Elementary School
Free Mathematics Practice

Build confidence with large numbers, ordering, rounding, estimation, and number lines.

• Place value up to large numbers, including reading and writing values into millions and beyond
• Comparing and ordering whole numbers, and locating numbers correctly on number lines
• Rounding to the nearest 10, 100, and 1000, with reasonableness checks through estimation
• Using estimation strategies to check whether answers make sense in everyday calculations
• Roman numerals where taught within the primary curriculum

Strengthen speed and accuracy in addition, subtraction, multiplication, division, and mixed calculations.

• Addition and subtraction with regrouping using reliable written methods
• Short and long multiplication with attention to place value
• Short and long division, including remainders and sensible interpretation of answers
• Order of operations using BODMAS or BIDMAS in multi-step expressions
• Mental mathematics techniques, inverse operations, and estimation for quick checking

Develop number reasoning through factors, multiples, prime numbers, divisibility, and common multiples.

• Identifying factors, multiples, prime numbers, and composite numbers
• Using prime factorisation as a clear method for solving structured number problems
• Finding HCF and LCM by listing or factor methods
• Applying divisibility tests such as 2, 3, 5, 9, and 10
• Solving practical problems involving shared intervals, repeated events, and fraction simplification

Work confidently with equivalent fractions, comparisons, operations, and fraction word problems.

• Proper fractions, improper fractions, and mixed numbers
• Equivalent fractions, simplification, and ordering fractions with common denominators
• Adding and subtracting fractions at the appropriate primary level
• Multiplying and dividing fractions where required by the level taught
• Finding fractions of quantities and solving multi-step fraction word problems

Connect fractions, decimals, percentages, ratio, and proportional reasoning in realistic contexts.

• Place value in decimals and operations involving decimal numbers
• Conversions between fractions, decimals, and percentages
• Finding percentages of quantities, discounts, and simple percentage change
• Ratio notation, simplification, and sharing amounts in a given ratio
• Proportion and unitary method problems, including scaling recipes and maps

Introduce early algebraic thinking through patterns, rules, missing values, and simple equations.

• Recognising number patterns and finding rules, next terms, and missing terms
• Input-output tables and rule-based thinking
• Simple expressions and collecting like terms at elementary level
• Solving simple linear equations with one unknown
• Translating short word statements into equations or missing-number sentences

Improve diagram-based reasoning with 2D and 3D shapes, angle facts, symmetry, and transformations.

• Classifying 2D shapes such as triangles, quadrilaterals, and polygons by their properties
• Recognising 3D shapes through faces, edges, vertices, and simple nets
• Using angle facts including types of angles, angles on a line, and angles in basic shapes
• Line symmetry and rotational symmetry in familiar figures
• Elementary transformations such as reflection, translation, and rotation

Handle measurement-based calculations involving perimeter, area, and volume in practical tasks.

• Perimeter of rectangles and composite rectilinear shapes
• Area of rectangles and triangles, and related primary-level area tasks
• Area of compound shapes by splitting figures into familiar parts
• Volume of cubes and cuboids, including simple capacity interpretation
• Multi-step word problems that combine measures with arithmetic operations

Apply mathematics to everyday life through units, elapsed time, money, scales, and conversions.

• Metric units for length, mass, and capacity such as mm, cm, m, km, g, kg, ml, and l
• Unit conversions and mixed-unit calculations
• Reading clocks, finding elapsed time, and interpreting timetables
• Money calculations involving totals, change, and multi-item purchases
• Reading scales on rulers, thermometers, measuring jugs, and similar instruments

Interpret charts and tables, compare data, and solve quantitative reasoning problems with confidence.

• Reading and interpreting tables, bar charts, line graphs, and pictograms
• Working with averages such as mean, and where taught, median or mode
• Comparing datasets and calculating totals and differences from displayed information
• Using simple probability language such as likely, unlikely, impossible, and certain
• Logical quantitative reasoning through patterns, missing values, and multi-step word problems