Welcome to SJS and an Evening of Maths!

Calculation Strategies

Calculating The purpose of the National Numeracy Strategy was to improve standards in Mathematics. Emphasis upon developing pupils’ mental calculation strategies and their understanding.

Calculating Younger children are encouraged to use mental strategies to calculate but when the numbers become ‘too big’ they begin the process of using pencil and paper to support these mental calculations. These ‘jottings’ develop into expanded methods of calculating which support the mental methods and make the processes clear. In the later primary years, children are taught conventional written methods, many of which you will recognise. However the route to reach these methods you may not recognise.

Written Methods of Calculation   Aim – by the end of Key Stage 2, majority of children are able to use an efficient written method for each operation with confidence and understanding.

Expanded methods lead children into compact methods so that they understand structure and efficiency.   An expanded form is needed before the steps in the traditional standard written method are meaningful and can be used with understanding. AIM – To develop the children’s understanding of the process rather than the process itself.

Attitudes Towards Maths Jo Boaler – Professor of Maths at Stanford University Everyone can learn Maths to a high level Believe in yourself – Growth Mindset - Persistence Struggle and learning from mistakes are really important - Challenge Speed is not important It is important to think visually and creatively. Maths is not just about calculations. It is about patterns and space, thinking deeply and seeing things differently and making connections. You can achieve whatever you want to!

Importance of knowing basic number facts.

1284 + 863 1 2 8 4 + 8 6 3 2 1 4 7 1 1

8034 - 1863 7 9 8 0 3 4 - 1 1 1 8 6 3 6 1 7 1

23 484 ÷ 6 3 9 1 4 ) 2 3 4 8 4 5 2 6

Partitioning 98 = 90 + 8 523 = 500 + 20 + 3 1 578 = 1 000 + 500 + 70 + 8

Addition

Number Line

Partitioning 47 + 72 = 40 + 70 + 7 + 2 = 110 + 9 = 119

Adding by Partitioning Vertically 1 5 6 + 2 3 2 3 0 0 1 0 0 + 200 8 0 5 0 + 3 0 8 6 + 2 3 8 8

Partitioning Vertically 2 3 7 8 2 3 7 8 + 1 1 4 9 + 1 1 4 9 3 5 2 1 7 Formal Written Method Partitioning Vertically 2 3 7 8 2 3 7 8 + 1 1 4 9 + 1 1 4 9 3 5 2 1 7 1 3 0 0 0 4 0 0 1 1 0 1 7 3 5 2 7

Adding the least significant digits first Adding the most significant digits first Adding the least significant digits first 468 468 + 276 + 276 400 + 200 = 600 600 14 60 + 70 = 130 130 130 8 + 6 = 14 14 600 744 744 744

I have £7587 in my savings account I have £7587 in my savings account. I get five numbers in the National Lotto game and win £5675. How much money do I have now? 7587 + 5675 12 ( 7 + 5) 150 ( 80 + 70) 1100 ( 500 + 600) 12000 (7000 + 5000) 13262

1284 + 863 1 2 8 4 + 8 6 3 2 1 4 7 1 1

Adding Decimals

Partitioning Vertically 6 5 . 4 + 3 9 . 3 6 5 . 4 + 3 9 . 3 . 7 Formal Written Method Partitioning Vertically 6 5 . 4 + 3 9 . 3 6 5 . 4 + 3 9 . 3 . 7 1 4 . 0 1 0 4 1 . 7 9 0 . 0 1 0 4 . 7

Subtraction

Number Line

847 - 63 +7 +30 +700 +40 +7 63 70 100 800 840 847 =784

Subtraction by counting up. 502 - 198 = 304 502 - 198 +2 +300 +2 2 (to 200) 300 (to 500) 198 200 500 502 2 (to 502) 304

Counting Up

Counting Up

Expanded Column Subtraction

Subtracting Decimals

Subtraction by counting up. 24.3 - 7.9 = 16.4 24.3 - 7.9 +0.1 +2.0 +10.0 +4.3 0.1 (to 8.0) 2.0 (to 10.0) 7.9 8.0 10.0 20.0 24.3 10.0 (to 20.0) 4.3 (to 24.3) 1 6 .4

Decimals

Division

Grouping

Using appropriate chunks The easy way to divide!

72 ÷ 4 = 18 18 4 72 we know 10 x 4 40 32 we know 8 x 4 32 We highlight the times table we are using. We circle the number of groups.

84 ÷ 6 = 14 14 6 84 we know 10 x 6 60 24 we know 4 x 6 24 We highlight the times table we are using. We circle the number of groups.

112 ÷ 8 = 14 14 8 112 we know 10 x 8 80 32 we know 4 x 8 32

23 484 ÷ 6 3 9 1 4 ) 2 3 4 8 4 5 2 6

The Grid Method The fun way to multiply!

Mental Multiplication using Partitioning

27 x 4 = ? 36 x 3 = ? X 3 30 90 6 18 = 108 X 4 20 80 7 28 = 108

Partition each number first 25 x 35= 20 + 5 30 + 5 X 20 5 30

25 x 35= X 20 5 30 600 150 100 25 7 5 + 1 2   8 7 5

Multiplying using the Grid Method X 70 3 50 3500 150 8 560 24 3650 + 584 4234

37 x 86 30 7 x 2580 + 2400 560 80 602 3182 42 180 6 1 2580 602

Does your word problem match the calculation? If a baker bakes 52 loaves of bread every day, how many will he have baked in 7 days? Charlie has packed his soldiers into 4 boxes ready to move house. In each box he has managed to pack 65 soldiers. How many soldiers does Charlie have altogether in the boxes? For the Oscars, 76 special goody bags have been prepared. Each bag has 6 special presents inside. How many presents has the organiser had to buy for these bags? Nine children each bring in 47p towards their class’ Comic Relief fund. How much money did they bring in altogether? At a theme park, 92 people each paid an £8 entrance fee. How much did the park make from these people? Now have a go at writing your own word problems based on these calculations……….. 71x9= 53x9= 68x4= Does your word problem match the calculation?