Maths

Identify tenths as part of a whole

Describe and represent tenths as a decimal number

Count tenths in different ways

Describe and write decimal numbers with tenths in different ways

Compare and order decimal numbers with tenths

 In this unit pupils will describe represent and order tenths as a decimal fraction. They will round a decimal number with tenths to the nearest whole number. In the future unit pupils will identify hundredths as part of a whole and describe and represent hundredths as a decimal fraction. They will compare and order decimal numbers with hundredths.

In the prior unit pupils explained the relationship between multiplying and dividing a number by 10 and multiples of 10.  In this unit pupils will describe, represent and order tenths as a decimal fraction. They will round a decimal number with tenths to the nearest whole number.

In this unit pupils will describe, represent and order tenths as a decimal fraction. They will round a decimal number with tenths to the nearest whole number and calculate mentally with decimal numbers including tenths.

Understand tenths as part of a whole, represent and calculate mentally

Explain that decimal numbers with tenths can be composed additively

Explain that decimal numbers with tenths can be composed multiplicatively

Use known facts and mental strategies to calculate with decimal numbers within and across a whole

Use knowledge of column addition and subtraction to calculate with decimal numbers

Use representations to round a decimal number with tenths to the nearest whole number

In this unit pupils will calculate with decimal numbers using column addition and subtraction. In the future unit pupils will identify hundredths as part of a whole and describe and represent hundredths as a decimal fraction. They will compare and order decimal numbers with hundredths.

In the prior unit pupils identified tenths as part of a whole and describe and represented tenths as a decimal fraction. They counted tenths in different ways and compared and ordered decimal numbers with tenths. In this unit pupils will calculate with decimal numbers using column addition and subtraction.

In this unit pupils will extend their understanding of formal calculation strategies to use column methods to add and subtract with decimal numbers.

Compose and calculate with decimals including column addition and subtraction

Identify hundredths as part of a whole

Describe and represent hundredths as a decimal number

Describe and write decimal numbers with hundredths in different ways

Compare and order decimal numbers with hundredths

Explain that decimal numbers with hundredths can be partitioned in different ways

In this unit pupils will identify hundredths as part of a whole and describe and represent hundredths as a decimal fraction. They will compare and order decimal numbers with hundredths. In the future unit pupils will use their knowledge of decimal place value to convert between and compare metres and centimetres and explain that different lengths can be composed additively and multiplicatively.

In the prior unit pupils described, represented and ordered tenths as a decimal fraction. They rounded a decimal number with tenths to the nearest whole number. In this unit pupils will identify hundredths as part of a whole and describe and represent hundredths as a decimal fraction. They will compare and order decimal numbers with hundredths.

In this unit pupils will identify hundredths as part of a whole and describe and represent hundredths as a decimal fraction. They will compare and order decimal numbers with hundredths.

Understand hundredths as parts of a whole and represent

Use knowledge of decimal place value to convert between and compare metres and centimetres

Explain that different lengths can be composed additively and multiplicatively

Use knowledge of decimal place value to solve problems in different contexts

Use knowledge of place value to calculate with decimal numbers up to and bridging one tenth

Use knowledge of column addition and subtraction to calculate with decimals: tenths and hundredths

Round a decimal number with hundredths to the nearest tenth

Round a decimal number with hundredths to the nearest whole number

Read and write numbers with up to 3 decimal places

Compare and order numbers with up to 3 decimal places

Solve problems with numbers with up to 3 decimal places

In this unit pupils will use their knowledge of decimal place value to convert between and compare metres and centimetres explaining that different lengths can be composed additively and multiplicatively.  In the future unit pupils will explain represent and compare whole pounds and pence.  They will convert quantities of money between pounds and pence and find change. 

In the prior unit pupils identified hundredths as part of a whole and described and represented hundredths as a decimal fraction. They compared and ordered decimal numbers with hundredths. In this unit pupils will use their knowledge of decimal place value to convert between and compare metres and centimetres explaining that different lengths can be composed additively and multiplicatively.

In this unit pupils will use their knowledge of decimal place value to convert between and compare metres and centimetres explaining that different lengths can be composed additively and multiplicatively.

Use knowledge of decimals to solve problems in different contexts: length

Represent a change story using addition and subtraction symbols

Interpret numbers greater than and less than zero in different contexts

Read and write negative numbers

Explain how the value of a number relates to its position from zero

Identify and place negative numbers on a number line

Interpret sets of negative and positive numbers in a range of contexts

Use knowledge of positive and negative numbers to calculate intervals

Explain how negative numbers are used on a coordinate grid

Use knowledge of positive and negative numbers to interpret graphs

Solve problems involving positive and negative numbers in a range of contexts

In this unit pupils will  interpret numbers greater than and less than zero. They will read and write negative numbers explain, how the value of a number relates to its position from zero positioning on a number line. In the future unit pupils will estimate the value and position of numbers including negative numbers on unmarked or partially marked number lines and calculate intervals across zero.

