Maths

Explain how a combination of different parts can be equivalent to the same whole

Identify structures within stories and use knowledge of structures to create stories

Identify the missing part using knowledge of relationships and structures

Use a model to interpret a part-part-whole problem with three addends

Create stories to match structures presented in a model

Use knowledge of additive structure to solve problems

Use mental strategies and known facts to calculate the value of a missing part

Use written strategies and known facts to calculate the value of a missing part

Represent an equation in a part-part-whole model correctly

Use part-part-whole structures to solve additive problems in a range of contexts

In this unit pupils will identify structures within stories. They will use their knowledge of structures to create stories and use their knowledge of additive structures to solve problems. In the future it pupils will use the concept of 'same sum' to simplify and solve addition problems.

In the prior unit pupils used the most efficient and reliable strategy to find the change. In this unit pupils will  identify structures within stories and use their knowledge of structures to create stories and use their knowledge of additive structures to solve problems.

In this unit pupils will identify the mathematical structures within stories and use their knowledge of additive structures to create stories and to solve problems.

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

Using redistribution with addition of integers

Using redistribution with addition of decimal fractions

Using balanced equations to calculate redistribution

Use a balanced equation to calculate unknown parts

Explain how adjusting one part affects the sum

Solve addition calculations mentally by using known facts

Solve addition calculations mentally by using known facts in a range of contexts

Solve calculations with missing parts

Use equivalence and compensation strategies to solve problems

Use equivalence and compensation strategies to solve addition problems in a range of contexts

In this unit pupils used the concept of same sum to simplify and solve addition problems. In the future unit pupils will solve calculations with missing addends and use the same difference rule to balance equations. They will explain how increasing or decreasing the minuend affects the difference.

In the prior unit pupils identified structures within stories using their knowledge of structures to create stories. They used their knowledge of additive structures to solve problems. In this unit pupils used the concept of same sum to simplify and solve addition problems

In this unit pupils used the concept of same sum to simplify and solve addition problems.

Use equivalence and compensation to simplify and solve addition calculations

Explain and represent constant difference for subtraction

Explain how constant difference can make written calculations more efficient

Use constant difference to balance equations and find unknowns

Explain how increasing or decreasing the minuend affects the difference

Solve subtraction calculations mentally by using known facts

Explain how adjusting the minuend can make mental calculation easier

Explain how adjusting the subtrahend affects the difference: reduction structure

Explain how adjusting the subtrahend affects the difference: partitioning

Calculate the difference using knowledge of an adjusted subtrahend: difference structure

Use equivalence and compensation strategies to solve subtraction problems in a range of contexts

In this unit pupils will explain how increasing or decreasing the minuend affects the difference and solve subtraction calculations mentally using known facts explaining how adjusting the minuend can make mental calculation easier In the future unit pupils will explain how to balance equations with addition or subtraction expressions and use their knowledge of balancing equations to solve problems

In the prior unit pupils used the concept of same sum to simplify and solve addition problems  In this unit pupils will explain how increasing or decreasing the minuend affects the difference and solve subtraction calculations mentally by using known facts explaining how adjusting the minuend can make mental calculation easier

In this unit pupils will explain how increasing or decreasing the minuend affects the difference and solve subtraction calculations mentally by using known facts explaining how adjusting the minuend can make mental calculation easier.

Use equivalence and compensation to simplify and solve subtraction problems

Explain how ten thousand can be composed

Explain how one hundred thousand can be composed

Read and write numbers up to one million using a place value chart

Read and write numbers up to one million in a range of contexts

Position five-digit multiples of 1,000 on a marked but unlabelled number line

Position 6-digit multiples of 1,000 on a marked but unlabelled number line

Count forwards and backwards in powers of 10 to and from any multiple of 1,000

Explain that 10,000 is composed of 5,000s, 2,500s and 2,000s

Explain that 100,000 is composed of 50,000s, 25,000s and 20,000s

Read the scales of graphs and measures using knowledge of the composition of 10,000 and 100,000

In this unit pupils will explain how one hundred thousand can be composed and read and write numbers up to one million. In the future unit pupils will identify and place the position of 6-digit multiple of one thousand numbers, on a marked, but unlabelled number line. They will read scales, in graphing and measures contexts, by using their knowledge of the composition of 10000 and 100000. 

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

In this unit pupils will explain how one hundred thousand can be composed and read and write numbers up to one million.

