Longfield Primary School Maths Parents’ Workshop Years 1, 2, 3 25 September 2012

Aims To explain how we teach your child the main operations +, -, x and ÷ in KS1 and in Year 3. To give you some ideas of how you can help and support your child at home.

Maths – when do we use it?

Conserving number

Addition vocabulary + altogether more than count on plus add total and

+ Addition Adding practically using objects or pictures. Encourage your child to put the larger number in their head and count on. They can use their fingers to do the counting on if they need to. 7 + 5 = 12

Addition Number Track 6 + 5 = ? Counting on

Counting on using a number line Addition Counting on using a number line Counting on 4 from zero Counting on 4 from 5. Make sure you emphasise counting the jumps. (Not the numbers.)

Addition 5 Using an empty number line to count on in 1s. 5 9 10 5 + 4 Start at zero, jump on 5 then jump on 4. 5 9 10 5 + 4 Start on 5 then jump on 4.

Addition Using a hundred square to count on and back in 1s and 10s. We encourage children to do this practically with the hundred square and then using a mental image.

2 2 4 4 Place value Different value Same number 2 tens 2units 4 units

Place value This is a ten stick – it is made up of 10 cubes joined together. This is a unit or one. It is one cube on its own.

Place value What number do these make? 3 tens and 4 units = 34

Start on any number Addition 32 + 6 = 38 25 + 40 = 65 Need to understand place value – the 4 in 40 means 4 tens. So you move down 4 squares in the column to add 40.

Number bonds Knowing pairs of numbers that make 10 and then 20 is really important. Year 1 children need to know number bonds for 10 by the end of the year. Then move onto bonds for 20. 10 + 0, 9 + 1, 8 + 2, 7 + 3, 6 + 4, 5 + 5, 4 + 6, 3 + 7, 2 + 8, 1 + 9, 0 + 10 Game – Ping pong.

Partitioning Partitioning is splitting a number into different parts. So we teach children to partition into tens and ones (units). 18 = 10 + 8 12 = 10 + 2 27 = 20 + 7 This is the beginning of understanding place value – The 1 in 18 means 1 ten, the 2 in 27 means 2 tens.

Addition Once children can partition, they can use this knowledge to add using an empty number line. 24 + 5 = 29 Step 1 29 24 24 + 15 = 39 Step 2 + 10 34 39 24

Your turn! Use an empty number line to do this calculation 36 + 23 = 59 +10 +10 36 46 56 59

Next step is to become more efficient by adding the units in one jump. And then add the tens in one jump 34 + 23 = 57 +20 +3 34 54 57

Bridging through 10 or a multiple of 10 can help children become more efficient.

Your turn! 37 + 56 = Remember to start from the larger number.

Your turn! 37 + 56 = 93 Remember to start from the larger number. + 30 +4 +3 86 90 93 56

Addition in Year 3 Year 3 children continue to use empty number lines to support addition. They will start to add 2 digit numbers that bridge 100, and then 3 digit numbers. They also are taught to use an empty number line to help them compensate for numbers that are near multiples of 10 49 + 73 = 49 is 1 less than 50. 50 is a much easier number to add than 49. So first add 50. Then subtract 1. +50 122 73 -1 123

Your turn! 59 + 123 = 182 + 60 -1 123 182 183

Year 3 Addition 67 267 + 24 + 85 11 ( 7 + 4) 12 ( 7 + 5) Adding the least significant digits first. (Units in these calculations). In Year 2 tens were added first. Vertical (column) addition is a change from Year 2 where calculations were horizontal. Mental strategies still more important – add hundreds or tens first. No ‘carrying’ in this method – children need to understand what they are adding; units, tens or hundreds and this method makes it explicit. 67 267 + 24 + 85 11 ( 7 + 4) 12 ( 7 + 5) 80 (60 + 20) 140 (60 + 80) 91 200 352

Your turn! 89 + 64 256 + 78 13 ( 9 + 4) 140 (80 + 60) 14 ( 8 + 6) 120 ( 70 + 50) 200 153 __334

Subtraction vocabulary - take away minus count back less than subtract difference between decrease how many left take from

Subtraction As with addition, start by using objects or pictures. 6 – 3 = 3 Cross out 3. Count what is left.

Subtraction 20 – 7 = 13 Subtract by counting back. Remember to count the jumps.

5 10 – 5 = Using a number line to count back. To subtract multiples of 10 count up the columns. To subtract small numbers count back along the rows.