In the prior unit pupils compared and ordered 4-digit numbers They learned to round and rounded 4-digit numbers to the nearest 1000, 100 and 10, counted backwards through 0. In this unit pupils will interpret numbers greater than and less than zero. They will read and write negative numbers, explain how the value of a number relates to its position from zero, positioning on a number line.

In this unit pupils will interpret numbers greater than and less than zero. They will read and write negative numbers, explain how the value of a number relates to its position from zero, positioning on a number line.

Negative numbers

Multiply a 2-digit number by a 1-digit number using partitioning and representations (one regroup)

Multiply a 2-digit number by a 1-digit number using partitioning and representations (two regroups)

Multiply a 2-digit number by a 1-digit number using partitioning

Multiply a 2-digit number by a 1-digit number using expanded multiplication (no regroups)

Multiply a 2-digit number by a 1-digit number using short multiplication (no regroups)

Multiply a 2-digit number by a 1-digit number using expanded multiplication (regrouping 1s to 10s)

Multiply a 2-digit number by a 1-digit number using short multiplication (regrouping 1s to 10s)

Multiply a 2-digit number by a 1-digit number using expanded multiplication (regrouping 10s to 100s)

Multiply a 2-digit number by a 1-digit number using short multiplication (regrouping 10s to 100s)

Estimate and multiply a 2-digit by a 1-digit number using expanded and short multiplication

In this unit pupils will multiply a 2-digit number by a single-digit number using partitioning and representations using expanded multiplication and using short multiplication. In the future unit pupils will multiply a 3-digit number by a single-digit number using expanded and short multiplication.

In the prior unit pupils explained the relationship between multiplying and dividing a number by 10 and multiples of 10. In this unit pupils will multiply a 2-digit number by a single-digit number using partitioning and representations using expanded multiplication and using short multiplication.

In this unit pupils will multiply a 2-digit number by a single-digit number using partitioning and representations using expanded multiplication and using short multiplication.

Multiplication by partitioning leading to short multiplication (2 by 1-digit)

Multiply a 3-digit by a 1-digit number using partitioning

Multiply a 3-digit by a 1-digit number with no regroups

Multiply a 3-digit by a 1-digit number with one or two regroups

Multiply a 3-digit by a 1-digit number with multiple regroups

Use estimation to support accurate calculation

In this unit pupils will learn to multiply a 3-digit number by a single-digit number using expanded and short multiplication.  In the future unit pupils will learn why the product stays the same when one factor is doubled and the other is halved and explain the effect on the product when scaling the factors by the same amount.

In the prior unit pupils multiplied a 2-digit number by a single-digit number using partitioning and representations and used expanded multiplication and short multiplication. In this unit pupils will multiply a 3-digit number by a single-digit number using expanded and short multiplication.

In this unit pupils will multiply a 3-digit number by a single-digit number using expanded and short multiplication.

Multiplication by partitioning leading to short multiplication (3 by 1-digit)

Divide a 2-digit by a 1-digit number using partitioning and representations (no remainders)

Divide a 2-digit by a 1-digit number using partitioning (with regrouping)

Divide a 2-digit by a 1-digit number using representations with exchanging and remainders

Divide a 2-digit by a 1-digit number using short division (no regrouping )

Divide a 2-digit by a 1-digit number using short division (with regrouping)

Divide a 2-digit number using short division (with regrouping and remainders)

Divide a 3-digit by a 1-digit number using partitioning and representations (no remainders)

Divide a 3-digit number using partitioning and representations (one regroup)

Divide using partitioning and representations (multiple regroups and remainder)

Divide a 3-digit by a 1-digit number using short division

Divide using short division with regrouping and remainders

Use short division when the hundreds digit is smaller than the divisor

Use efficient division strategies to solve problems

Solve problems involving multiplication and division

Solve problems involving multiplication and division in a range of contexts

In this unit pupils will divide a 2-digit and 3-digit number by a single-digit number using partitioning and representations with exchanging and remainders. They will divide a 2-digit number by a single-digit number using short division. In the future unit pupils will  use their knowledge of multiplication and division to solve comparison and change problems.

In the prior unit pupils interpreted a division story with a remainder and represented it with an equation. They explained how the remainder related to the divisor. In this unit pupils will divide a 2-digit and a 3-digit number by a single-digit number using partitioning and representations and divide a 2-digit number by a single-digit number by using short division.

In this unit pupils will divide a 2-digit and a 3-digit number by a single-digit number using partitioning and representations and divide a 2-digit number by a single-digit number by using short division.

