Study Hub
Year 6 Maths Study Guides
Every lesson below links to a pupil-friendly study guide with key notes, vocabulary, common mistakes, and quick questions with answers.
Addition and subtraction of fractions
- Add and subtract non-related fractions with different denominators Study Guide
- Explain how to add related unit fractions with a representation or image Study Guide
- Explain how to add related unit fractions without a representation or image Study Guide
- Explain how to subtract related unit fractions Study Guide
- Explain how to write a fraction in its simplest form Study Guide
- Explain with and without an image how to add and subtract related non-unit fractions Study Guide
- Explain with and without images how to add and subtract related non-unit fractions bridging a whole Study Guide
- Reason about how to write a fraction in its simplest form Study Guide
- Use knowledge of adding and subtracting related unit fractions to solve problems Study Guide
- Use knowledge of fractions in their simplest form when solving addition and subtraction problems Study Guide
Area, perimeter, position and direction
- Describe the relationship between scale factors and perimeters of two shapes Study Guide
- Draw and complete simple shapes by plotting positions on the full coordinate grid Study Guide
- Draw and translate simple shapes on the full coordinate grid Study Guide
- Explain how to calculate the area of a parallelogram Study Guide
- Explain how to calculate the area of a triangle Study Guide
- Reflect simple shapes in the axes on a full coordinate grid Study Guide
- Solve problems involving area and perimeter Study Guide
- Solve problems involving missing coordinates Study Guide
- Use the area of a parallelogram formula to calculate unknown measurements Study Guide
- Use the area of a triangle to calculate unknown measurements Study Guide
Calculating using knowledge of equivalence in addition and subtraction
- Explain how to balance equations with addition and subtraction expressions Study Guide
- Explain how to balance equations with addition expressions Study Guide
- Explain how to balance equations with addition or subtraction expressions Study Guide
- Explain how to balance equations with subtraction expressions Study Guide
- Use knowledge of balancing equations to solve problems Study Guide
Comparing fractions
- Explain how to compare non-related fractions finding equivalent fractions with common denominators Study Guide
- Explain how to compare pairs of non-related fractions by comparing to a half Study Guide
- Explain how to compare pairs of non-related fractions using fraction sense Study Guide
- Explain which strategy for comparing non-related fractions is most efficient Study Guide
- Order sets of non-related fractions using a range of strategies Study Guide
Draw, compose and decompose shapes
- 3D shapes can be composed from 2D nets Study Guide
- Any parallelogram can be decomposed and the parts rearranged to form a rectangular parallelogram Study Guide
- Reason about compound shapes using the relationship between side lengths and area and perimeter Study Guide
- Reason about shapes using the relationship between side lengths and area and perimeter Study Guide
- Shapes with the same areas can have different perimeters and vice versa Study Guide
- The same 3D shapes can be composed from different 2D nets Study Guide
- Two congruent triangles can be arranged to compose a parallelogram Study Guide
- Use knowledge of shape properties to draw shapes accurately using rulers and protractors Study Guide
- Use knowledge of shape properties to sketch and identify shapes Study Guide
- When a 2D shape is decomposed and the parts rearranged, the areas remains the same Study Guide
Mean average
- Explain how the mean changes when the total quantity or number of values changes Study Guide
- Explain how to calcluate the mean of a set of data including a value of zero Study Guide
- Explain how to use the mean to make comparisons between two sets of data Study Guide
- Explain the relationship between the mean and sharing equally Study Guide
- Explain why the mean is useful and when it is not appropriate Study Guide
Multiples of 1,000
- Count forwards and backwards in powers of 10 to and from any multiple of 1,000 Study Guide
- Explain how one hundred thousand can be composed Study Guide
- Explain how ten thousand can be composed Study Guide
- Explain that 10,000 is composed of 5,000s, 2,500s and 2,000s Study Guide
- Explain that 100,000 is composed of 50,000s, 25,000s and 20,000s Study Guide
- Position 6-digit multiples of 1,000 on a marked but unlabelled number line Study Guide
- Position five-digit multiples of 1,000 on a marked but unlabelled number line Study Guide
