The 100 chart
Explore the chart, then count forwards and backwards from any number.
Grasp Maths
Visual Reference
Explore interactive diagrams, visual models and formula references to help you see how a concept works. For short year-specific reminders, open Maths Notes from a Year page.
Number foundations
Counting, place value and number facts — the building blocks everything else in maths rests on.
Number bonds
Ten-frames for bonds to 10 and 20, then find-the-missing-part practice.
Counting
Count a set of objects one at a time, then practise counting in steps.
Place value
Base-10 blocks up to 9,999, reading numbers from blocks, and a drag-and-drop place value chart to thousandths.
Comparing and ordering numbers
Explore <, > and =, then practise comparing pairs and ordering sets.
Decimals
Tenths and hundredths on a shaded grid, digit identification and rounding.
Odd and even numbers
The odd/even stripe pattern on the 100 chart, then quick-fire practice.
Doubling and halving
Doubles up to double 20 as two equal rows, then mixed practice.
The four operations
Column methods for numbers and decimals — how to actually work out the answer, not just recall it.
Addition
Step through column addition with carrying, for whole numbers and decimals.
Subtraction
Step through column subtraction with borrowing, for whole numbers and decimals.
Multiplication
Long multiplication via partial products, up to 9 digits by up to 3, plus decimal multiplication.
Times tables
The 12×12 grid to explore, then quick-fire fact practice.
Multiplying by powers of 10
The digit-shift rule for ×10 up to ×1,000,000.
Division
Bus-stop (short) division with 1 and 2-digit divisors, for whole numbers and decimals.
Dividing by powers of 10
The digit-shift rule for ÷10 up to ÷10,000.
Number
Core number facts, conversions and rules used across every year group.
Factors, multiples and primes
Factors, multiples, prime factorisation, HCF and LCM.
Negative numbers
Add, subtract, multiply and divide with negative numbers.
Order of operations (BODMAS)
Brackets, orders, division and multiplication, addition and subtraction -- in that order.
Rounding and estimation
Round to decimal places or significant figures, then estimate a calculation.
Units of measurement
Enter a value and convert instantly between metric, imperial and metric-imperial units for length, mass, capacity and time.
Bounds and error intervals
Slide a rounded measurement to see its lower and upper bounds, then see how bounds combine in a rectangle's area.
Fractions basics
What a fraction means — numerator, denominator and parts of a whole.
Equivalent fractions
Scale a fraction up or down and it stays the same size, then simplify to lowest terms.
Comparing fractions
Which fraction is bigger, on a number line — same denominator and different denominators.
Adding and subtracting fractions
Combine fractions that share a denominator.
Multiplying and dividing fractions
Multiply, divide, convert mixed ↔ improper, and find a fraction of an amount.
Fractions, decimals and percentages
The same amount, three ways — a 100-square grid links them together.
Percentages of an amount
The 10%-building-block method for finding any percentage.
Percentage change
Increase, decrease, reverse percentages and compound growth/decay.
Standard form
Write very large and very small numbers as a coefficient times a power of 10.
Recurring decimals
Turn a recurring decimal into an exact fraction using the multiply-and-subtract method.
Ratio and proportion
Simplify ratios and share an amount in a given ratio.
Financial maths
Profit and loss, simple and compound interest, depreciation, VAT and best buys.
Compound measures
Speed, density, pressure and flow rate -- explore the formula triangle for each and see every rearrangement.
Measurement
Everyday measures -- length, mass, capacity, time, money and temperature -- built from hands-on visual tools.
Length and distance
Compare and order lengths, then measure objects against a ruler in cm and mm.
Mass and weight
Balance two masses to compare heavier and lighter, then read a weighing scale in kilograms and grams.
Capacity
Explore full, empty and everything in between, then read a measuring jug in millilitres and litres.
Time
Read an analogue clock in words, 12-hour and 24-hour digital format, then work out how long something takes.
Money
Add coins and notes to see a running total, then practise working out change.
Temperature
Read a thermometer including negative temperatures, then work out how much a temperature has changed by.
Scale drawings and maps
Convert between map distance and real distance using a map scale, then scale a floor plan up to real-world dimensions.
Algebra
Rules for manipulating and solving algebraic expressions and equations.
Rules of algebra
Collect like terms and expand a single bracket -- the two rules everything else builds on.
Solving equations
One and two-step linear equations, solved by doing the same thing to both sides.
