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Year 6 maths

Year 6 maths runs to 170 lessons across a 36 week year, for children aged 10 to 11 in Key Stage 2. Every lesson is listed below in teaching order.

The vocabulary a child meets this year includes equivalent, whole, part, expression, compose, represent, additive structure, multiplicative structure, bar model, combination structure, solution, part-whole structure.

These lessons are written by Oak National Academy, the government-funded curriculum body, and are free to anyone. StudyDen sequences them, marks the answers and keeps the record.

Every Year 6 maths lesson

In the order they are taught. 170 lessons.

Use knowledge of part-part-whole structure to solve additive problems

  1. Explain how a combination of different parts can be equivalent to the same whole
  2. Identify structures within stories and use knowledge of structures to create stories
  3. Identify the Missing Part Using Knowledge of Relationships and Structures
  4. Use a model to interpret a part-part-whole problem with three addends
  5. Create stories to match structures presented in a model
  6. Use Knowledge of Additive Structure to Solve Problems
  7. Use Mental Strategies and Known Facts to Calculate the Value of a Missing Part
  8. Use Written Strategies and Known Facts to Calculate a Missing Part
  9. Represent an Equation in a Part-Part-Whole Model Correctly
  10. Use Part-Part-Whole Structures to Solve Additive Problems in a Range of Contexts

Use equivalence and compensation to simplify and solve addition calculations

  1. Using Redistribution with Addition of Integers
  2. Using Redistribution with Addition of Decimal Fractions
  3. Using Balanced Equations to Calculate Redistribution
  4. Use a Balanced Equation to Calculate Unknown Parts
  5. Explain How Adjusting One Part Affects the Sum
  6. Solve Addition Calculations Mentally by Using Known Facts
  7. Solve Addition Calculations Mentally Using Known Facts
  8. Solve Calculations with Missing Parts
  9. Use Equivalence and Compensation Strategies to Solve Problems
  10. Use Equivalence and Compensation Strategies to Solve Addition Problems in a Range of Contexts

Use equivalence and compensation to simplify and solve subtraction problems

  1. Explain and Represent Constant Difference for Subtraction
  2. Constant Difference: Smarter Subtraction
  3. Use Constant Difference to Balance Equations and Find Unknowns
  4. Explain how increasing or decreasing the minuend affects the difference
  5. Solve Subtraction Calculations Mentally by Using Known Facts
  6. Adjusting the Minuend for Smarter Mental Subtraction
  7. Adjusting the Subtrahend: How Subtracting More or Less Changes the Difference
  8. Explain how adjusting the subtrahend affects the difference: partitioning
  9. Calculate the Difference Using an Adjusted Subtrahend: Difference Structure
  10. Use Equivalence and Compensation Strategies to Solve Subtraction Problems

Multiples of 1,000

  1. Explain How Ten Thousand Can Be Composed
  2. Explain How One Hundred Thousand Can Be Composed
  3. Read and Write Numbers Up to One Million Using a Place Value Chart
  4. Read and Write Numbers Up to One Million
  5. Position five-digit multiples of 1,000 on a marked but unlabelled number line
  6. Position 6-digit multiples of 1,000 on a marked but unlabelled number line
  7. Count Forwards and Backwards in Powers of 10 to and from Any Multiple of 1,000
  8. Explain that 10,000 is composed of 5,000s, 2,500s and 2,000s
  9. Explain that 100,000 is composed of 50,000s, 25,000s and 20,000s
  10. Reading Scales of Graphs and Measures: 10,000 and 100,000

Understand place value within numbers with up to 7 digits

  1. Powers of 10 and Their Multiples
  2. Composition of One Million and 10 Million
  3. Problem Solving Using Knowledge of the Composition of Powers of 10
  4. Read and Write Numbers Up to 10 Million
  5. Representing Numbers Up to 10 Million

Order, compare and calculate with numbers up to 8 digits

  1. Determine the Value of Digits in Numbers up to 10 Million
  2. Compare Numbers with Up to Eight Digits
  3. Use Knowledge of the Composition of Seven-Digit Numbers to Solve Problems
  4. Add and Subtract Mentally Without Bridging a Boundary
  5. Add Multiples of Powers of 10 Crossing the Millions Boundary
  6. Subtract Multiples of Powers of 10 Crossing the Millions Boundary
  7. Composition of Seven-Digit Numbers
  8. Using Patterns in Counting Sequences
  9. Estimate and Identify Numbers on Number Lines
  10. Solving problems using column addition and subtraction