Division by partitioning leading to short division (2 and 3-digits by 1-digit)

Explain what area is

Measure area using counting with squares as a strategy

Explain how to make different shapes with the same area

Explain how to compare the area of different shapes

Solve problems involving counting and drawing the areas of different shapes

In this unit pupils will explain what area is and measure using counting as a strategy. They will make different shapes with the same area and compare the area of different shapes. In the future unit pupils will calculate the area of a rectangle using multiplication and use their knowledge of area to solve problems.

In the prior unit pupils completed and composed symmetrical shapes from two congruent shapes and investigated lines of symmetry in 2D shapes. In this unit pupils will explain what area is and measure using counting as a strategy. They will make different shapes with the same area and compare the area of different shapes.

In this unit pupils will explain what area is and measure using counting as a strategy. They will make different shapes with the same area and compare the area of different shapes.

Understand the concept of area

Measure the area of flat shapes using square centimetres

Measure the area of flat shapes using square metres

Explain how to calculate the area of a rectangle using multiplication

Calculate the areas of rectangles using multiplication

Calculate the area of shapes made from 2 rectangles by decomposing the shape in different ways

Calculate the area of compound rectilinear shapes

Choose an efficient way to decompose a compound shape to calculate the area

Calculate missing dimensions in rectangles and compound rectilinear shapes

Calculate the area of shapes made from 2 or more rectangles

Use knowledge of area to solve problems in a range of contexts

In this unit pupils will calculate the area of a rectangle using multiplication and use their knowledge of area to solve problems. In the future unit pupils will explain what volume is using a range of contexts and describe the units used to measure volume. They will explain how to calculate the volume of a cuboid.

In the prior unit pupils explained area and measured using counting as a strategy. They made different shapes with the same area and compared the area of different shapes. In this unit pupils will calculate the area of a rectangle using multiplication and use their knowledge of area to solve problems.

In this unit pupils will calculate the area of a rectangle using multiplication and use their knowledge of area to solve problems.

Link area of rectangles to multiplication

Compare and describe lengths using knowledge of multiplication

Solve comparison and change problems using multiplication

Compare and describe lengths using knowledge of division

Solve comparison and change problems using division

Solve problems involving comparison and change

Compare and describe measurements involving mass and capacity

Compare and describe measurements involving time and money

Describe changes in measurement using knowledge of multiplication and division

Use knowledge of multiplication and division to solve comparison and change problems

Solve comparison and change problems in a range of contexts

In this unit pupils will learn to compare and describe measurements using multiplication and division. In the future unit pupils will apply memorised unit conversions to convert between units of measure with larger to smaller units and smaller to larger units and solve problems involving converting between units of time and money. 

 In the prior unit pupils used their knowledge of decimal place value to convert between and compare metres and centimetres and explained that different lengths can be composed additively and multiplicatively. In this unit pupils will learn to compare and describe measurements using multiplication and division.

In this unit pupils will learn to compare and describe measurements using multiplication and division, applying their understanding of scaling as a structure of multiplication.

Compare and describe measurements using knowledge of multiplication and division

Multiplying and dividing a number by 10, 100 and 1,000

Multiplying and dividing a number by 10, 100 and 1,000 including bridging 1

Explain how to multiply and divide a number by 10, 100 and 1,000

Converting units of length

Converting units of mass and capacity

Multiply tenths by whole numbers

Multiply hundredths by whole numbers

Solve measures problems using knowledge of multiplying decimal fractions

The relationship between multiplying by 0.1 and dividing by 10

The relationship between multiplying by 0.01 and dividing by 100

Multiply 1-digit numbers by decimals

Multiply 1-digit numbers by decimal fractions using written methods

Predicting the size of a product

Divide decimal fractions by 1-digit numbers

Divide decimal fractions by 1-digit numbers using written methods

In this unit pupils will explain the effect of multiplying and dividing a number by 10, 100 and 1,000 and use their knowledge of multiplying decimal fractions by whole numbers to solve measures problems. In the future unit pupils will apply memorised unit conversions to convert between units of measure. They will solve measures problems involving different units including imperial units.

In the prior unit pupils calculated with decimal numbers using column addition and subtraction. In this unit pupils will explain the effect of multiplying and dividing a number by 10, 100 and 1,000 and use their knowledge of multiplying decimal fractions by whole numbers to solve measures problems.

In this unit pupils will explain the effect of multiplying and dividing a number by 10, 100 and 1,000 and use their knowledge of multiplying decimal fractions by whole numbers to solve measures problems.

