Number and Place Value

Key Vocabulary

At home you could…

Before children start Year 3, they need to be able to read any 2 digit number and partition it into different combinations of tens and ones. Children explain what they know about numbers verbally or using pictures. They can compare and order numbers with confidence.

In Year 3, children will read 3 digit numbers and partition it into different combinations of hundreds, tens and ones. They will be able to represent 3 digit numbers in the concrete, pictorial and abstract ways as shown below. Children will be able to compare and order numbers up to 1,000.

Children will be expected to explain what they know about a number using accurate mathematical vocabulary. They will problem solve and reason using their knowledge.

• Hundreds
• Tens
• Ones
• More than
• Less than

Count forwards and backwards up to 1,000.

Talk about the numbers you see when going for walks in the area.

Find numbers on ingredients you have in the kitchen.

Addition and Subtraction

Before children start Year 3, they need to be able to add and subtract 2 digit numbers using an efficient method. This could be using a written method, drawing pictures or using concrete resources. Children will also recall all number bonds to 10 and use these to calculate number bonds to 20.

In Year 3, children will add and subtract numbers with up to 4 digits. They will use formal written methods and apply efficient calculation methods to solve problems. Children will be able to explain why they have chosen to use a particular method. Here are some examples of how your child will calculate using concrete and pictorial methods. By the end of Year 3, your child should be confident at using the column method to calculate with and without exchanges.

• Add
• Subtract
• Estimate
• Exchange

Use number bonds to add and subtract, for example, 1 + 9 = 10 so 1 + 19 = 20.

Watch the youtube videos and follow the methods to practise adding and subtracting.

https://www.youtube.com/watch?v=pf5KpEGJpoM&t=4s

https://www.youtube.com/watch?v=4hkhY9gnHmo&t=4s

Add up the shopping in the supermarket.

Find the change when paying in cash.

Before children start Year 3, they need to be able to identify that a fraction is a part of a whole. They will be able to compare and order fractions and add and subtract fractions with the same

In Year 3, children will continue to talk about more complex fractions as parts of a whole. They will count up and down in tenths, represent fractions pictorially, add and subtract fractions with the same denominators, compare and order fractions. Children will use their knowledge of fractions to solve problems and reason mathematically.

• Part
• Whole
• Half
• Quarter
• Third
• Tenth
• Numerator
• Denominator

Help in the kitchen by cutting whole foods in halves/quarters/parts.

Find fractions of foods you eat e.g. chocolate bars which have segments.

Cut shapes into different fractions.

Fold paper to show different fractions.

Before children start Year 3, they need to be able to name and describe 2D and 3D shapes. They should be secure in using the vocabulary of sides, vertices, faces, edges and lines of symmetry.

In Year 3, children will apply their previous knowledge of shapes to recognise shapes in different orientations. They will understand different types of turns and angles and be able to recognise some of these in 2D shapes or on the faces of 3D shapes. Children will learn different types of lines: horizontal, vertical, parallel and perpendicular.

• 2D
• 3D
• Side
• Vertices
• Face
• Edge
• Symmetry
• Acute Angle
• Right Angle
• Obtuse Angle
• Horizontal
• Vertical
• Parallel
• Perpendicular

Go on a shape hunt.

Draw symmetrical shapes and patterns.

Before children start Year 3, they need to be able to tell the time to the nearest 15 minutes: o’clock, half past, quarter past and quarter to. They also need to be able to read scales in ones, twos, fives and tens. They will be introduced to length, mass and capacity.

In Year 3, children will explore measures for length, mass and capacity. They will measure accurately and apply their knowledge to compare and calculate with different measures. Children will tell the time to the nearest 5 minutes and calculate with money.

• Long
• Short
• Heavy
• Light
• Full
• Empty
• Pounds
• Pence
• O’clock
• Half Past
• Quarter Past
• Quarter to

• Cook and bake together by measuring ingredients on weighing scales.
• Use measuring jugs and different containers to explore and play with liquids.
• Measure your child’s height regularly.
• Tell the time at different points of the day.
• Allow your child to wear a watch and ask them what the time is.
• Ask your child to help you work out the change when shopping.
• Ask your child to add amounts when shopping.

Before children start Year 3, they need to be able to recall their 2, 5 and 10 times tables and related division facts. They will already know how to use these facts to solve problems.

In Year 3, children will learn their 3, 4 and 8 times tables. They will use these facts to solve multiplication and division problems. Children will see multiplication and division represented using concrete resources, pictorial representations including arrays and in abstract ways. They will begin to use formal written methods to multiply and divide 2 and 1 digit numbers.

• Multiply
• Divide
• Estimate
• Exchange

Practise your times tables.

Divide and share items/foods out.

Count in different number patterns.

Creating own multiplication and division triangles,

Find and learning counting songs.

Times tables

Number Bonds

Before children start Year 4, they need to be able to read any 1, 2 and 3 digit number and partition these. Children explain what they know about numbers verbally or using pictures. They can compare and order numbers with confidence.

