Addition and Subtraction Facts Within 20

---

Concepts

This study delivers 1 primary concept and 3 secondary concepts.

Primary concept: Number bonds within 20 (MA-Y1-C008)

Type: Knowledge | Teaching weight: 2/6

Number bonds are pairs of numbers that add together to make a given total. Knowing number bonds to 10 and to 20 fluently — both the addition facts and the related subtraction facts — is one of the most important early arithmetic skills. Mastery means pupils can instantly recall any number bond to 20 (e.g. 7 + 13 = 20, 20 – 13 = 7, 13 = 20 – 7) without counting, and can use these known facts flexibly to derive related calculations.

Teaching guidance: Use ten frames and double ten frames as primary concrete tools because their structure (5+5 per frame) makes complements visible. Part-whole models (bar model) help pupils see the relationship between the parts and the whole. Practise bonds to 10 first until secure, then extend to 20. Use 'bond collector' games, missing number activities and rapid-fire oral practice. Ensure pupils see all three forms of each bond: a + b = c, c – b = a, b = c – a. The curriculum explicitly states pupils should reason with bonds in 'several forms'. Key vocabulary: number bond, total, sum, part, whole, make, add, plus, subtract, minus, equals, missing number Common misconceptions: Pupils memorise addition bonds but do not automatically recognise the related subtraction fact (e.g. knowing 7 + 6 = 13 but not knowing 13 – 6 = 7). They may know bonds to 10 but not extend them: knowing 3 + 7 = 10 but not recognising 13 + 7 = 20. Pupils often rely on counting on rather than instant recall, which is appropriate initially but must give way to automatic recall by end of KS1.

Differentiation

Model response (Entry): 7 yellow counters. 3 + 7 = 10.

Model response (Developing): 6 goes with 4 to make 10. 7 goes with 13 to make 20.

Model response (Expected): 8 + 6 = 14. 14 – 6 = 8.

Model response (Greater Depth): 8 + 7 = 15, 15 – 7 = 8, 15 – 8 = 7. I also know that 17 + 8 = 25 because it is 10 more.

Representation stages (CPA)

Secondary concept: Addition as combining and augmenting (MA-Y1-C009)

Type: Knowledge | Teaching weight: 2/6

Addition describes two distinct situations: combining two separate groups into one (aggregation: 3 apples + 4 apples = 7 apples) and increasing a quantity by adding more (augmentation: I had 3 apples and got 4 more). Pupils need to recognise and work with both structures. Mastery means pupils can represent addition in multiple ways (concrete objects, number line, number sentence) and select appropriate strategies for different problems.

Differentiation

Secondary concept: Subtraction as taking away and finding the difference (MA-Y1-C010)

Type: Knowledge | Teaching weight: 2/6

Subtraction also describes two distinct situations: taking away (removing objects from a group: 7 – 3 = 4, removing 3 from a group of 7) and finding the difference (how many more is 7 than 3?). Both structures result in the same calculation but require different reasoning and contexts. Mastery means pupils can interpret subtraction problems correctly and choose appropriate strategies.

Differentiation

Secondary concept: Missing number problems (MA-Y1-C011)

Type: Knowledge | Teaching weight: 3/6

Missing number problems, such as 7 = ? – 9, require pupils to reason about the relationship between numbers in an equation rather than simply computing an answer. These problems lay the foundations of algebraic thinking, requiring pupils to understand the equals sign as expressing equivalence (not just 'the answer comes after') and to use inverse operations to find unknowns. Mastery means pupils can work flexibly with the equals sign in all positions and use known facts to deduce missing values.

Differentiation

---

Thinking lens: Cause and Effect (primary)

Key question: What caused this to happen, and how do we know? Why this lens fits: Missing number problems make the causal structure of addition and subtraction explicit: pupils reason about what value must have caused the given result, applying if-then logic. Question stems for KS1:

What made that happen?

What will happen if...?

Why did it change?

Can you finish: it happened because...?

Secondary lens: Patterns — Number bonds reveal the complementary pattern of a given total — knowing that 7 + 3 = 10 immediately implies 3 + 7, 10 - 3, and 10 - 7, training pupils to see a family of related facts.

---

Session structure: Practical Application + Worked Example Set

This study uses 2 vehicle templates:

Practical Application (main structure)

A hands-on sequence where pupils apply knowledge and skills to solve a practical problem or create a functional outcome. Begins with a real-world context, builds skills through rehearsal, guides design or planning, supports making or problem-solving, and concludes with evaluation against success criteria.

context → skill_rehearsal → design → make_or_solve → evaluate Assessment: Practical outcome (solution, product, program) evaluated against defined success criteria, with written or verbal explanation of the process and decisions made.

Worked Example Set

A mastery-oriented mathematics sequence moving through the concrete-pictorial-abstract progression with activation and reasoning extension phases. Begins by activating prior knowledge, introduces new concepts with physical manipulatives, transitions to pictorial representations, develops abstract fluency, applies in context, and extends through reasoning challenges.

activation → concrete → pictorial → abstract → application → reasoning_extension Assessment: Graduated practice set moving from guided examples to independent application, with reasoning task requiring explanation of method and justification of answers. Teacher note: Use the WORKED EXAMPLE SET template: begin by activating what children already know using a quick warm-up. Introduce new concepts using physical objects they can touch and move. Move to pictures and drawings that represent the same idea. Then show how to record it using numbers and symbols. Let children practise with similar examples and talk about their thinking. KS1 question stems:

Can you show me with the objects?

