Maths

Reasoning with large whole numbers

Problem solving with integer addition and subtraction

Line graphs and timetables

Multiplication and division

2-D shape, perimeter and area

Fractions and decimals

Angles

Fractions, decimals and percentages

Transformations

Converting units of measure

Calculating with whole numbers and decimals

2-D and 3-D shape

Volume

Problem solving with whole numbers and decimals

Equivalent fractions

 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.

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

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.

Compose and calculate with decimals including column addition and subtraction

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.

Understand hundredths as parts of a whole and represent

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.

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

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.

Negative numbers

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.

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

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.

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

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.

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

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.

Understand the concept of area

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.

Link area of rectangles to multiplication

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.

Compare and describe measurements using knowledge of multiplication and division

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.

Calculating with decimal fractions

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.

Understand the concept of volume

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.

Multiply 3 or more numbers (commutative and associative laws)

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.

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

 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.

Use common factors and multiples to solve calculations efficiently

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.

Multiply a proper fraction by a whole number

In this unit pupils will multiply an improper fraction and a mixed number by a whole number. In the future unit pupils will find unit and non-unit fractions of whole numbers and explore parts and wholes.

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

Multiply improper fractions and mixed numbers by a whole number

In this unit pupils will find unit and non-unit fractions of whole numbers and explore parts and wholes. In the future unit pupils will use representations to describe and compare two fractions. They will  explain the relationship within families of equivalent fractions and use their knowledge of common equivalents to compare fractions with decimals.

In the prior unit pupils multiplied an improper fraction and a mixed number by a whole number. In this unit pupils will find unit and non-unit fractions of whole numbers and explore parts and wholes.

Find unit and non-unit fractions of whole numbers exploring parts and wholes

In this unit pupils will use representations to describe and compare two fractions. They will  explain the relationship within families of equivalent fractions and use their knowledge of common equivalents to compare fractions with decimals. In the future unit pupils will explain how to write a fraction in its simplest form when solving addition and subtraction problems. 

In the prior unit pupils will find unit and non-unit fractions of whole numbers and explore parts and wholes. In this unit pupils will use representations to describe and compare two fractions. They will  explain the relationship within families of equivalent fractions and use their knowledge of common equivalents to compare fractions with decimals.

Comparing fractions using equivalence and decimals

In this unit pupils will apply memorised unit conversions to convert between units of measure, solve problems involving converting between units of time and money. In the future unit pupils will explain how one hundred thousand can be composed and read and write numbers up to one million 

In the prior unit pupils explained the effect of multiplying and dividing a number by 10, 100 and 1,000 and used their knowledge of multiplying decimal fractions by whole numbers to solve measures problems. In this unit pupils will apply memorised unit conversions to convert between units of measure  and solve problems involving converting between units of time and money. 

Converting units

In this unit pupils will compare the size of angles where there is a clear visual difference and use the terms acute, obtuse and reflex when describing the size of angles or amount of rotation with relation to right angles using a unit called degrees. In the future unit pupils will use knowledge of shape properties to draw, sketch and identify shapes.

In the prior unit pupils completed and composed symmetrical shapes from two congruent shapes and investigate lines of symmetry in 2D shapes. In this unit pupils will compare the size of angles where there is a clear visual difference and use the terms acute, obtuse and reflex when describing the size of angles or amount of rotation with relation to right angles using a unit called degrees.

Maths

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