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Common Core · England KS3 cross-references

Grade 7 mathematics

Extend rational arithmetic into proportional models, equations, geometry, sampling and probability.
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Ten units · thirty guided lesson blocks · seventy worked examples · ten diagrams · 300 practice checks · twenty unit papers · six grade papers · ten teacher-marked investigations · ten readiness and correction papers · ten optional challenge and proof workshops. Each three-week unit includes discussion, worked examples, activities and review. Timing can change with evidence of understanding.

Unit 1: Adding and subtracting rational numbers
  1. Model addition with direction
  2. Subtract by adding the opposite
  3. Choose efficient equivalent calculations

Common Core: 7.NS.A.1

England KS3: Number: signed arithmetic and number lines

Next stage: Signed coefficients and transformations of algebraic expressions.

Unit 2: Products, quotients and decimal expansions
  1. Explain the sign of a product
  2. Divide rational numbers consistently
  3. Connect fractions, decimals and applications

Common Core: 7.NS.A.2 · 7.NS.A.3

England KS3: Number: rational operations and recurring decimals

Next stage: Rational coefficients, exact calculations and modelling limits.

Unit 3: Proportional relationships in every representation
  1. Calculate rates with fractional quantities
  2. Identify a constant of proportionality
  3. Interpret proportional graphs

Common Core: 7.RP.A.1 · 7.RP.A.2

England KS3: Ratio and proportion: rates, equations and straight-line graphs

Next stage: Slope, intercept and linear functions.

Unit 4: Percent change and financial reasoning
  1. Use percentage multipliers
  2. Solve reverse percentages and simple interest
  3. Interpret percentage error and rates

Common Core: 7.RP.A.3

England KS3: Ratio and proportion: percentage change and financial mathematics

Next stage: Exponential change, compound models and financial literacy.

Unit 5: Linear expressions and multi-step equations
  1. Rewrite expressions to reveal meaning
  2. Solve equations with two operations
  3. Solve and interpret inequalities

Common Core: 7.EE.A.1 · 7.EE.A.2 · 7.EE.B.3 · 7.EE.B.4

England KS3: Algebra: rational coefficients, brackets, equations and inequalities

Next stage: Linear equations, inequalities and constrained modelling.

Unit 6: Scale drawings, constructions and sections
  1. Use and reproduce scale drawings
  2. Construct triangles from conditions
  3. Describe cross-sections

Common Core: 7.G.A.1 · 7.G.A.2 · 7.G.A.3

England KS3: Geometry: scale drawings, constructions and cross-sections

Next stage: Similarity, geometric construction and spatial visualisation.

Unit 7: Angles, circles and solid measures
  1. Reason with angle relationships
  2. Explain circle formulas
  3. Solve composite and solid problems

Common Core: 7.G.B.4 · 7.G.B.5 · 7.G.B.6

England KS3: Geometry and measures: angle reasoning, circles, area and volume

Next stage: Geometric formulas, algebraic modelling and dimensional checks.

Unit 8: Sampling and population claims
  1. Distinguish a population from a sample
  2. Use a sample to estimate a population
  3. Investigate sampling variability

Common Core: 7.SP.A.1 · 7.SP.A.2

England KS3: Statistics: sampling, bias and inference

Next stage: Statistical inference, study design and evaluating evidence.

Unit 9: Comparing distributions responsibly
  1. Compare centre in the context of spread
  2. Choose appropriate measures
  3. Make informal comparative inferences

Common Core: 7.SP.B.3 · 7.SP.B.4

England KS3: Statistics: comparing distributions using centre and spread

Next stage: Comparative inference and interpretation of variability.

Unit 10: Probability models and compound events
  1. Interpret and estimate probability
  2. Build and critique models
  3. List compound outcomes and simulate

Common Core: 7.SP.C.5 · 7.SP.C.6 · 7.SP.C.7 · 7.SP.C.8

England KS3: Probability: experiments, sample spaces and combined events

Next stage: Probability models, conditional reasoning and simulations.

Suggested full-year sequence

  1. Week 1 — Use the ready-made Entry diagnostic from your course map. Discuss methods and identify prerequisite support needs.
  2. Weeks 2–10 — Units 1–3: three weeks per unit, with explanation, guided practice and independent application.
  3. Week 11 — Assign Cumulative review 1, then revisit misconceptions across units 1–3.
  4. Weeks 12–20 — Units 4–6: connect new learning to earlier methods and retain worked corrections.
  5. Week 21 — Assign the Midyear assessment, covering units 1–6, then release feedback and reteach before proceeding.
  6. Weeks 22–30 — Units 7–9: practise selecting methods across topics, including data and geometric representations.
  7. Week 31 — Use Cumulative review 2 with the unit 7–9 investigations. Compare approaches and address misconceptions.
  8. Weeks 32–34 — Unit 10: synthesise the grade’s ideas and prepare a portfolio of explanations.
  9. Week 35 — Assign the End-of-grade assessment, which samples all ten units. Use unit assessments for additional coverage, release feedback and plan revisions.
  10. Week 36 — Use the Transition and readiness review with a portfolio conference. Revisit diagnostic gaps and plan support or extension; a total alone does not determine placement.

Readiness is more than a score

Keep worked corrections, explain why a method works, interpret units and assumptions, and solve unfamiliar problems. Use the unit transfer tasks for teacher feedback. Automatically correct answers are practice evidence, not a placement decision.

Review the next grade’s prerequisites with a teacher; provide consolidation where understanding is insecure and richer problems where it is secure.

Materials are an expanded teaching edition awaiting independent subject review. KS3 connections are editorial; they do not imply complete coverage of every additional England requirement.