Rounding and solving problems with numbers up to 7 digits

  1. Rounding 7-Digit Numbers to the Nearest Million
  2. Rounding Seven-Digit Numbers to Any Power of 10
  3. Solving Calculations Efficiently
  4. Explore Mental and Written Strategies to Solve Problems
  5. Solve Problems: Choosing the Most Efficient Strategy

Draw, compose and decompose shapes

  1. Use knowledge of shape properties to sketch and identify shapes
  2. Draw Shapes Accurately Using Rulers and Protractors
  3. 3D Shapes Can Be Composed from 2D Nets
  4. The Same 3D Shapes Can Be Composed from Different 2D Nets
  5. Decomposing 2D Shapes: Why the Area Never Changes
  6. Any Parallelogram Can Be Decomposed and Rearranged into a Rectangle
  7. Two Congruent Triangles Can Be Arranged to Compose a Parallelogram
  8. Shapes with the Same Areas Can Have Different Perimeters and Vice Versa
  9. Reason About Shapes Using the Relationship Between Side Lengths, Area and Perimeter
  10. Reason About Compound Shapes Using Side Lengths, Area and Perimeter

Using equivalence to calculate

  1. Explain why the product stays the same when one factor is doubled and the other is halved
  2. Explain the effect on the product when scaling the factors up and down by the same amount
  3. Use Knowledge of Equivalence When Scaling Factors to Solve Problems
  4. Explain the Effect on the Quotient When Scaling the Dividend and the Divisor by 10
  5. Explain the effect on the quotient when scaling the dividend and the divisor by the same amount

Multiplying and dividing by 2-digit numbers

  1. Explain how to multiply a 3-digit number by a 2-digit number
  2. Long Multiplication: Regrouping Ones to Tens
  3. Long Multiplication with Regrouping: Two 2-Digit Numbers
  4. Long Multiplication: 3-Digit × 2-Digit Numbers
  5. Long Multiplication: 4-Digit × 2-Digit Numbers
  6. Explain how to use the associative law to multiply efficiently
  7. Factorise or Long Multiply? Choosing the Smartest Method
  8. Dividing Numbers with Up to 4 Digits by Multiples of 10
  9. Using Short and Long Division to Divide by a 2-Digit Divisor
  10. Dividing by a 2-digit divisor including using long division
  11. Solve Problems with 4-Digit Dividends Using Factors and Long Division
  12. Dividing by a 2-Digit Divisor with a Remainder
  13. Use Long Division with Fraction Remainders
  14. Use Long Division with Decimal Remainders
  15. Solve Problems Involving Remainders in Context

Area, perimeter, position and direction

  1. Explain how to calculate the area of a parallelogram
  2. Use the area of a parallelogram formula to calculate unknown measurements
  3. Explain how to calculate the area of a triangle
  4. Use the Area of a Triangle to Calculate Unknown Measurements
  5. Solve Problems Involving Area and Perimeter
  6. Describe the relationship between scale factors and perimeters of two shapes
  7. Draw and Complete Simple Shapes by Plotting Positions on the Full Coordinate Grid
  8. Draw and Translate Simple Shapes on the Full Coordinate Grid
  9. Reflect Simple Shapes in the Axes on a Full Coordinate Grid
  10. Solve Problems Involving Missing Coordinates

Addition and subtraction of fractions

  1. Explain how to write a fraction in its simplest form
  2. Reason About How to Write a Fraction in Its Simplest Form
  3. Simplifying Fractions in Addition and Subtraction
  4. Adding Related Unit Fractions with a Representation or Image
  5. Adding Related Unit Fractions Without a Representation
  6. Explain how to subtract related unit fractions
  7. Use knowledge of adding and subtracting related unit fractions to solve problems
  8. Adding and Subtracting Related Non-Unit Fractions
  9. Adding and Subtracting Related Non-Unit Fractions That Bridge a Whole
  10. Add and Subtract Non-Related Fractions with Different Denominators

Comparing fractions

  1. Comparing Non-Related Fractions Using Common Denominators
  2. Comparing Fractions by Using One Half as a Benchmark
  3. Explain how to compare pairs of non-related fractions using fraction sense
  4. Explain which strategy for comparing non-related fractions is most efficient
  5. Order Sets of Non-Related Fractions Using a Range of Strategies

