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Common Core · England KS3 cross-references

Grade 6 mathematics

Build reliable number sense, ratio reasoning, early algebra, geometry and statistical thinking.
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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: Factors, division and decimal fluency
  1. Explain whole-number division
  2. Calculate with decimals
  3. Use common factors and multiples

Common Core: 6.NS.B.2 · 6.NS.B.3 · 6.NS.B.4

England KS3: Number: written operations, factors, multiples and prime factorisation

Next stage: Arithmetic fluency supports rational coefficients and algebraic factorisation.

Unit 2: Fraction division and meaningful quotients
  1. Interpret fraction division
  2. Derive the reciprocal method
  3. Solve mixed-number problems

Common Core: 6.NS.A.1

England KS3: Number: four operations with fractions and mixed numbers

Next stage: Fractional rates and rational algebraic coefficients.

Unit 3: Ratios, rates and percent models
  1. Describe and scale ratios
  2. Compare unit rates and convert units
  3. Connect percentages to quantities

Common Core: 6.RP.A.1 · 6.RP.A.2 · 6.RP.A.3

England KS3: Ratio and proportion: equivalent ratios, unit rates and percentages

Next stage: Proportional relationships, slope and dimensional analysis.

Unit 4: Signed numbers and the coordinate plane
  1. Interpret opposites and zero
  2. Distinguish order and distance
  3. Locate points and measure axis-aligned distances

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

England KS3: Number and algebra: negative numbers, ordering, absolute value and four quadrants

Next stage: Coordinate geometry, transformations and directed quantities.

Unit 5: Expressions, powers and equivalence
  1. Read powers and algebraic structure
  2. Evaluate with substitution
  3. Justify equivalent expressions

Common Core: 6.EE.A.1 · 6.EE.A.2 · 6.EE.A.3 · 6.EE.A.4

England KS3: Algebra: notation, substitution, collecting terms and brackets

Next stage: Symbolic manipulation, formulas and polynomial structure.

Unit 6: Equations and inequalities as constraints
  1. Test and represent a solution
  2. Solve one-step equations
  3. Represent an inequality’s solution set

Common Core: 6.EE.B.5 · 6.EE.B.6 · 6.EE.B.7 · 6.EE.B.8

England KS3: Algebra: modelling, solving linear equations and inequalities

Next stage: Equation solving and feasible solution sets.

Unit 7: Relationships, tables and graphs
  1. Choose dependent and independent quantities
  2. Build a table from an equation
  3. Graph and interpret a relationship

Common Core: 6.EE.C.9

England KS3: Algebra: relationships between variables and linear graphs

Next stage: Functions, slope, intercept and mathematical modelling.

Unit 8: Area, nets and fractional volume
  1. Decompose and rearrange areas
  2. Count fractional cubes and use volume
  3. Use nets to calculate surface area

Common Core: 6.G.A.1 · 6.G.A.2 · 6.G.A.3 · 6.G.A.4

England KS3: Geometry and measures: area, nets, surface area and volume

Next stage: Geometric decomposition, scaling and spatial reasoning.

Unit 9: Statistical questions and distributions
  1. Ask questions that anticipate variation
  2. Represent a distribution
  3. Describe centre, spread and shape

Common Core: 6.SP.A.1 · 6.SP.A.2 · 6.SP.A.3 · 6.SP.B.4

England KS3: Statistics: distributions, charts and measures of centre and spread

Next stage: Interpreting statistical evidence and variability.

Unit 10: Summaries, variability and evidence
  1. Calculate and interpret mean and median
  2. Measure variation with IQR and MAD
  3. Choose a summary and communicate limitations

Common Core: 6.SP.B.5

England KS3: Statistics: averages, spread, outliers and contextual conclusions

Next stage: Statistical comparison, evidence-based claims and Grade7 sampling.

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.