' contributions in discussion requires being able to articulate your own thinking — the self-explanation habit applied in a social context
- Explaining Mathematical Reasoning soft
The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
- Showing Your Working hard
Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
- Numbers up to 10 into pairs soft
Explaining part-part-whole decompositions exercises showing and telling
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Number bonds to 9 soft
Explaining how to find number bonds to 10 exercises showing thinking with objects
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Listening and responding soft
Explaining mathematical reasoning orally requires basic listening and responding skills
- What the equals sign means soft
Determining whether equations are true/false exercises evaluating and justifying
- Reading +, −, and = symbols hard
Deep understanding of = requires already being able to read and write number sentences
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- 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
- Exploring Ideas Through Talk soft
Conversational skills provide foundation for evaluating viewpoints
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Expressing & Justifying Opinions soft
Oral expression skills support understanding formality in speech
- Exploring Ideas Through Talk soft
Conversational skills provide foundation for evaluating viewpoints
- Feeling of not understanding soft
Using talk to explore ideas and speculate requires noticing what you don't yet understand — the comprehension-monitoring habit in a spoken register
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Questioning First Impressions soft
Evaluating ethical dimensions of real-world issues and forming reasoned positions requires the habit of questioning your own assumptions before accepting your first instinct
- Vocabulary: self hard
Questioning own assumptions requires precise vocabulary of 'assumption', 'bias', and 'perspective'
- Patterns in Your Own Reactions soft
Noticing that your first read of a situation might be wrong requires awareness of your own patterns of assumption and reaction
- Vocabulary: self hard
Noticing own patterns requires vocabulary of 'pattern', 'trigger', and 'reflect'
- Feelings Versus Actions hard
Noticing patterns in your reactions requires first understanding that feelings and responses are separable — you can only track a pattern once you're aware of the gap between feeling and action
- Naming Your Feelings hard
Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
- Vocabulary: self hard
Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
- Feeling of not understanding soft
Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Vocabulary: self hard
Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
- Spotting Patterns soft
Noticing recurring patterns in your own reactions is the PSD form of the universal pattern-recognition habit
- Connecting New & Old Ideas soft
Spotting patterns across domains is an extension of the habit of connecting new ideas to existing ones
- Thinking Before Starting hard
Making connections between new and old ideas requires the habit of activating prior knowledge first
- Persisting When It's Hard hard
Activating prior knowledge requires the foundational habit of persistent engagement with new material
- Your Impact on Others hard
Questioning your assumptions about social situations requires first having practised the harder skill of seeing yourself from another person's perspective
- Teaching It Back soft
Reflecting on how your behaviour landed on others requires being able to articulate your own thinking and intentions clearly — the self-explanation habit applied to social experience
- Explaining Mathematical Reasoning soft
The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
- Showing Your Working hard
Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
- Numbers up to 10 into pairs soft
Explaining part-part-whole decompositions exercises showing and telling
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Number bonds to 9 soft
Explaining how to find number bonds to 10 exercises showing thinking with objects
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Listening and responding soft
Explaining mathematical reasoning orally requires basic listening and responding skills
- What the equals sign means soft
Determining whether equations are true/false exercises evaluating and justifying
- Reading +, −, and = symbols hard
Deep understanding of = requires already being able to read and write number sentences
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- 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
- Vocabulary: self hard
Reflecting on impact on others requires vocabulary of 'impact', 'perspective', and 'reflect'
- Patterns in Your Own Reactions hard
Reflecting on the impact of your behaviour on others requires first having noticed patterns in your own reactions — you need self-knowledge before you can examine your social footprint
- Vocabulary: self hard
Noticing own patterns requires vocabulary of 'pattern', 'trigger', and 'reflect'
- Feelings Versus Actions hard
Noticing patterns in your reactions requires first understanding that feelings and responses are separable — you can only track a pattern once you're aware of the gap between feeling and action
- Naming Your Feelings hard
Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
- Vocabulary: self hard
Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
- Feeling of not understanding soft
Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Vocabulary: self hard
Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
- Spotting Patterns soft
Noticing recurring patterns in your own reactions is the PSD form of the universal pattern-recognition habit
- Connecting New & Old Ideas soft
Spotting patterns across domains is an extension of the habit of connecting new ideas to existing ones
- Thinking Before Starting hard
Making connections between new and old ideas requires the habit of activating prior knowledge first
- Persisting When It's Hard hard
Activating prior knowledge requires the foundational habit of persistent engagement with new material
- Feelings Versus Actions soft
Reflecting on impact requires understanding that your actions were choices, not automatic responses to feelings — the feelings/actions distinction underpins social accountability
- Naming Your Feelings hard
Understanding that feelings and actions are separate requires first being able to name and identify what you are feeling
- Vocabulary: self hard
Noticing and naming feelings requires the basic vocabulary of self-awareness and reflection
- Feeling of not understanding soft
Naming what you are feeling is emotional comprehension monitoring — the universal habit of noticing what's happening inside applied to emotional experience
- Asking for Help hard
Noticing confusion and acting on it requires already knowing that asking for help is a valid response to being stuck
- Vocabulary: self hard
Understanding the feelings-actions separation requires vocabulary to distinguish and name each component
- Understanding Why soft
Questioning your assumptions about why someone acted a certain way is elaborative interrogation applied to social cognition — asking 'why do I think this?' rather than accepting the first explanation
- Teaching It Back hard
Asking 'why does this work?' requires first being able to explain what you know — interrogation builds on explanation
- Explaining Mathematical Reasoning soft
The universal self-explanation habit (LtL 7-8) builds on the maths-specific practice of explaining reasoning when prompted (MT 6-7)
- Showing Your Working hard
Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects
- Numbers up to 10 into pairs soft
Explaining part-part-whole decompositions exercises showing and telling
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Number bonds to 9 soft
Explaining how to find number bonds to 10 exercises showing thinking with objects
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Listening and responding soft
Explaining mathematical reasoning orally requires basic listening and responding skills
- What the equals sign means soft
Determining whether equations are true/false exercises evaluating and justifying
- Reading +, −, and = symbols hard
Deep understanding of = requires already being able to read and write number sentences
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- 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
Unlocks1
- Online Identity and MisinformationhardAges 12—13