Quadratics: factorising, formula, completing the square
The same two roots, found three ways -- and how each method connects to the others.
Straight line graphs
y = mx + c -- read off the gradient and y-intercept, find a line from two points or a point and gradient, and work out parallel/perpendicular gradients.
Algebraic fractions
Simplify, multiply, divide, add and subtract fractions that contain x.
Rearranging formulae
Make a different letter the subject of a formula -- undo operations in reverse order.
Inequalities
Solve like an equation -- except the sign flips when you multiply or divide by a negative.
Simultaneous equations
Eliminate one variable by subtracting matching coefficients, then substitute back.
Sequences
Find the nth term rule of a linear sequence, then jump straight to any term.
Laws of indices
Multiply, divide and raise powers of the same base, plus zero, negative and fractional indices.
Surds
Simplify, add, subtract, multiply and rationalise surds -- exact answers, no rounding.
Expanding double brackets
FOIL -- First, Outer, Inner, Last -- to turn two brackets into a single quadratic expression.
Curved graphs
Recognise quadratic, cubic and reciprocal graph shapes -- roots, turning points and which way the curve opens.
Trigonometric graphs
The shapes of sin(x), cos(x) and tan(x) -- period, amplitude, and the values worth memorising.
Direct and inverse proportion
y = kx grows together; y = k/x grows apart -- see both with a live graph and value table.
Functions
Composite functions fg(x) and inverse functions f⁻¹(x), worked step by step.
Iteration
Solve equations numerically by repeating a formula until the answer settles down.
Algebraic proof
Prove a statement is true for every integer using n, not just a few examples.
Completing the square
Rewrite a quadratic as a(x + p)^2 + q -- and find its exact turning point, even when it doesn't factorise.
Shape, space and measure
Formulas and rules for area, volume, angles and circle geometry.
Polygons
Drag the number of sides and watch interior and exterior angles update live, with the sum formulas proved for every case.
2D and 3D shapes
Select a shape to highlight its properties, then drag each shape onto its matching name.
Position, direction and turns
Drag a star around a house to explore position words, then turn an arrow through quarter, half and three-quarter turns.
Area, perimeter and volume
Formulas for every 2-D shape and 3-D solid, including surface area, plus a draggable circle sector and arc.
Dimensions
Work out whether a formula could represent a length, an area or a volume by counting how many lengths multiply together in each term.
Circle theorems
The 9 circle theorem rules with labelled diagrams.
Angle facts
Drag an angle to see what it's called, then practise the core angle rules.
Lines of symmetry
Drag a mirror line around a shape and see it turn green when it lands on a real line of symmetry.
Pythagoras and trigonometry
See a squared + b squared = c squared proved with real squares, then select Opposite, Adjacent or Hypotenuse to explore SOH CAH TOA.
Sine and Cosine Rules
Step through worked examples of the sine and cosine rules for triangles that don't have a right angle.
3D Trigonometry
Find the space diagonal of a cuboid and the angle it makes with the base, by spotting the right-angled triangle hidden inside.
Congruence and similarity
Compare pairs of shapes and see whether they're congruent, similar, or neither -- with the ratio maths shown for each.
Vectors
Drag a vector around a grid to see its column notation and magnitude, then explore vector addition drawn tip-to-tail.
Transformations
Drag, select and explore translations, reflections, rotations and enlargements on a coordinate grid.
Bearings
Drag a compass arrow to read a three-figure bearing, then explore how back bearings relate by 180 degrees.
Constructions and loci
Step through the perpendicular bisector and angle bisector constructions, then explore the four standard loci.
Geometric proof
Pick a parallel-line angle relationship or a triangle congruence condition and see the reasoning, not just the answer.
Data handling and probability
Rules for averages, probability and reading statistical diagrams.
Averages and range
Adjust real data, frequency tables and box plots to see how mean, median, mode, range and IQR are calculated.
Probability and tree diagrams
The probability scale, combined events, tree diagrams, Venn diagrams, and how experimental probability settles toward the theoretical value.
Charts and diagrams
Bar charts, pictograms, line graphs, pie charts, scatter graphs and sample bias, all built from adjustable real data.
Stem-and-leaf diagrams
Build a stem-and-leaf plot from raw data and watch it sort live, then read averages straight off a completed plot.
Histograms and cumulative frequency
See why unequal class widths need frequency density, then build a cumulative frequency curve and estimate the median.