Calculating with decimal fractions

Explain what volume is in a range of contexts

Describe the units used to measure volume

Explain how to calculate the volume of a cuboid and a cube

Explain how to calculate the volume of compound shapes

Use knowledge of calculating volume to solve problems in a range of contexts

In this unit pupils will explain what volume is using a range of contexts and describe the units used to measure volume. They will explain how to calculate the volume of a cuboid and explain what a cube number is. In the future unit pupils will explain the use of the commutative and distributive laws when multiplying three or more numbers. 

In the prior unit pupils calculated the area of a rectangle using multiplication and used their knowledge of area to solve problems. In this unit pupils will explain what volume is using a range of contexts and describe the units used to measure volume. They will explain how to calculate the volume of a cuboid.

In this unit pupils will explain what volume is using a range of contexts and describe the units used to measure volume. They will explain how to calculate the volume of a cuboid.

Understand the concept of volume

Explain the use of the commutative and associative laws when multiplying three or more numbers

Apply commutative and associative laws to simplify multiplications

Explain the reasons for changing two-factor multiplication calculations to three-factor calculations

Apply the commutative and associative laws to simplify volume calculations

Apply the commutative and associative laws to simplify problems in a range of contexts

In this unit pupils will explain the use of the commutative and associative laws when multiplying three or more numbers. In the future unit pupils will explain reasons for changing 2-factor multiplication calculations to 3-factor multiplications explaining what a factor is and how to use arrays and multiplication/division facts to find them. They will identify prime numbers and composite numbers.

 In the prior unit pupils explained volume using a range of contexts and described the units used to measure volume. They explained how to calculate the volume of a cuboid and explained what a cube number is. In this unit pupils will explain the use of the commutative and associative laws when multiplying three or more numbers.

In this unit pupils will explain the use of the commutative and associative laws to rearrange and simplify calculations when multiplying three or more numbers.

Multiply 3 or more numbers (commutative and associative laws)

Explain what a factor is and use arrays and multiplication and division facts to find them

Explain how to find all the factors of a number systematically

Use a complete list of factors to explain when a number is a square number

Explain how to identify a prime number or a composite number

Explain how to identify a prime factor of a number

In this unit pupils will understand and use the concept of factorisation, explaining what a factor is and how to use arrays and multiplication/division facts to find them. They will identify prime numbers, square numbers and composite numbers. In the future unit pupils will explain how to identify a multiple or common multiple to solve problems in a range of contexts.

In the prior unit pupils explained the use of the commutative and associative laws when multiplying three or more numbers. In this unit pupils will understand and use the concept of factorisation, explaining what a factor is and how to use arrays and multiplication/division facts to find them. They will identify prime numbers, square numbers and composite numbers.

In this unit pupils will understand and use the concept of factorisation, explaining what a factor is and how to use arrays and multiplication/division facts to find them. They will identify prime numbers, square numbers and composite numbers.

Understand and use the concept of factorisation (square and prime numbers)

Explain how to identify common factors between two or more numbers

Explain how to identify a common multiple of two or more numbers

Use knowledge of properties of number to solve problems

Explain how to use the factor pairs of 100 to solve calculations efficiently

Use properties of numbers and the commutative and associative laws to simplify calculations

 In this unit pupils will explain how to identify a multiple or common multiple to solve problems in a range of contexts. In the future unit pupils will explain why the product stays the same when one factor is doubled and the other is halved and use knowledge of equivalence when scaling factors to solve problems.

In the prior unit pupils understood and used the concept of factorisation, explaining what a factor is and how to use arrays and multiplication/division facts to find them. They identified prime numbers, square numbers and composite numbers. In this unit pupils will explain how to identify common factors and multiples and use this with knowledge commutative and associative laws to solve problems.

In this unit pupils will explain how to identify common factors and multiples and use this knowledge of properties of number along with knowledge of the commutative and associative laws to solve problems in a range of contexts.

Use common factors and multiples to solve calculations efficiently

Explain the relationship between repeated addition of unit fractions and multiplication of fractions

Explain the relationship between repeated addition of fractions and multiplication of fractions

Multiply a proper fraction by a whole number where the product is within a whole

Multiply a proper fraction by a whole number where the product is greater than a whole

Solve problems involving multiplying proper fractions by whole numbers

In this unit pupils will explain the relationship between repeated addition of a proper fraction and multiplication of fractions with both unit and not-unit fractions. They will multiply a proper fraction by a whole number. In the future unit pupils will multiply an improper fraction and a mixed number by a whole number.

In the prior unit pupils added mixed numbers. They subtracted a proper fraction from a mixed number and subtracted a mixed number from a mixed number. In this unit pupils will explain the relationship between repeated addition of a proper fraction and multiplication of fractions with both unit and not-unit fractions. They will multiply a proper fraction by a whole number.

In this unit pupils will explain the relationship between repeated addition of a proper fraction and multiplication of fractions with both unit and not-unit fractions. They will multiply a proper fraction by a whole number.

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