In Year 4, children will read 4 digit numbers and partition it into different combinations of hundreds, tens and ones. They will be able to represent 4 digit numbers in the concrete, pictorial and abstract ways as shown below. Children will be able to compare and order numbers up to 1,000.

Children will be expected to explain what they know about a number using accurate mathematical vocabulary. They will problem solve and reason using their knowledge.

• Thousands
• Hundreds
• Tens
• Ones
• More than
• Less than

Before children start Year 4, they need to be able to add and subtract 4 digit numbers using an efficient method. This could be using a written method, drawing pictures or using concrete resources. Children will also recall all number bonds to 20.

In Year 4, children will add and subtract numbers with up to 4 digits. They will use formal written methods and apply efficient calculation methods to solve problems. Children will be able to explain why they have chosen to use a particular method. Here are some examples of how your child will calculate using concrete and pictorial methods. By the end of Year 4 your child should be confident at using the column method to calculate with and without exchanges.

• Add
• Subtract
• Estimate
• Exchange

Use number bonds to add and subtract, for example, 1 + 9 = 10 so 1 + 19 = 20.

Watch the youtube videos and follow the methods to practise adding and subtracting.

https://www.youtube.com/watch?v=pf5KpEGJpoM&t=4s

https://www.youtube.com/watch?v=4hkhY9gnHmo&t=4s

Add up the shopping in the supermarket.

Find the change when paying in cash.

Before children start Year 4, they need to be able to identify that a fraction is a part of a whole. They will be able to compare and order fractions and add and subtract fractions with the same

In Year 4, children will continue to talk about more complex fractions as parts of a whole. They will count up and down in hundredths, represent fractions pictorially, add and subtract fractions with the same denominators, compare and order fractions. They will use their fraction knowledge to understand decimals and convert between both. Children will use their knowledge of fractions to solve problems and reason mathematically.

• Part
• Whole
• Half
• Quarter
• Third
• Tenth
• Numerator
• Denominator
• Equivalent
• Decimal
• Convert
  • Hundredth

Help in the kitchen by cutting whole foods in halves/quarters/parts.

Find fractions of foods you eat e.g. chocolate bars which have segments.

Cut shapes into different fractions.

Fold paper to show different fractions.

Before children start Year 4, they need to be able to name and describe 2D and 3D shapes. They should be secure in recognising different types of angles and lines in shapes.

In Year 4, children will use their knowledge of angles and descriptive vocabulary to describe, sort and classify shapes. They will complete symmetrical shapes and patterns and identify where symmetry can be found. Children will use their knowledge of turns and movement to describe position and direction on a grid.

• 2D
• 3D
• Side
• Veticies
• Face
• Edge
• Symmetry
• Acute angle
• Right angle
• Obtuse angle
• co-ordinate
• Quadrant

Go on a shape hunt.

Draw symmetrical shapes and patterns.

Use a compass to describe position on a map (North, East, South, West)

Use a map to explore a location by reading co-ordinates.

Before children start Year 4, they need to be able to tell the time to the nearest 5 minutes. They need to understand pounds and pence and be able to calculate with money. Children should be able to measure length, mass and capacity accurately and use their knowledge of measure to solve problems.

In Year 4, children will be able to convert between measures. They will use their knowledge of number and scales to estimate an item’s length, mass or capacity. In length, children will find the area and perimeter of shapes. Children will be able to read the time to the nearest minute and convert between analogue and digital times.

• Long
• Short
• Heavy
• Light
• Fulkl
• Empty
• Area
• Perimeter
• O’clock
• Half past
• Quarter past
• Quarter to
• Analogue
• Digital

Cook and bake together by measuring ingredients on weighing scales.

Use measuring jugs and different containers to explore and play with liquids.

Measure your child’s height regularly.

Tell the time at different points of the day.

Allow your child to wear a watch and ask them what the time is.

Ask your child to help you work out the change when shopping.

Ask your child to add amounts when shopping.

Before children start Year 4, they need to be able to recall their 2, 5 and 10 times tables and related division facts. They will already know how to use these facts to solve problems.

In Year 4, children will learn their 3, 4 and 8 times tables. They will use these facts to solve multiplication and division problems. Children will see multiplication and division represented using concrete resources, pictorial representations including arrays and in abstract ways. They will continue to recall and practice to become fluent in formal written methods when multiplying and dividing 2 by 1 and 2 digit numbers calculations as well as two-step word problems.

• Multiply
• Divide
• Estimate
• Exchange

Practise your times tables.

Divide and share items/foods out.

Count in different number patterns.

Creating own multiplication and division triangles,

Find and learning counting songs.

Before children start Year 4, they need to be able to read and understand pictograms and bar graphs where the scale is more than one.

In Year 4, children will create and read bar graphs and line graphs. They will compare different types of data collection and justify how data can be collected in a suitable way.

• Pictogram
• Tally
• Bar graph
• Line graph

Create a tally of different colour cars you see.

Create a bar graph of favourite animals in your family.

Create a pictogram of favourite foods in your family.