Multiples of 1,000

Powers of 10 and their multiples

Composition of one million and 10 million

Problem solving using knowledge of the composition of powers of 10

Read and write numbers up to 10 million

Representing numbers up to 10 million

 In this unit pupils will identify and place the position of 6-digit multiple of one thousand numbers on a marked, but unlabelled, number line. They will read scales by using their knowledge of the composition of 10000 and 100000. In the future unit pupils will use representations to identify and explain patterns in powers of 10 and read numbers with up to 7 digits efficiently.

In the prior unit pupils explained how one hundred thousand can be composed and read and wrote numbers up to one million. In this unit pupils will identify and place the position of 6-digit multiple of one thousand numbers, on a marked, but unlabelled number line They will read scales in graphing and measures contexts by using their knowledge of the composition of 10000 and 100000. 

In this unit pupils will identify and place the position of 6-digit multiple of one thousand numbers, on a marked, but unlabelled number line They will read scales in graphing and measures contexts by using their knowledge of the composition of 10,000 and 100,000.

Understand place value within numbers with up to 7 digits

Determine the value of digits in numbers up to 10 million

Compare numbers with up to eight digits

Use knowledge of the composition of seven-digit numbers to solve problems

Add and subtract mentally without bridging a boundary

Add multiples of powers of 10 crossing the millions boundary

Subtract multiples of powers of 10 crossing the millions boundary

Composition of seven-digit numbers

Using patterns in counting sequences

Estimate and identify numbers on number lines

Solving problems using column addition and subtraction

In this unit pupils will estimate the value and position of numbers, including negative numbers, on unmarked or partially marked number lines and calculate intervals across 0. In the future unit pupils will use their knowledge of the composition of seven-digit numbers to solve problems, adding and subtracting numbers whilst crossing the millions boundary.

 In the prior unit pupils identified and placed the position of 6-digit multiple of one thousand numbers on a marked, but unlabelled, number line. They read scales by using their knowledge of the composition of 10000 and 100000. In this unit pupils will use representations to identify and explain patterns in powers of 10 and read numbers with up to 7 digits efficiently.

In this unit pupils will use representations to identify and explain patterns in powers of 10 and read numbers with up to 7 digits efficiently. They will order and compare numbers with up to 8 digits and calculate with numbers of this scale.

Order, compare and calculate with numbers up to 8 digits

Rounding 7-digit numbers to the nearest million

Rounding seven-digit numbers to any power of 10

Solving calculations efficiently

Explore mental and written strategies to solve problems

Solve problems explaining which strategy is most efficient

In this unit pupils will use their knowledge of the composition of 7-digit numbers to solve problems adding and subtracting numbers whilst crossing the millions boundary They will round  7-digit numbers to the nearest million and nearest hundred thousand and solve addition and subtraction problems. In the future unit pupils round to any number of decimal places and learn about significant figures.

In the prior unit pupils estimated the value and position of numbers, including negative numbers, on unmarked or partially marked number lines and calculated intervals across 0. In this unit pupils will use their knowledge of the composition of seven-digit numbers to solve problems, adding and subtracting numbers whilst crossing the millions boundary.

In this unit pupils will use their knowledge of the composition of seven-digit numbers to round them and to solve problems, adding and subtracting numbers whilst crossing the millions boundary.

Rounding and solving problems with numbers up to 7 digits

Use knowledge of shape properties to sketch and identify shapes

Use knowledge of shape properties to draw shapes accurately using rulers and protractors

3D shapes can be composed from 2D nets

The same 3D shapes can be composed from different 2D nets

When a 2D shape is decomposed and the parts rearranged, the areas remains the same

Any parallelogram can be decomposed and the parts rearranged to form a rectangular parallelogram

Two congruent triangles can be arranged to compose a parallelogram

Shapes with the same areas can have different perimeters and vice versa

Reason about shapes using the relationship between side lengths and area and perimeter

Reason about compound shapes using the relationship between side lengths and area and perimeter

In this unit pupils will use knowledge of shape properties to draw, sketch and identify shapes  In the future unit pupils will explain how to calculate the area of a parallelogram and a triangle and describe the relationship between scale factors and side lengths of two shapesThey will describe positions in all four quadrants drawing and translating simple shapes and reflecting them in the axes

In the prior unit pupils compared the size of angles with 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 this unit pupils will use knowledge of shape properties to draw, sketch and identify shapes

In this unit pupils will use knowledge of shape properties to draw, sketch and identify shapes.

