Topic summaries
Addition and Subtraction
Checking & Accuracy
Use rounding, inverse operations and reasonableness checks to test addition and subtraction answers.
Addition and Subtraction
Early Calculations
Counting on/back, number bonds and simple one-step problems.
Addition and Subtraction
Fluency & Related Facts
Recall facts within 20 and use place value to derive related addition and subtraction facts to 100.
Addition and Subtraction
Large Number Calculation
Add and subtract numbers with more than four digits using place value, formal methods and sensible estimates.
Addition and Subtraction
Mental & Written Methods
Choose efficient mental strategies or formal written methods for 3- and 4-digit addition and subtraction.
Addition and Subtraction
Multi-Step Problems
Break two-step and multi-step addition and subtraction problems into ordered, checkable stages.
Algebra
Enumerating Possibilities
List the combinations that satisfy a condition, work systematically in order, and make sure no possibility is missed.
Algebra
Equations with Two Unknowns
Understand equations that contain two unknowns, find pairs of numbers that satisfy them, and recognise that they can have many solutions.
Algebra
Expressing Problems Algebraically
Use a letter for an unknown number, write expressions from word descriptions, and write and solve simple equations.
Algebra
Number Sequences
Understand sequences and their terms, find the term-to-term rule of a linear sequence, and continue and describe sequences.
Algebra
Simple Formulae
Understand a formula as a rule, substitute numbers in place of letters, and use formulae written in words and in symbols.
Algebra
Use of Symbols
Understand that a letter represents a number, write multiplication in algebra without the times sign, and collect like terms to simplify expressions.
Fractions, Decimals & Percentages
Complex Fractions
Simplify fractions using common factors, convert between mixed numbers and improper fractions, and add and subtract fractions with different denominators using equivalence.
Fractions, Decimals & Percentages
Decimal Equivalents
Write tenths and hundredths as decimals, recall the decimal equivalents of common fractions, and compare decimals to two decimal places.
Fractions, Decimals & Percentages
Equivalence & Simple Fractions
Name the numerator and denominator, recognise equivalent fractions, and add and subtract fractions that share the same denominator.
Fractions, Decimals & Percentages
Halves & Quarters
Recognise, name and find one half and one quarter of shapes, objects and quantities, understanding that the parts of a fraction must be equal.
Fractions, Decimals & Percentages
Percentages
Understand a percentage as parts per hundred, convert between fractions, decimals and percentages, and find a percentage of an amount.
Fractions, Decimals & Percentages
Tenths & Hundredths
Understand that tenths and hundredths come from dividing a whole into 10 or 100 equal parts, count in tenths and hundredths, and link them through equivalent fractions.
Geometry - Position and Direction
Coordinates in the First Quadrant
Identify the axes of a coordinate grid, read and write coordinates in the first quadrant as along then up, and plot points to complete a polygon.
Geometry - Position and Direction
Full Coordinate Grid
Identify the four quadrants of a coordinate grid, use the origin and negative coordinates, and locate points anywhere on the full grid.
Geometry - Position and Direction
Reflection
Understand a reflection as a flip across a mirror line, reflect shapes in lines parallel to the axes, and recognise that the reflected shape keeps the same size.
Geometry - Position and Direction
Translation
Understand a translation as a slide, describe it in units left or right and up or down, and recognise that the shape stays the same size and the same way up.
Geometry - Position and Direction
Translation on the Coordinate Plane
Translate points and shapes on the coordinate grid by changing their coordinates, moving every vertex the same way and predicting where vertices will land.
Geometry - Position and Direction
Turns & Positions
Describe position and direction, name whole, half and quarter turns, relate a quarter turn to a right angle, and tell clockwise from anti-clockwise.
Geometry - Properties of Shapes
Angles
Understand an angle as an amount of turn, identify right, acute and obtuse angles, and understand that an angle's size does not depend on the length of its lines.
Geometry - Properties of Shapes
Circles & Polygons
Name the parts of a circle and use the relationship between radius and diameter, and distinguish regular from irregular polygons.
Geometry - Properties of Shapes
Finding Missing Angles
Use angle facts about straight lines, points, triangles, quadrilaterals and vertically opposite angles to find unknown angles.
Geometry - Properties of Shapes
Lines & Symmetry
Identify horizontal, vertical, parallel and perpendicular lines, find lines of symmetry in 2-D shapes, and recognise that a shape can have more than one line of symmetry.
Geometry - Properties of Shapes
Shape Properties
Describe 2-D shapes by their sides and vertices and 3-D shapes by their faces, edges and vertices, and sort shapes by their properties.
Geometry - Properties of Shapes
Shape Recognition
Recognise and name common 2-D and 3-D shapes, including in different orientations, understanding that turning a shape does not change its name.