- Read and write numbers up to one million in a range of contexts Study Guide
- Read and write numbers up to one million using a place value chart Study Guide
- Read the scales of graphs and measures using knowledge of the composition of 10,000 and 100,000 Study Guide
Multiplication and division of fractions
- Explain how to divide a fraction by a whole number efficiently Study Guide
- Explain how to divide a non-unit fraction by a whole number Study Guide
- Explain how to divide a unit fraction by a whole number Study Guide
- Explain how to multiply two non-unit fractions Study Guide
- Explain how to multiply two unit fractions Study Guide
Multiplying and dividing by 2-digit numbers
- Dividing by a 2-digit divisor including using long division Study Guide
- Dividing by a 2-digit divisor with a remainder Study Guide
- Dividing numbers with up to 4 digits by multiples of 10 Study Guide
- Explain how to multiply a 3-digit number by a 2-digit number Study Guide
- Explain how to use long multiplication to multiply a 3-digit by a 2-digit number Study Guide
- Explain how to use long multiplication to multiply a 4-digit by a 2-digit number Study Guide
- Explain how to use long multiplication to multiply two 2-digit numbers regrouping ones to tens Study Guide
- Explain how to use long multiplication to multiply two 2-digit numbers with regrouping Study Guide
- Explain how to use the associative law to multiply efficiently Study Guide
- Explain when it is efficient to use factorising or long multiplication to multiply by 2-digits Study Guide
- Solve problems involving remainders in context Study Guide
- Solve problems with 4-digit dividends using factors and long division Study Guide
- Use long division with decimal remainders Study Guide
- Use long division with fraction remainders Study Guide
- Using short and long division to divide by a 2-digit divisor Study Guide
Order of operations
- Combine division with addition and subtraction Study Guide
- Combine multiplication with addition and subtraction Study Guide
- Explain how the distributive law applies to division expressions with a common divisor Study Guide
- Explain how the distributive law applies to multiplication expressions with a common factor Study Guide
- Use knowledge of the order of operations to solve equations Study Guide
Order, compare and calculate with numbers up to 8 digits
- Add and subtract mentally without bridging a boundary Study Guide
- Add multiples of powers of 10 crossing the millions boundary Study Guide
- Compare numbers with up to eight digits Study Guide
- Composition of seven-digit numbers Study Guide
- Determine the value of digits in numbers up to 10 million Study Guide
- Estimate and identify numbers on number lines Study Guide
- Solving problems using column addition and subtraction Study Guide
- Subtract multiples of powers of 10 crossing the millions boundary Study Guide
- Use knowledge of the composition of seven-digit numbers to solve problems Study Guide
- Using patterns in counting sequences Study Guide
Ratio and proportion
- Describe the relationship between two factors in a ratio context Study Guide
- Explain how and why scaling is used to make and interpret maps Study Guide
- Explain how to represent ratio and to calculate unknown values Study Guide
- Identify and describe the relationship between irregular polygons using scale factors Study Guide
- Identify and describe the relationship between regular polygons using scale factors Study Guide
- Representing ratio in different ways Study Guide
- Solve problems involving ratio Study Guide
- Solve problems involving scaling and ratio Study Guide
- Use knowledge of multiplication and division to solve scaling problems in a range of contexts Study Guide
- Use multiplication and division to calculate unknown values in ratio problems Study Guide
Rounding and solving problems with numbers up to 7 digits
Solving problems with two unknowns
- Compare the structure of problems with one or two unknowns Study Guide
- Explain how to balance an equation with two unknowns Study Guide
- Explain how to represent an equation with a bar model Study Guide
- Explain how you know you have found all the possible solutions to a problem with two unknowns Study Guide
- Explain why there is sometimes only one solution to a problem Study Guide
- Represent and solve problems with two unknowns efficiently Study Guide
- Represent the structure of a problem with two unknowns in context Study Guide
- Solve problems with two unknowns in a range of contexts Study Guide
- Solve problems with two unknowns with one, several and infinite solutions Study Guide
- Use a bar model to represent spatial problems with two unknowns Study Guide
Statistics