Draw, compose and decompose shapes

Explain why the product stays the same when one factor is doubled and the other is halved

Explain the effect on the product when scaling the factors up and down by the same amount

Use knowledge of equivalence when scaling factors to solve problems

Explain the effect on the quotient when scaling the dividend and the divisor by 10

Explain the effect on the quotient when scaling the dividend and the divisor by the same amount

 In this unit pupils will explain why the product stays the same when one factor is doubled and the other is halved using knowledge of equivalence. They will explain the effect on the quotient when scaling the dividend and divisor by the same amount. In the future unit pupils will describe the relationship between two factors and use a ratio grid to calculate unknown values. 

 In the prior unit pupils explained how to identify a multiple or common multiple to solve problems in a range of contexts. In this unit pupils will explain why the product stays the same when one factor is doubled and the other is halved using knowledge of equivalence. They will explain the effect on the quotient when scaling the dividend and divisor by the same amount.

In this unit pupils will explain why the product stays the same when one factor is doubled and the other is halved using knowledge of equivalence. They will explain the effect on the quotient when scaling the dividend and divisor by the same amount.

Using equivalence to calculate

Explain how to multiply a 3-digit number by a 2-digit number

Explain how to use long multiplication to multiply two 2-digit numbers regrouping ones to tens

Explain how to use long multiplication to multiply two 2-digit numbers with regrouping

Explain how to use long multiplication to multiply a 3-digit by a 2-digit number

Explain how to use long multiplication to multiply a 4-digit by a 2-digit number

Explain how to use the associative law to multiply efficiently

Explain when it is efficient to use factorising or long multiplication to multiply by 2-digits

Dividing numbers with up to 4 digits by multiples of 10

Using short and long division to divide by a 2-digit divisor

Dividing by a 2-digit divisor including using long division

Solve problems with 4-digit dividends using factors and long division

Dividing by a 2-digit divisor with a remainder

Use long division with fraction remainders

Use long division with decimal remainders

Solve problems involving remainders in context

In this unit pupils will learn to multiply a 3-digit by a 2-digit number They will use accurately short and long division and use a ratio chart to solve short and long division. In the future unit pupils will add, subtract, divide and multiply with integers, decimals, positive and negative values.

In the prior unit pupils will multiply a 3-digit number by a single-digit number using expanded and short multiplication. In this 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 this unit pupils will extend their understanding of formal calculation strategies to multiply and divide by 2-digit numbers, explaining when other strategies are more efficient.

Multiplying and dividing by 2-digit numbers

Explain how to calculate the area of a parallelogram

Use the area of a parallelogram formula to calculate unknown measurements

Explain how to calculate the area of a triangle

Use the area of a triangle  to calculate unknown measurements

Solve problems involving area and perimeter

Describe the relationship between scale factors and perimeters of two shapes

Draw and complete simple shapes by plotting positions on the full coordinate grid

Draw and translate simple shapes on the full coordinate grid

Reflect simple shapes in the axes on a full coordinate grid

Solve problems involving missing coordinates

In this unit pupils will explain how to calculate the area of a parallelogram and a triangle describing the relationship between scale factors and side lengths. They will describe positions in all four quadrants drawing and translating simple shapes and reflecting them in the axes In the future unit pupils extend their knowledge of plotting coordinates by now plotting non-integer values.

In the prior unit pupils used knowledge of shape properties to draw, sketch and identify shapes. In this unit pupils will explain how to calculate the area of a parallelogram and a triangle. They will describe the relationship between scale factors and side lengths of two shapes. They will describe positions in all 4 quadrants drawing and translating simple shapes and reflecting them in the axes.

In this unit pupils will explain how to calculate the area of a parallelogram and a triangle. They will describe the relationship between scale factors and side lengths. They will describe positions in all 4 quadrants.

Area, perimeter, position and direction

Explain how to write a fraction in its simplest form

Reason about how to write a fraction in its simplest form

Use knowledge of fractions in their simplest form when solving addition and subtraction problems

Explain how to add related unit fractions with a representation or image

Explain how to add related unit fractions without a representation or image

Explain how to subtract related unit fractions

Use knowledge of adding and subtracting related unit fractions to solve problems

Explain with and without an image how to add and subtract related non-unit fractions

Explain with and without images how to add and subtract related non-unit fractions bridging a whole

Add and subtract non-related fractions with different denominators

In this unit pupils will explain how to write a fraction in its simplest form when solving addition and subtraction problems and how to add and subtract related fractions. In the future unit pupils will use their fraction sense to fraction addition, subtraction and comparison explaining how to compare pairs of non-related fractions by converting to common denominators and using fraction sense.

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

In this unit pupils will explain how to write a fraction in its simplest form when solving addition and subtraction problems.

