Скачать презентацию Aims to inspire pupils confidence in mathematics

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Aims: • to inspire pupils’ confidence in mathematics; • to develop their ability to use and apply mathematics across the curriculum; • to share ways in which you can help your child at home and the fun you can have with maths; • to explain some of the methods used at school.

Big Maths (mental strategies) • Daily 20 minute mental arithmetic, this is split into 4 sections: • Counting e. g. counting in 7 s, 0. 2 s, 1/5 s • Learn its: facts that they need to know and this should be supported at home e. g. times tables and number bonds • It’s nothing new: applying their learning so 5+6=11, 0. 5+0. 6=1. 1, 500+600=1100 • Calculations: linked to addition, subtraction, multiplication and division • The children take an assessment on a Friday (Big Maths Beat That), designed to increase their fluency, accuracy and speed.

The main focus of this workshop is to explain the progression in calculations for all four operations. Addition Subtraction Multiplication Division In the New National Curriculum, which will be implemented in schools from September 2014, it is expected that children should be using formal written methods for all operations by the end of Year 4.

Mental Calculations The ability to calculate mentally forms the basis of all methods of calculation. This involves: • instant recall of number facts (+ - x ÷); • having a secure understanding of place value and the number system; • having a range of strategies to apply to a calculation; • understand the language and rules of maths.

Written Calculations • Throughout their primary years, children should progress from informal jottings to efficient written methods for each of the four operations. • Standard written methods should only be introduced when a child has a secure knowledge and understanding of the process involved and can clearly explain the strategies they have used. • Children become secure with these methods when they have regular practice and persevere!

Addition Stage 1 The Empty Number Line Stage 2 Partitioning 48 + 36 = 84 40 8 30 40 + 30 + 8 + 6 40 + 30 = 70 8 + 6 = 14 70 + 14 = 84 6

Addition Stage 3: The Expanded Method 48 + 36 U HT U 40 + 8 4 8 6 30 + 6 5 2 1 T 80 + 4 H 9 0 0 10 T 1 0 0 U 7 1 0 0 7

Addition Stage 4: Standard Written Method t u 48 +36 8 4 1 htu 156 + 75 231 11 u. 1/10 3. 6 + 1. 6 5. 2 1

Subtraction Stage 1: Number Line Method

Subtraction Stage 2: Partitioning 43 - 27 = 16 43 – 4 20 43 – 20 = 2 3 23 – 7= 16 3 20 7 7

Subtraction Stage 3: The Expanded Column Method and Dienes 43 - 27 = 16 to subtract 7 units we need to exchange a ten for ten units T U - 2 7 10 + 30 40 + 3 - 20 + 7 10 + 6

Subtraction Stage 4: Standard Written Method 3 4 3 1 3 4 3 5 12 1 - 2 7 - 1 5 7 1 6 2 7 8

Multiplication – Factors and Repeated Addition Understand that … 24 x 20 = 24 x 2 x 10 24 Use factors to multiply x 50 = 24 x 5 x 10 Understand multiplication as repeated addition 2+2+2+2=8 4 x 2=8 2 multiplied by 4 4 lots of 2

Multiplication – Arrays and the Number Line Understand multiplication as an array Understand how to represent arrays on a number line

Multiplication – Place Value apparatus Use place value apparatus to represent the multiplication of U x TU alongside the grid method 4 x 23 10 10 3 4 10 40 40 20 4 ( 2 x 10 ) 80 80 + 12 = 92 3 12

Multiplication – Grid Method Multiplying 14 x 33 30 3 10 30 = 330 + 4 120 12 = 132 462 Children should be able to explain their strategy orally and by using informal jottings.

Multiplication – Expanded & Standard Written Method Multiplying 56 x 27 56 × 27 42 (7 × 6) 350 (50 × 7) 120 (20 × 6) 1000 (20 × 50) 1512 1 56 × 27 1120 (56 × 20) 392 (56 × 7) 1512 1

Division– Using the Number Line Represent ‘groups’ for division on a number line using apparatus alongside the line 0 3 18 divided into groups of 3 18 3 = 6 6 9 12 15 18 3 = 6 0 18 18

Division – Repeated Subtraction 18 18 ÷ 3 = 6 -3 18 15 -3 12 - 15 - -3 3 (1 x 3) 9 - 6 3 (1 x 3) 6 -3 - 3 (1 x 3) 3 3 0 3 (1 x 3) 12 -3 9 3 (1 x 3) -3 3 (1 x 3) 0 Understand division as repeated subtraction using a vertical line and apparatus to make the links

Division – The Chunking Method Children need to see that as the numbers get larger, large chunk subtraction is the more efficient method. Multiples of the divisor (large chunks) are taken away. Multiplication facts are needed to see the size of the ‘chunk’. What facts do I know about the 7 timestable? 518 ÷ 7 = 74 100 ÷ 7 = 14 r 2 - 70 ( 10 x 7 ) 30 - 28 2 1 x 7=7 518 2 x 7 = 14 - 350 ( 50 x 7 ) 100 (4 x 7) ( 20 x 7 ) 0 20 x 7 = 140 50 x 7 = 350 100 x 7 = 700 28 - 28 5 x 7 = 35 10 x 7 = 70 168 - 140 Fact Box (4 x 7)

Division – The Standard Written Method 560 ÷ 24 2 3 r 8 24 5 6 0 - 48 0 - 7 2 8