Can you draw a picture to help you work it out?

What number sentence matches what you did?

Can you explain how you got your answer?

---

Why this study matters

Number bonds to 10 and 20 are the essential facts that underpin all later arithmetic. Pupils must move from counting all (combining two groups and counting from 1) to counting on (starting from the larger number) and eventually to known facts recalled from memory. The part-whole model is the key representation: it shows that addition and subtraction are inverse operations on the same structure, not two separate operations. Missing number problems develop early algebraic thinking.

---

Pitfalls to avoid

Pupils always count from 1 rather than counting on from the larger number -- model the counting-on strategy explicitly

Treating the equals sign as 'the answer comes next' rather than 'both sides are the same' -- use balance problems like 5 + 3 = ☐ + 2

Not recognising that subtraction can mean 'take away' OR 'find the difference' -- teach both models

Number bonds learned by rote without understanding the part-whole relationship -- always link to the part-whole model

---

Mathematical reasoning skills (KS1)

These disciplinary skills should be woven through teaching, not taught in isolation:

Problem solving with unfamiliar and complex structures — Formulate and solve problems that require choosing from a wide range of mathematical knowledge, devising strategies for problems with no immediately obvious method, and persevering through multi-stage solutions in unfamiliar contexts.

Critical evaluation and error analysis — Critically evaluate the validity of mathematical arguments and solutions presented by others, identifying errors in reasoning or calculation, explaining why a result is or is not correct, and constructing counter-examples to disprove false claims.

Algebraic and procedural fluency — Manipulate algebraic expressions, formulae and equations accurately and efficiently, applying learned procedures to a wide range of numerical and symbolic contexts, including working with negative numbers, surds, indices and standard form.

Estimation, checking and reasonableness — Use rounding, inverse operations and known facts to estimate answers before calculating, check the reasonableness of results in context, and identify errors in worked examples by comparing expected and actual outcomes.

Problem solving in varied and unfamiliar contexts — Apply mathematics to solve multi-step problems presented in a range of contexts, breaking problems into manageable parts, selecting appropriate representations and methods, and interpreting results in relation to the original problem.

Mathematical reasoning and justification — Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and constructing chains of reasoning using mathematical language to justify conclusions, including identifying when a result cannot be true.

---

Vocabulary word mat

Prior knowledge (retrieval plan)

Pupils should already know the following from earlier units:

---

Scaffolding and inclusion (Y1)

---

Access and Inclusion

Likely barriers

This study has high demands on: Abstractness Without Concrete Anchor (Understanding addition as both combining (aggregation) and augmenting requires grasping two distinct conceptual structures. Without concrete demonstrations of both, children may develop a narrow understanding limited to one structure.), Language Load (Addition word problems require parsing sentence structures to identify the operation. Children with receptive language needs may understand addition conceptually but be blocked by the linguistic framing of word problems.), Working Memory Load (Number bonds within 20 require holding a target number and a part simultaneously while computing the missing part. The fluency expectation (instant recall) demands automaticity that takes longer to develop for children with working memory difficulties.).

Moderate demands on: Time Pressure (Number bond fluency is often assessed through timed activities. Children with processing speed difficulties may know the bonds but be unable to produce them within the expected time window.).

Universal supports

Apply by default for all learners:

Extended Processing Time — Allowing the child more time to process information and formulate responses without any time pressure or implied urgency. This is not 'extra time' in the exam access arrangement sense — it is the removal of time constraints that have no pedagogical justification. Processing speed varies naturally across children; slower processing does not indicate lower understanding.

Chunked Instructions — Breaking multi-step instructions into individual steps, presented one at a time with visual numbering. The child completes each step before the next is revealed. This reduces working memory load and prevents the common pattern where a child hears a 4-step instruction, begins step 1, and by the time they finish has forgotten steps 2-4.

Calm / Low-Stimulation Mode — A presentation mode that removes or minimises sensory stimulation: no animations, no sound effects, no gamification elements, no time pressure visuals, muted colour palette, and minimal transitions. Essential for children with sensory processing difficulties, autism, or anxiety, for whom standard 'engaging' design features are actively distressing.

Vocabulary Pre-Teaching — Explicitly teaching key vocabulary before the main lesson begins, so that unfamiliar terms do not block access to the concept. Pre-teaching uses the define-show-use-check pattern: define the word simply, show it in context with visual support, use it in a sentence, then check the child can use it themselves. Typically targets 2-4 key words per session.

Text-to-Speech — Machine reading of on-screen text aloud so the child can listen rather than decode. TTS allows children with reading difficulties to access text-based content through their auditory channel, separating the act of reading from the target learning objective. The child controls playback: play, pause, speed, repeat.

