ON CALCULATION

Welcome to our Maths Talk

Aim of the Presentation

To provide an overview of the different calculation strategies taught at North Ealing as pupils’s knowledge and understanding progresses from Reception through Key Stage 1 and Key Stage 2 to the end of Year 6.

National Curriculum expectations

EYFS - Expected

Mathematics – Number Early Learning Goals Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.

Mathematics – Shape, Space and Measure Early Learning Goals Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.

National Curriculum expectations

Year 2 and Year 6 – currently still working on the old National Curriculum.

The end of year expectation in Year 2 is a Level 2.

The end of year expectations in Year 6 is a Level 4.

National Curriculum expectations

Years 1, 3, 4 & 5 – are working to the new National Curriculum.

The end of year expectations in Year 1 is– Stage 1 secure.The end of year expectations in Year 3 is – Stage 3 secure.The end of year expectation in Year 4 is– Stage 4 secure.The end of year expectation in Year 5 is – Stage 5 secure.

The early stages of counting and calculating

There are four main skills that children need to develop before they can count.

 1. Recognition of the sounds of the numbers. 2. The understanding of one-to-one correspondence. 3. The understanding of "How many are there?" 4. The number of objects is the same however they are

arranged.  

The next stage is for your child to recognise numbers as symbols which can taught by playing number recognition games.

 Once children recognise numbers they will want to start writing them themselves.

Skill 1

Children need to learn the sounds of the numbers 'one, two, three...'.

Children can start to recognise the sound of numbers from an early age if they hear number songs and rhymes and hear people counting. Some examples of rhymes are:

Five currant buns in the baker's shop 1, 2, 3, 4, 5 Once I caught a fish alive Five fat sausages frying in a pan 1 potato, 2 potato, 3 potato, 4

Books and stories that include numbers can help too. At story time make a point of counting the characters and the key items in the pictures. Some examples of books are:

  Goldilocks and the Three Bears The Three Billy Goats Gruff The Very Hungry Caterpillar The Three Little Pigs  

Skill 2

Before learning to count a child needs to understand 'one to one correspondence'. This means being able to match one object to one other object or person.

You can practice 'one to one correspondence' in all sorts of different contexts. Laying the table is a good idea. Alternatively you can do this in a play situation as indicated below.

Dough CakesMake some dough cakes and ask your child to give one to each of their soft toys. Use very small numbers at first.

Skill 3

Children need to understand what is meant by 'How many are there?' 

CountingAs you count objects together touch each one. This helps children to understand they are counting one thing at a time. Also, only count up to three at first and do not progress until your child can do this successfully. Gradually add one more number at a time. Counting opportunities arise with everyday objects such as cutlery or biscuits. Ask your child to guess how many objects there are before counting them together. It is important to build confidence through positive comments.

Counting Game/Throwing games Games which involve throwing a number of objects, such as rolled up socks, in a waste paper bin or cardboard box can give good counting practice.

 Counting trays Use paper plates for this activity. Write a number on the plate. Provide a pile of dried pasta or bricks and show your child how to count the appropriate number onto each plate before he or she has a try. Underline 6 and 9 to avoid confusion.  Counting everyday objects You will find many daily opportunities to count aloud together. Cooking is a wonderful way to introduce a child to practical maths and extend vocabulary. You can count baking cases, spoons of sugar or chocolate button decorations. Later you can use buns for simple addition and subtraction sums.

Skill 4

The number of objects is the same however they are arranged. 

Ordering NumbersMake some cards with numbers on one side and the corresponding number of spots on the reverse.

  

EstimatingDeveloping the ability to estimate is also a useful skill. Asking a child to guess how many items are on a tray will help to develop this. Always count them out together afterwards, so that the child can see how close he or she was.

 Recognising the SymbolsA fun way to help recognition of numbers is to select a few number cards. Take one from the pile without letting your child see it. Ask him or her to guess which one you have as you gradually expose the number from behind a screen (e.g. a book) If your child guesses wrongly explain what the number is. Introduce a few numbers at first and build up slowly.

Number Formation Guide  Encourage your child to form numbers in the standard way. Bad habits are difficult to break, so following

our simple guide can help to prevent problems at a later stage

Number Formation Guide

Spots indicate the starting position of the pencil. The pencil should remain on the paper, following the arrows. For the numbers four and five, the pencil must be raised before completing the second part of each number. Crosses indicate the second starting positions.

ADD, PLUS, SUM, ALTOGETHER, TOTAL, MAKE

Addition

Early stages of Addition

Children begin to relate addition to combining two groups of objects. 

Make a record in pictures, words or symbols construct number sentences to go with practical activities.

 

Construct number sentences to go with practical activities (movable and non-movable objects). 

Use games, songs and practical activities to begin using vocabulary. 

Solve simple word problems using their fingers.Can find one more to ten.