Multiplication and division of fractions

  1. Explain How to Multiply Two Unit Fractions
  2. Explain how to multiply two non-unit fractions
  3. Explain how to divide a unit fraction by a whole number
  4. Dividing a Non-Unit Fraction by a Whole Number
  5. Explain how to divide a fraction by a whole number efficiently

Understanding percentages

  1. What Does Percent Mean? Representing Percentages in Different Ways
  2. Convert Percentages to Decimals and Fractions with a Denominator of 100
  3. Explain how to convert a percentage to a fraction without a denominator of 100
  4. Use Knowledge of Fraction-Decimal-Percentage Conversions to Solve Problems
  5. Use Knowledge of Calculating 50%, 10% and 1% of a Number to Solve Problems
  6. Use Knowledge of Calculating Common Percentages to Solve Problems
  7. Calculate Any Percentage of a Number and Solve Problems
  8. Finding the Whole When You Know a Percentage Part
  9. Solve Problems Where a Percentage Change Affects the Whole
  10. Solve Problems Involving Percentages in a Range of Contexts

Statistics

  1. Use Understanding of Angles, Fractions and Percentages to Interpret Pie Charts
  2. Use Understanding of Angles, Fractions and Percentages to Construct Pie Charts
  3. Interpret Line Graphs Representing Two Variables
  4. Construct Line Graphs Representing Two Variables in Familiar Contexts
  5. Interpret the Scales Used in Graphs, Including Pie Charts, to Solve Problems

Ratio and proportion

  1. Describe the relationship between two factors in a ratio context
  2. Representing Ratio in Different Ways
  3. Explain how to represent ratio and to calculate unknown values
  4. Use Multiplication and Division to Calculate Unknown Values in Ratio Problems
  5. Solve Problems Involving Ratio
  6. Explain how and why scaling is used to make and interpret maps
  7. Scaling Up: Using Multiplication and Division to Read Maps and Plans
  8. Solve Problems Involving Scaling and Ratio
  9. Scale Factors and Similar Polygons
  10. Identify and Describe the Relationship Between Irregular Polygons Using Scale Factors

Calculating using knowledge of equivalence in addition and subtraction

  1. Explain how to balance equations with addition expressions
  2. Explain how to balance equations with subtraction expressions
  3. Explain how to balance equations with addition or subtraction expressions
  4. Explain how to balance equations with addition and subtraction expressions
  5. Use Knowledge of Balancing Equations to Solve Problems

Solving problems with two unknowns

  1. Compare the Structure of Problems with One or Two Unknowns
  2. Represent the Structure of a Problem with Two Unknowns in Context
  3. Explain Why There Is Sometimes Only One Solution to a Problem
  4. Represent and Solve Problems with Two Unknowns Efficiently
  5. Use a bar model to represent spatial problems with two unknowns
  6. Explain How to Represent an Equation with a Bar Model
  7. Solve Problems with Two Unknowns in a Range of Contexts
  8. Explain how you know you have found all the possible solutions to a problem with two unknowns
  9. Explain how to balance an equation with two unknowns
  10. Solve Problems with Two Unknowns: One, Several, and Infinite Solutions

Order of operations

  1. Combine Multiplication with Addition and Subtraction
  2. Explain how the distributive law applies to multiplication expressions with a common factor
  3. Combine Division with Addition and Subtraction
  4. Explain how the distributive law applies to division expressions with a common divisor
  5. Use Knowledge of the Order of Operations to Solve Equations

Mean average

  1. Explain the Relationship Between the Mean and Sharing Equally
  2. Calculating the Mean Average — Including Zero
  3. Explain how the mean changes when the total quantity or number of values changes
  4. Using the Mean to Compare Two Sets of Data
  5. Explain why the mean is useful and when it is not appropriate

Each of the 21 units has a free printable Year 6 maths worksheet, with the answers on a separate page.

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Common questions

What does Year 6 maths cover?
Year 6 maths runs to 170 lessons across a 36 week year, covering equivalent, whole, part, expression, compose, represent and more.
How many maths lessons are in Year 6?
170 lessons, sequenced in teaching order across the school year.
How old is a child in Year 6?
Children in Year 6 are 10 to 11 years old during the school year in England and Wales.