Visual Supports — Providing visual representations alongside or instead of verbal/written information: icons, diagrams, picture cues, symbol-supported text, visual timetables, and graphic organisers. Visual supports make abstract information concrete and persistent (the child can refer back to them), reducing reliance on auditory processing and transient memory.

Targeted options

Scaffolded Recording Template — Providing a partially completed template that structures the child's written output: tables with pre-drawn columns, partially completed sentences, labelled diagram outlines, or writing frames with section headings. The child fills in the content rather than creating the structure from scratch. This separates the organisational demand from the subject knowledge demand. (targets: Working Memory Load)

Adaptive Difficulty Stepping — Using the DifficultyLevel data to present tasks at a level matched to the child's current attainment, stepping up only when the child demonstrates readiness. For a child working at 'entry' level while peers are at 'expected', this means presenting entry-level tasks with the option to progress — never assuming the child should start where their year group expects. The DifficultyLevel descriptions, example_tasks, and common_errors drive the adaptive presentation. (targets: Working Memory Load, Abstractness Without Concrete Anchor)

Micro-Breaks — Scheduled brief pauses within a session, built into the task flow rather than requiring the child to self-regulate. Micro-breaks of 30-90 seconds occur at natural break points (between task sections, after a challenging question). They may include a simple breathing prompt, a brief stretch, or simply a pause screen. These are preventative — they reduce fatigue before it becomes shutdown. (targets: Working Memory Load)

Word Bank — Providing a curated set of words the child may need during a writing or response task, displayed persistently on screen. This offloads spelling from working memory, allowing the child to focus on content, sentence structure, and ideas. The word bank contains domain-specific vocabulary, connectives, and high-frequency words the child is known to struggle with. (targets: Working Memory Load)

Concrete Manipulatives (Extended) — Maintaining access to physical or on-screen manipulatives beyond the point where the curriculum typically moves to pictorial or abstract representation. Some children with dyscalculia or learning difficulties need to remain at the concrete stage significantly longer than their peers. This is a pedagogically valid position — concrete understanding IS mathematical understanding, not a lesser version of it. (targets: Working Memory Load, Abstractness Without Concrete Anchor)

Sentence Starters / Frames — Providing the opening words or structure of a response so the child can focus on the content rather than the composition. Sentence starters reduce the executive function demand of generating and organising language from scratch. They range from simple openers ('I think... because...') to full frames with multiple slots ('The ___ is similar to the ___ because they both ___'). (targets: Working Memory Load, Language Load)

Worked Example First — Showing a fully worked example of the type of task the child will be asked to complete before they attempt their own. The worked example is annotated to show the thinking process, not just the answer. This reduces the cognitive load of figuring out both WHAT to do and HOW to do it simultaneously. Particularly effective for procedural tasks in maths and structured writing in English. (targets: Abstractness Without Concrete Anchor)

Simplified Language Wrapper — Rewriting task instructions, questions, and explanations using simpler sentence structures, shorter sentences, and more common vocabulary — while preserving the full complexity of the underlying concept. The mathematical, scientific, or literary idea is not simplified; only the language surrounding it is made more accessible. This requires careful judgement about which words are domain-essential (keep) versus incidental complexity (simplify). (targets: Language Load)

Explicit Inference Teaching — Directly teaching the strategies for making inferences rather than assuming children can 'read between the lines' naturally. This includes: identifying clue words in text, connecting text evidence to background knowledge, using 'because' chains to build reasoning, and explicitly labelling inference as a skill ('we are going to practise noticing what the author is hinting at'). Essential for children with autism or social communication difficulties who process language literally. (targets: Language Load)

Use with caution

Scaffolded Recording Template — construct risk: conditional. Unsafe when assessing: open_ended_response_demand

Word Bank — construct risk: conditional. Unsafe when assessing: vocabulary_novelty

Concrete Manipulatives (Extended) — construct risk: conditional. Unsafe when assessing: abstractness_without_concrete_anchor

Sentence Starters / Frames — construct risk: conditional. Unsafe when assessing: open_ended_response_demand

Extended Processing Time — construct risk: conditional. Unsafe when assessing: time_pressure

Simplified Language Wrapper — construct risk: conditional. Unsafe when assessing: language_load

Text-to-Speech — construct risk: conditional. Unsafe when assessing: decoding_demand

---

Knowledge organiser

Core facts (expected standard):

Number bonds within 20: Instant recall of all addition and subtraction bonds within 20, including relating addition bonds to their subtraction inverses.

---

Graph context

Node type: MathsTopicSuggestion | Study ID: MTS-KS1-002 Concept IDs:

MA-Y1-C008: Number bonds within 20 (primary)

MA-Y1-C009: Addition as combining and augmenting

MA-Y1-C010: Subtraction as taking away and finding the difference

MA-Y1-C011: Missing number problems

Cypher query:

``cypher

MATCH (ts:MathsTopicSuggestion {suggestion_id: 'MTS-KS1-002'})

-[:DELIVERS_VIA]->(c:Concept)

-[:HAS_DIFFICULTY_LEVEL]->(dl)

RETURN c.name, dl.label, dl.description

``

---

Generated from the UK Curriculum Knowledge Graph — zero LLM generation.