Create a line graph for how long it takes an ice cube to melt and change temperature.

Times tables

Number Bonds

By the end of Year 4 pupils should…

By the end of Year 5 pupils should…

• Understand place value of numbers up to 10,000
• Count in multiples of 6, 7 , 9 , 25 and 1000
• Add and subtract up to 4 digit numbers.
• Recall all multiplication and division facts up to 12 x 12
• Multiply 2 and 3 digit numbers by a one digit number using formal method.
• Recognise equivalent fractions of ¼, ½ and ¾
• Convert kilometres to metres, hours to minutes and centimetres to metres.
• Calculate the perimeter of rectangles and squares.
• Identify and label the features of quadrilaterals and triangles.
• Read and interpret bar charts and pictogram tables.

• Understand place value of numbers up to 1,000,000
• Count forward or backwards in 10, 100, 1000, 10,000 and 100,000.
• Add and subtract more than 4 digit numbers.
• Identify multiples, factors and factor pairs.
• Recall prime numbers up to 19 and identify prime numbers to 100.
• Multiply numbers up to 4 digits by a one or two digit number using formal written method, including long multiplication for two digit numbers.
• Divide numbers up to 4 digits by a one digit number including remainders.
• To identify square and cube numbers (² , ³ )
• Add and subtract fractions with the same denominator and denominators that are multiples of the same number.
• Recognise decimal numbers as fractions (e.g 0.38 = 38/100)
• Write fractions as mixed numbers and improper fractions when they go over 1 whole.
• Calculate the area of rectangles.
• Identify 3D shapes from 2D representations.

Count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

Skip counting forwards and backwrads in steps of powers of 10 (i.e. 10, 100, 1000, 10 000, 100 000) should be in corporated into transition activities and practised regularly.

In Y5 pupils work with numbers up to 1 000 000 as well as tenths, hundredths and thousandths.

Using known facts and understanding of place value to derive.

Using the following language makes logic explicit: I know three ones plus four ones is equal to seven ones. Therefore, three ten thousands plus four ten thousands is equal to seven ten thousands.

In Y5 extend to multiples of 10 000 and 100 000 as well as tenths, hundredths and thousandths.

These derived facts should be used to estimate and check answers to calculations.

Partitioning one number and applying known facts to add.

Pupils can use this strategy mentally or with jottings as needed.

Pupils should be aware of the range of choices available when deciding how to partition the number that is to be added.

They should be encouraged to count on from the number of greater value as this will be more efficient. However, they should have an understanding of the commutative law of addition, that the parts can be added in any order.

Pupils have experience with smaller numbers from previous years and so the focus should be on developing flexibility and exploring efficiency.

Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

Avoid saying that you “add a zero” when multiplying by ten and instead use the language of place holder.

Use place value counters and charts to visualise and then notice what happens to the digits.

Using known facts and place value to derive multiplication facts.

Emphasis is placed on understanding the relationship (10 times or 100 times greater) between a known number fact and one to be derived, allowing far larger ‘fact families’ to be derived from a single known number fact.

Knowledge of commutativity is further extended and applied to find a range of related facts.

Pupils should work with decimals with up to two decimal places.

These derived facts should be used to estimate and check answers to calculations.

Deriving facts from known facts

Pupils use their growing knowledge of multiplication facts, place value and derived facts to multiply mentally.

Understanding of the inverse relationship between multiplication and division allows corresponding division facts to be derived.

Using knowledge of multiples to divide.

Using an area model to partition the whole into multiples of divisor (the number you are dividing by).

Short division

Dividing a 4-digit numbers by 1-digit numbers

The thought process of the traditional algorithm is as follows:

• How many 4s in 8? 2
• How many 4s in 5? 1 with 1 remaining so regroup
• How many 4s in 12? 3
• How many 4s in 8? 2

• Digit
• Number
• Addition
• Subtaction
• Multiplication
• Division
• Fraction
• Decimal
• 2D Shape
• 3D Shape
• Equivalent
• Quadrilateral
• Triangles
• Numerator
• Denominator
• Perimeter
• Area

• Quiz them on their times table knowledge! Try asking them questions about their tables out of order such as ‘What is 4 x7? What is 6 x 3?’. When your child is secure, try asking them the inverse, ‘What is 25 ÷ 5? What is 88 ÷ 8?’
• If you are cooking with measurements, ask your child to help measure, add together measurements or even multiply/ divide. ‘The recipe says we need 550ml but we want to cook enough for 1, can you divide the amount by 4?’
• When eating cakes or pizza, ask your child what fraction they are eating. Can they simplify it?
• Roll multiple dice, ask your child if can they half the number/ can they double the number? What would 1000 more or less be?

Four operation vocabulary

• Use formal written methods of calculation for all four operations; understand and apply order of operations when calculating
• Your child will know which method to use in school and it is important they only use the methods taught in school.
• Please do not teach your child alternative methods as this can become confusing for your child. If you would like support with helping your child at home, please speak to a member of the Year 6 team.

Maths Fluency