Addition and subtraction of fractions

Explain how to compare non-related fractions finding equivalent fractions with common denominators

Explain how to compare pairs of non-related fractions by comparing to a half

Explain how to compare pairs of non-related fractions using fraction sense

Explain which strategy for comparing non-related fractions is most efficient

Order sets of non-related fractions using a range of strategies

In this unit pupils will use their fraction sense to explain how to compare pairs of non-related fractions either by converting to common denominators or using fraction knowledge and understanding. In the future unit pupils will learn how to multiply 2 unit fractions and 2 non-unit fractions They will learn how to divide a unit fraction and a non-unit fraction by a whole number 

In the prior unit pupils explained how to write a fraction in its simplest form when solving addition and subtraction problems and added and subtracted related fractions.  In this unit pupils will use their fraction sense to explain how to compare pairs of non-related fractions either by converting to common denominators or using fraction knowledge and understanding.

In this unit pupils will use their fraction sense to explain how to compare pairs of non-related fractions either by converting to common denominators or using fraction knowledge and understanding.

Comparing fractions

Explain how to multiply two unit fractions

Explain how to multiply two non-unit fractions

Explain how to divide a unit fraction by a whole number

Explain how to divide a non-unit fraction by a whole number

Explain how to divide a fraction by a whole number efficiently

In this unit pupils will learn how to multiply 2 unit fractions and 2 non-unit fractions. They will learn how to divide a unit fraction and a non-unit fraction by a whole number. In the future unit pupils will explain what percent means and how to represent a percentage in different ways. They will learn how to convert percentages to decimals and fractions and solve conversion problems.

 In the prior unit pupils used fraction sense to fraction addition, subtraction and comparison, explaining how to compare pairs of non-related fractions by converting to common denominators or using fraction sense. In this unit pupils will learn how to multiply 2 unit fractions and 2 non-unit fractions. They will learn how to divide a unit fraction and a non-unit fraction by a whole number. 

In this unit pupils will learn how to multiply 2 unit fractions and 2 non-unit fractions. They will learn how to divide a unit fraction and a non-unit fraction by a whole number.

Multiplication and division of fractions

Explain what percent means and represent a percentage in different ways

Explain how to convert percentages to decimals and fractions with a denominator of 100

Explain how to convert a percentage to a fraction without a denominator of 100

Use knowledge of fraction-decimal-percentage conversions to solve problems in a range of contexts

Use knowledge of calculating 50%, 10% and 1% of a number to solve problems in a range of contexts

Use knowledge of calculating common percentages of a number to solve problems in a range of contexts

Use knowledge of calculating any percentage of a number to solve problems in a range of contexts

Explain how to solve problems where the percentage part and size is known but the whole is unknown

Solve problems where the known percentage part and size represents a change to the whole

Solve problems involving percentages in a range of contexts

In this unit pupils will explain what percent means and how to represent a percentage in different ways. They will learn how to convert percentages to decimals and fractions and solve conversion problems. In the future unit pupils will interpret and construct pie charts and line graphs. They will read scales  linked to fractions angles percentages and understanding proportional relationships.

In the prior unit pupils learned how to multiply 2 unit fractions and 2 non-unit fractions. They learned how to divide a unit fraction and a non-unit fraction by a whole number. In this unit pupils will explain what percent means and how to represent a percentage in different ways. They will learn how to convert percentages to decimals and fractions and solve conversion problems.

In this unit pupils will explain what percent means and how to represent a percentage in different ways. They will learn how to convert percentages to decimals and fractions and solve conversion problems.

Understanding percentages

Use understanding of angles, fractions and percentages to interpret pie charts

Use understanding of angles, fractions and percentages to construct pie charts

Interpret line graphs representing two variables in familiar contexts

Construct line graphs representing two variables in familiar contexts

Interpret the scales used in graphs, including pie charts, to solve problems

In this unit pupils will interpret and construct pie charts and line graphs and use these to solve problems. They will read scales in graphing and measures contexts linking to fractions, angles, percentages and understanding proportional relationships In the future unit pupils will learn how to calculate the mean of a set of data and use the mean to make comparisons between two sets of information

In the prior unit pupils explained what percent meant and how to represent a percentage in different ways. They learned how to convert percentages to decimals and fractions and solved conversion problems. In this unit pupils will interpret and construct pie charts and line graphs. They will read scales  linked to fractions angles percentages and understanding proportional relationships.

In this unit pupils will interpret and construct pie charts and line graphs. They will read scales linked to fractions angles percentages and understanding proportional relationships.

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