Mathematics Checkpoint Practice

This underpins every strand and is assessed through multi-step problems, explanations, and real-life contexts.

• Selecting strategies: working systematically, trial-and-improvement, simplifying, breaking into steps
• Checking reasonableness: estimation, bounds, sense-checking answers
• Recognising patterns and using them to solve problems
• Multi-step problems combining strands (number + algebra + geometry, etc.)
• Explaining why a method works; using counterexamples to test statements
• Using correct notation, units, and clear mathematical communication
• Choosing suitable rounding/significant figures; understanding rounding error (as taught)

Core fluency is heavily tested, including non-calculator reasoning-style items.

• Operations with integers, including negative numbers; order of operations (BIDMAS/PEMDAS)
• Factors, multiples, primes; common factors and common multiples
• Squares, cubes, square roots (and cube roots where taught); powers of 10
• Place value for large and small numbers; multiplying/dividing by powers of 10
• Rounding to decimal places and significant figures; estimating calculations to check answers
• Divisibility tests; even/odd reasoning and pattern-based arguments

A major Checkpoint focus because it drives many applied and contextual questions.

• Equivalent fractions; simplifying; mixed numbers and improper fractions (convert between)
• Operations with fractions (+, −, ×, ÷), including with mixed numbers
• Decimal operations; converting between fractions and decimals (terminating vs recurring where taught)
• Percentages of amounts; increase/decrease; reverse percentages (if taught)
• Ratio: simplifying, sharing in a ratio, unit ratio, comparing ratios in context
• Proportion and scaling in real contexts; direct proportion reasoning; rates and proportional relationships

Real-world problems combining conversions, rates, and multi-step calculations.

• Metric unit conversions: mm–cm–m–km; g–kg; mL–L; time conversions where used
• Rates: speed = distance/time; rearranging; unit rate and comparison (best value/best buy)
• Money-style contexts: multi-step cost problems, discounts, unit pricing; interpreting tables
• Accuracy and bounds (where included): rounding limits such as “to the nearest cm”
• Estimation and sense-checking in measurement and finance-style items

Tested procedurally and through reasoning about structure and equivalence.

• Using letters as variables; forming expressions from word statements
• Collecting like terms; simplifying with brackets (including negatives)
• Expanding single brackets; factorising simple common factors
• Substitution: evaluate expressions for given values (including negatives/fractions)
• Using formulas in context; rearranging simple formulas (where covered)
• Recognising equivalent expressions; basic identity-style reasoning

Structured questions with algebraic solutions and graphical interpretation.

• Solving linear equations: one-step and multi-step; brackets; unknowns on both sides
• Word problems that translate into linear equations
• Solving linear inequalities; representing on number lines; interpreting in context
• Coordinates: plotting points; reading coordinates; using tables to build graphs (as taught)
• Straight-line graphs: interpreting gradient as rate of change (intro level)
• Simultaneous equations (only if included in your programme)

Spot patterns, describe rules, and generalise with simple algebra.

• Continue sequences; find term-to-term rules; identify arithmetic sequences (common difference)
• Nth term for simple linear sequences (where included); using nth-term rules
• Function machines: input/output rules; reverse operations (find input from output)
• Shape patterns (tiles/matchsticks) leading to expressions or rules
• Linking patterns to straight-line relationships and graphs (where taught)

High-frequency Checkpoint items on properties, reasoning, and angle rules.

• Angles on a line/at a point; vertically opposite angles
• Parallel lines: corresponding, alternate, and co-interior angles
• Triangle angle sum; exterior angles; polygon angle reasoning (as taught)
• Properties of triangles (isosceles/equilateral/right-angled) and quadrilaterals
• Circle basics where taught: radius, diameter, chord, arc; symmetry/angle ideas
• Construction skills where included: perpendicular/angle bisectors; constructing triangles

Diagram-based and multi-step calculations plus transformations and scale.

• Perimeter of composite shapes; area of triangles/parallelograms/trapezia (as taught)
• Area of composite shapes by splitting into known parts
• Volume and surface area of cuboids/prisms (as taught)
• Pythagoras (only if taught): missing side in right triangles; contextual problems
• Scale drawings; map scale; similarity in simple contexts; enlargement scale factors
• Transformations: reflection, rotation, translation; symmetry; enlargement (simple cases)
• Position and bearings (where taught): three-figure bearings; interpreting diagrams

Interpret data displays, choose appropriate averages, and reason about probability.

• Data types (discrete/continuous) and basic bias awareness (concept level)
• Representing data: frequency tables; bar charts; line graphs; pie charts/scatter graphs (where taught)
• Averages: mean, median, mode; range; choosing the most appropriate average for a context
• Reading charts accurately; comparing categories; describing trends; drawing supported conclusions
• Probability scale 0–1; theoretical probability; experimental probability
• Simple combined events (two-way tables/sample spaces) where included; fairness and predictions