Difference What is the difference between 3 and 6? 6 – 3 = 3 (count back) or count on from 3 to 6.

Counting back: First partitioning and counting back in tens and ones. Then helping children to become more efficient by subtracting the units in one jump (by using the known fact 7 – 3 = 4).

Subtracting the tens in one jump and the units in one jump. Bridging through ten can help children become more efficient.

Your turn! 78 – 45 = 33 - 40 -5 33 38 78

Subtraction in Year 3 Continue to use empty number lines with increasingly larger numbers. Partitioning demonstrated using arrow cards (started in Year 2). 4 0 0 5 0 6

Partitioning before subtracting Subtraction – Year 3 Partitioning before subtracting 89 = 80 + 9 - 57 50 + 7 30 + 2 = 32 -

Beginning to exchange Your turn! 83 - 47

Your turn!

Multiplication vocabulary x groups of lots of times table times multiplied by multiply double

Multiplication Counting in 10s

Multiplication Counting in 2s

Multiplication Counting in 5s

Multiplication Children need to learn multiplication tables and multiplication facts. Yes – learn to recite tables but also need to know table facts at random. e.g. 8 lots of ten are? And answer questions like “ How many tens in 80?” Not secure in times tables until able to do this quickly. Should be working on 10x, 2x and 5x tables in Year 1, continue and work on 3x and 4x in Year 2. Secure in Year 3.

Multiplication Repeated addition 10 + 10 + 10 + 10 = 40 Problem solving There are 10 pencils in a pack. How many pencils are there in 4 packs? Repeated addition 10 + 10 + 10 + 10 = 40

Multiplication 3 times 5 is the same as 5 + 5 + 5 = 15 or 3 lots of 5 or 3 x 5 On a number line 5 5 5 5 10 15

Multiplication As an array 3 x 5 = 15 5 x 3 = 15

Problem solving There are 15 apples in a tray. Ling has 4 trays of apples. How many apples does Ling have altogether? Show how you work it out. Ella’s dad washes some cars. He uses 12 buckets of water. Each bucket has 5 litres of water. How many litres of water does he use altogether? Your turn! Can you draw pictures or make jottings to show how you could work one or both of these out?

Ella’s dad washes some cars. He uses 12 buckets of water Ella’s dad washes some cars. He uses 12 buckets of water. Each bucket has 5 litres of water. How many litres of water does he use altogether? 10 15 20 25 30 35 40 45 50 55 60 Or 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 60 Or count in 5s 12 times. Or 12 x 5 =60

There are 15 apples in a tray. Ling has 4 trays of apples. How many apples does Ling have altogether? Show how you work it out. 151415 15 151415 151415 151415 15 15 15 10 + 5 10 + 5 10 + 5 10 + 5 4 lots of 10 10 20 30 40 4 lots of 5 5 10 15 20 40 + 20 = 60

Multiplication – Year 3 Partitioning 38 x 5 = (30 x 5) + (8 x 5) = 150 + 40 = 190

Division vocabulary share equally divide divided by groups halve half

Division Children start by understanding equal groups and sharing items out in play and problem solving. Count in 2s, 10s and 5s. Sharing equally. There are 6 sweets. How many sweets can 3 children have each?

Grouping There are 6 sweets. How many children can have 2 each? Division

2 4 6 8 10 12 14 16 Count in 2s until you get to 16. So how can you work out a division sum using times tables? Count in 2s until you get to 16. 2 4 6 8 10 12 14 16

Division using an empty number line How many groups of 5 are there in 25? 25 ÷ 5 = 5 5 5 5 5 5 0 5 10 15 20 25

Your turn! 6 groups of 5 make 30. So 6 teams. There are 30 children in the class. They need to be in teams of 5. How many teams will there be? Use an empty number line to work it out. 5 5 5 5 5 5 0 5 10 15 20 25 30 6 groups of 5 make 30. So 6 teams.

How you can support your child at home Look for and talk about numbers in the environment Play games Shopping Counting on/back Number bonds Doubles/Halves Times tables Multiplication facts Division facts

Useful websites http://www.familylearning.org.uk/multiplication_games.html http://www.ictgames.com/resources.html http://www.bbc.co.uk/bitesize/ks1/maths/ http://www.comberps.newtownards.ni.sch.uk/maths_games_for_ks1.htm http://www.maths-games.org/time-games.html http://www.bbc.co.uk/schools/websites/4_11/site/numeracy.shtml http://www.woodlands-junior.kent.sch.uk/maths/index.html