Measurement
Area and Unit Conversion
Convert between units of measure and find the area of shapes by counting squares, keeping perimeter and area clearly apart.
Measurement
Area Formulae and Decimal Conversion
Use formulae to find the area of rectangles, triangles and parallelograms, handle composite shapes, and convert units using decimal notation, including miles and kilometres.
Measurement
Comparing Measures
Compare and order length and height, mass and weight, and capacity using the language of comparison, and solve simple practical problems.
Measurement
Imperial Units
Recognise common imperial units and use their approximate equivalences with metric units to convert and compare measures.
Measurement
Perimeter and Money
Measure and calculate the perimeter of simple 2-D shapes, and add and subtract amounts of money to give change.
Measurement
Standard Units and Time
Choose and use standard units for length, mass, capacity and temperature, compare with the inequality symbols, and tell the time to five minutes.
Measurement
Volume
Understand volume as the space a solid takes up, find the volume of cubes and cuboids, and compare and estimate volumes in cubic units.
Multiplication and Division
Developing Fluency
Calculate efficiently by multiplying and dividing by 10, 100 and 1000 with place value shifts, partitioning numbers using the distributive law, and deriving related facts.
Multiplication and Division
Early Concepts
Understand multiplication as equal groups and repeated addition and division as sharing and grouping, using the ×, ÷ and = symbols and the idea of commutativity.
Multiplication and Division
Factors, Multiples and Primes
Identify factors and factor pairs, find multiples and common multiples, recognise prime and composite numbers, and use common factors to solve problems such as simplifying fractions.
Multiplication and Division
Formal Written Methods
Use short and long multiplication and short and long division to calculate with larger numbers, and interpret remainders sensibly in the context of a problem.
Multiplication and Division
Order of Operations
Apply the order of operations (BIDMAS/BODMAS), use brackets to control the order of a calculation, and understand that the equals sign means both sides have the same value.
Multiplication and Division
Times Tables
Recall and derive multiplication and division facts up to 12 × 12 using skip counting, patterns and doubling, and link each fact to its matching division.
Number & Place Value
Counting and Representation
Learn to count forwards and backwards, read and write numbers, and represent them using pictures and objects.
Number & Place Value
Intro to Number & Place Value
Learn the basics of number sense and place value, including reading, writing, and comparing numbers.
Number & Place Value
Large Numbers up to Millions
Read, write, order and compare numbers up to 10,000,000 and learn to round large numbers and count in powers of ten.
Number & Place Value
Place Value Problem Solving
Apply place value skills to real‑world contexts including temperature changes, bank balances and other practical problems.
Number & Place Value
Rounding and Negative Numbers
Practise rounding to the nearest 10, 100 and 1,000 and discover how to work with negative numbers on a number line.
Number & Place Value
Three- and Four-Digit Numbers
Recognise the place value of each digit in numbers up to 1,000 and beyond, count in multiples and compare and order numbers.
Number & Place Value
Two‑Digit Numbers and Ordering
Understand tens and ones, identify one more and one less, and compare and order numbers up to 100.
Ratio and Proportion
Foundation for Formal Approaches
Solve problems like 'for every egg you need three spoonfuls of flour' as a foundation for more formal ratio work.
Ratio and Proportion
Intro to Ratio
Understanding what ratios are and how to work with them
Ratio and Proportion
Percentages for Comparison
Solve problems involving the calculation of percentages and use percentages to compare quantities.
Ratio and Proportion
Ratio Notation
Use the notation a:b to record ratios, simplify them and relate ratios to fractions.
Ratio and Proportion
Relative Sizes
Solving problems involving the relative sizes of two quantities where missing values can be found using integer multiplication and division facts.
Ratio and Proportion
Scale Factor
Solve problems involving similar shapes where the scale factor is known or can be found.
Ratio and Proportion
Unequal Sharing
Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.
Statistics
Answering Simple Statistical Questions
Sort data into categories, find the most, the fewest and the total, and answer 'how many more' questions by finding the difference.
Statistics
Bar Charts and Time Graphs
Read values from bar charts, use the scale and intervals on the axis correctly, compare bars, and read time graphs that show change over time.
Statistics
Pie Charts and Line Graphs
Read values and trends from line graphs, and understand that a pie chart shows proportions of a whole, connecting the whole circle to 360 degrees and 100 per cent.
Statistics
Problem Solving with Data
Solve sum, difference and comparison problems using data, and read values from tables and timetables by their rows and columns.
Statistics
Simple Charts
Read tally charts, pictograms, block diagrams and tables, using the key and counting in groups of five to find totals.
Statistics
The Mean Average
Understand the mean as an average, calculate it by adding the values and dividing by how many there are, and know that the mean is not the middle number.