Calculations slides Calculation and Progression

Beginning to understand Addition Children are taught to understand addition as combining two sets and counting on = At a party, I eat 2 cakes and my friend eats 4. How many cakes did we eat altogether? Children are encouraged to visualise the sum by drawing a picture. As the numbers get bigger, they are encouraged to use dots or tally marks.

I have 125 stickers in my sticker album. My friend has 164 more than me. How many does she have? Children are also encouraged to use numberlines for larger numbers. This is much more efficient than counting in ones cm+ 25cm= My sunflower is 47 cm tall. It grows another 25cm. How tall is it now? =

, Partitioning Children are encouraged to ‘break numbers up’ into place value columns and then recombine (put back together) to get the answer. Year 2/3 informal jottings may look like this =98 +

Partitioning extended into expanded vertical or horizontal layout method There are 432 boys and 356 girls in a school. How many children are there altogether? h t u h t u £ £12.49 £ p + 9p + £ p + 9p.

people visited Banbury Museum last year. The numbers increased by this year. How many people altogether visited this year? Carried digits are placed on top of the calculation. ‘on the shelf’ Progression- Moving on from ‘Expanded method’ to the traditional compact method

Subtraction Children are taught to understand subtraction as … Taking away (counting back) Finding the difference (counting up)

I had 5 balloons. Two blew away. How many did I have left? 5-2= 3 Lisa has 11 pencils. Tom has 4, How many more does Lisa have? 11-4 = 7

Subtraction and Numberlines Counting Back 84-27= 57 The tail of my kite measured 84 cm. 27cm broke off. How long is it now?

Subtraction and Numberlines Counting up to find the difference = The library owns 834 books. 378 are out on loan. How many are on the shelves? Principles of counting up (complementary addition) Number line runs from smallest to biggest) Children are counting up to multiples of 10 or 100 (friendly numbers).

Progression in subtraction Can also be shown vertically (introduced in Year 4 Autumn) = (up to nearest 100) 400 (up in hundreds) 34 (count up to target number

Expanded subtraction calculations (using partitioning) = Leading to Leading to

Multiplication -repeated addition and grouping 2x4 Each child has 2 eyes. How many eyes do 4 children have? +2 5x4 There are 5 tennis balls in a carton. How many in 4 cartons? Tally marks or dots drawn in groups. 4x3 A sweet costs 4p. How many do 3 sweets cost? Drawings of arrays give an image of the answer. They also help understanding that 4x3 is same as 3x4 Multiplication is introduced in Year 1 as counting in multiples, repeated addition and ‘lots of’

Multiplication 6 x 3 = There are 6 birthday cakes. Each cake has 3 candles on it. How many candles are there altogether? Repeated addition (3 jumps of 6) 13 x 7 = There are 13 chocolates in each box. How many are there in 7 boxes? 0 10 x 7 3 x

Multiplication -Grid Method Y3/4 By the end of year 3, the grid method is introduced. It is based on partitioning. 3 x 32 = x x 124 = x = 96 = 744

56 x 27 Multiplication -Grid Method x

Extension decimals and HTU x HTU 12 x 23.5 = x

243 x 126 Grid Method HTU x HTU , , , (Children would probably do this on a calculator!)

Column Multiplication- partitioning 12 4 x 8 x Then use standard short multiplication

Children are taught to understand division as sharing and grouping. 6 ÷ 2 6 lollies shared between 2 children. How many lollies will each child get? Division Sharing Children need to draw pictures and physically share out to grasp this concept.

Division as sharing and grouping 12 ÷ 4 = 12 apples are shared equally into 4 baskets. How many apples in each basket? I I I Tallying used instead of pictures. 4 apples are packed in a basket. How many baskets can you fill? OOOO OOOO OOOO OOOO

Number lines - grouping in Division 28÷ 7 = A rubber costs 7p. How many can I buy with 28p? You can work this out by ‘jumping along in groups of 7. This shows you would need 4 jumps of 7 to reach 28.

Division and bigger numbers 84÷ 6 = 14 I need 6 drawing pins to put up a picture. How many pictures can I put up with 84 pins? x 10 6 x

Division moving into formal short division 128g of flour were used to bake 4 cakes, how much flour was used per cake? children need to go a swimming gala. Each minibus holds 16 children. How many minibuses are needed? r

Discussing and evaluating Can I draw any jottings or pictures to help me? Do I need to use a written method? If the numbers are too big to work out mentally, do I need to use a calculator? Discussing the suitability and efficiency of different strategies is an important part of the Maths learning your child experiences. Children are often paired into ‘talk partners.’ Children should be encouraged to ask…… We should help them check the answer by estimating. Can I do this in my head?