 1 to 1 number recognition:

   

Addition

The children continue to use counters or other objects to support their addition.As they progress they are encouraged to hold the larger number in their head. Then they count on the lower number. Children are encouraged to then record this as a sum.

Addition

Using a number line, by starting on the biggest number and counting on the number they are adding

Addition

Children will begin to use blank number lines where they draw a line starting with the larger number and counting on the number they are adding. First counting on in jumps of tens and then ones.

 

Addition

Children may also use a hundred-square to support their understanding. They will be encouraged to jump down in 10s and forwards in units.

Addition

Expanded method200 + 20 + 2 0 + 50 + 3200 + 80 + 5

Addition

SUBTRACT, MINUS,

TAKE AWAY, DIFFERENCE, LEAVE, LESS

Subtraction

Early stages of Subtraction

Begin to relate subtraction to ‘Taking away’

 Make a record in pictures, words or symbols of subtraction activities already carried out.

 Use of games, songs and practical activities to begin using vocabulary.

 Construct numbers sentences to go with practical activities.

 Relate subtraction to taking away and counting how many objects are left.

 Can find one less to 10

Subtraction

The children use counters or other objects to support their subtraction. They count out the right amount of counters and they move away the number of counters they are taking away. They then count how many they have left.Children are encouraged to then record this as a sum.

Subtraction

11 – 7 = 4  -1 -1 -1 -1

0 1 2 3 4 5 6 7 8 9 10 11  

Subtraction

Partitioning:

47 - 32 =

Subtraction

Subtraction

The expanded method of Subtraction:Partitioning both numbers leads to the opportunity to use more formal methods of subtraction.

Subtraction

ARE YOU SMARTER THAN A 10 YEAR OLD?HTTPS: / /WWW.YOUTUBE.COM/WATCH?V=VBTKYDLBHFQ

Brain Break

Are you smarter than a 10 year old?

Use the numbers 1, 2, 3, 4, 5 and 6 only once to fill in the slots below

_ _ X _ _ _ _

Solution

5 4x 3162

MULTIPLY, TIMES, GROUPS OF,

LOTS OF, MULTIPLE.

Multiplication

Early stages of Multiplication

Real life contexts and use of practical equipment to count in repeated groups of the same size.

 Count in twos, fives and tens.

 Also chanting in 2s, 5s and 10s.

Multiplication

Array: _ rows of _

Multiplication

Repeated addition:3 times 5 is 5 + 5 + 5 = 15 or 3 lots of 5 or 5 x3Repeated addition can be shown easily on a number line:5 x 3 = 5 + 5 + 5

Multiplication

Repeated addition using times table facts:

  By using known times table facts shortcuts can be taken to reduce the number of steps to multiply.

Multiplication

The grid method:

Multiplication

The expanded method:

2 3 x 4

1 2 (4 x 3 = 12 ) + 8 0 (4 x 2 0 = 8 0) 9 2

Multiplication

DIVIDE, SHARE, EQUALS GROUPS

OF.

Division

Early stages of Division

Sort objects. Share objects into equal groups Use related vocabulary

Activities might include:  Separating a given number of objects into

two groups

Division

Repeated addition / subtraction:   18 ÷ 3

+3 +3 +3 +3 +3 +3

or

Division

Number line using times table facts:

Division

Chunking using times table facts:

Division

Short division: 

1 8 r 27 1 2 58

 

Division

Key things to remember

The aim is for pupils to be able to select an efficient method of their choice.

Having a good grasp of mental maths will help pupils achieve better results and also increase their confidence in mathematics.

This includes:- Knowing number bonds to 10, 20, 100, 100 etc.- The ability to add and subtract any numbers between 1 -20.- Being able to double and halve any number.- Recalling all multiplication facts with speed.- Learning the corresponding division facts.- Secure understanding of place value.

Glossary

Partitioning – splitting a number up according to place value e.g. HTURecombining – putting a number back together after partitioning (usually after a calculation) e.g. 23 + 13Inverse – opposite calculations e.g. addition and subtraction or multiplication and division.Grid Method – method used for short and long multiplication using partitioning of numbersChunking – method used for short and long division involving repeated subtraction.Expanded – method of addition and subtraction involving the skills of partitioning to aid understanding of place valueDecomposition – method of subtraction (traditional) often known as the formal vertical methodNumber line – Visual tool that can be used for all 4 number operationsCounting on – term used to aid subtraction of numbers that are close together e.g. 32 – 29 = ? Count on from the smaller number to find the difference between the two numbers.Finding the difference – a term used when referring to subtraction.Exchange – term used when carrying numbers from one place to another, traditionally referred to as borrowing.Arrays – visual way of showing ‘groups of’ when learning about multiplication / division.Number bonds – the different pairs of numbers which make up the same number.