- Construct line graphs representing two variables in familiar contexts Study Guide
- Interpret line graphs representing two variables in familiar contexts Study Guide
- Interpret the scales used in graphs, including pie charts, to solve problems Study Guide
- Use understanding of angles, fractions and percentages to construct pie charts Study Guide
- Use understanding of angles, fractions and percentages to interpret pie charts Study Guide
Understand place value within numbers with up to 7 digits
Understanding percentages
- Explain how to convert a percentage to a fraction without a denominator of 100 Study Guide
- Explain how to convert percentages to decimals and fractions with a denominator of 100 Study Guide
- Explain how to solve problems where the percentage part and size is known but the whole is unknown Study Guide
- Explain what percent means and represent a percentage in different ways Study Guide
- Solve problems involving percentages in a range of contexts Study Guide
- Solve problems where the known percentage part and size represents a change to the whole Study Guide
- Use knowledge of calculating 50%, 10% and 1% of a number to solve problems in a range of contexts Study Guide
- Use knowledge of calculating any percentage of a number to solve problems in a range of contexts Study Guide
- Use knowledge of calculating common percentages of a number to solve problems in a range of contexts Study Guide
- Use knowledge of fraction-decimal-percentage conversions to solve problems in a range of contexts Study Guide
Use equivalence and compensation to simplify and solve addition calculations
- Explain how adjusting one part affects the sum Study Guide
- Solve addition calculations mentally by using known facts Study Guide
- Solve addition calculations mentally by using known facts in a range of contexts Study Guide
- Solve calculations with missing parts Study Guide
- Use a balanced equation to calculate unknown parts Study Guide
- Use equivalence and compensation strategies to solve addition problems in a range of contexts Study Guide
- Use equivalence and compensation strategies to solve problems Study Guide
- Using balanced equations to calculate redistribution Study Guide
- Using redistribution with addition of decimal fractions Study Guide
- Using redistribution with addition of integers Study Guide
Use equivalence and compensation to simplify and solve subtraction problems
- Calculate the difference using knowledge of an adjusted subtrahend: difference structure Study Guide
- Explain and represent constant difference for subtraction Study Guide
- Explain how adjusting the minuend can make mental calculation easier Study Guide
- Explain how adjusting the subtrahend affects the difference: partitioning Study Guide
- Explain how adjusting the subtrahend affects the difference: reduction structure Study Guide
- Explain how constant difference can make written calculations more efficient Study Guide
- Explain how increasing or decreasing the minuend affects the difference Study Guide
- Solve subtraction calculations mentally by using known facts Study Guide
- Use constant difference to balance equations and find unknowns Study Guide
- Use equivalence and compensation strategies to solve subtraction problems in a range of contexts Study Guide
Use knowledge of part-part-whole structure to solve additive problems
- Create stories to match structures presented in a model Study Guide
- Explain how a combination of different parts can be equivalent to the same whole Study Guide
- Identify structures within stories and use knowledge of structures to create stories Study Guide
- Identify the missing part using knowledge of relationships and structures Study Guide
- Represent an equation in a part-part-whole model correctly Study Guide
- Use a model to interpret a part-part-whole problem with three addends Study Guide
- Use knowledge of additive structure to solve problems Study Guide
- Use mental strategies and known facts to calculate the value of a missing part Study Guide
- Use part-part-whole structures to solve additive problems in a range of contexts Study Guide
- Use written strategies and known facts to calculate the value of a missing part Study Guide
Using equivalence to calculate
- Explain the effect on the product when scaling the factors up and down by the same amount Study Guide
- Explain the effect on the quotient when scaling the dividend and the divisor by 10 Study Guide
- Explain the effect on the quotient when scaling the dividend and the divisor by the same amount Study Guide
- Explain why the product stays the same when one factor is doubled and the other is halved Study Guide
- Use knowledge of equivalence when scaling factors to solve problems Study Guide