How we teach maths at Wycliffe Primary

School

KS1 Monday 8th December 2015

2014 Curriculum Our coverage of the new curriculum is based on the Rising Stars planning framework. There is a considerable emphasis on teaching mental calculation strategies and opportunities to reason and explain maths orally. Rote learning of key facts is also a priority. In each unit, calculation methods are applied in a real practical context, for example money, length, mass or capacity.

Actions in School u  Implementation of planning scheme and calculation policies to

ensure consistent and progressive approach exists to secure good/outstanding progress in mental and written calculation in line with new curriculum requirements.

u  Re-introduction of Rainbow Passports, updated in line with the new curriculum, to promote learning of rote facts

u  Ensuring that using and applying is an integral part of all maths lessons at Wycliffe

u  Use of models and images, including practical resources, so children have visual and kinaesthetic references to enhance their mathematical understanding

u  Regular and constructive oral and written feedback given to

children in their maths books.

u  Share what we are doing with you!

Addition

Resources to help children with addition

Stages in addition:

1) Informal counting strategies e.g. counting songs, rhymes and games

2) Practical and pictorial addition – (a) count all

(b) count on

3) Use of number lines to count on from one number to another

!

4) Blank number lines: 8 + 6 = 14 (counting on in ones)

5) Blank number lines: 8 + 6 = 14 (chunking)

Progressing:

6) Partitioning 7) Horizontal expansion 7 6 + 4 7 = 70+40= 110

6 + 7= 13

110+13=123

4 7 = 40 + 7

7 6 = 70 + 6 110

+ 13 = 123

8) Vertical layout 76

+ 47

13

110

123

Base 10 (dienes) equipment and money are key resources to develop understanding in relation to this.

Mental Strategies required to add successfully   u Count forward in 1s, 2s, 5s and 10s etc… u Recall all addition pairs to 9 + 9 and complements in 10, (such as 7+ 3 =10) and apply them in calculations. Then extend to 20, including 8+6=14 etc (number bonds to 20) u Add mentally a series of one-digit numbers, (such as 5 + 8 + 4); u Add multiples of 10 (such as 60 + 70) or of 100, (such as 600 + 700) using the related addition fact, 6 + 7, and their knowledge of place value; u Partition two-digit and three-digit numbers into multiples of 100, 10 and 1 in different ways. It is important that children’s mental methods of calculation are practised and secured alongside their learning and use of an efficient written method for addition. u To be able to estimate and reason before a calculation.  

Vocabulary Add, addition, plus, more, increase

Score, total, altogether, equals

Sum

Number sentence

Record, draw, show me, jottings

Place Value (Thousands, Hundreds, Tens and units)

Count on, jump on

Subtraction

Resources to help children with subtraction

1. 

Stages in subtraction (these are not necessarily hierarchical)

•  Informal counting strategies e.g. counting songs, rhymes and games

•  Practical and pictorial subtraction

•  Use of number lines to count back from one number to another

! !!

•  Finding the difference between groups of objects or numbers

•  Using an empty number line to count up

1. 

Stages in Subtraction by Decomposition

6 7 – 3 2 = 6 2 – 2 7 = 1 6 2 – 2 7 =

Expanded layout – leading to decomposition 563 – 241 =

50 13 500 + 60 + 3 500 + 60 + 3 - 200 + 40 + 1 200 + 40 + 6 300 + 20 + 2 = 322 300 + 10 + 7 = 317

Again, Base 10 (dienes) equipment and money are key resources to develop understanding in relation to this.

Compact Method 563 – 271 = H T U 4 1

5 6 3 2 7 1

2 9 2

borrow or exchange ?

Vocabulary

Subtract, subtraction, minus, take away, less, leave, fewer, decrease, left, difference Equals

Number sentence

Record, draw, show me, jottings

Sum! Count on/count back

Place Value - Thousands, Hundreds, Tens and Units

Mental Strategies required to subtract successfully   u Count back in ones, and tens from any number u Recall all addition and subtraction facts to 10 and 20; u Subtract and add multiples of 10 (such as 160 – 70) using the related subtraction fact, 16 – 7, and their knowledge of place value; u Count on in ones and multiples of 10. u Partition two-digit and three-digit numbers into multiples of one hundred, ten and one in different ways (e.g. partition 74 into 70 + 4 or 60 + 14). u Be able to say a corresponding subtract fact for an addition. Understanding that these two operations are the inverse of each other.

Multiplication

Resources to help children with multiplication

10 20 30 40 50

5

50

60 55

45

35 40 30

25

20

15 10

2 4 6

Counting groups of objects

Grouping objects

Repeated addition 3 x 2 2 + 2 + 2 = 6

Arrays in real life

5 x 3 or 3 x 5

6 x 4 or 4 x 6

7 x 6 or 6 x 7

4 x 6 or 6 x 4

4 x 3 or 3 x 4

Arrays as a tool for solving answers

6 x 3 = 18

3 x 6 = 18

Across the corridor and down the stairs!

Solving multiplication problems

How many legs on 6 spiders?

Notation: 8 x 6 =

Repeated addition: 8 + 8 + 8 + 8 + 8 + 8 = 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 =

Array:

Using known facts: I know that 5 x 8 = 40, so 6 x 8 = 48

Jottings:

8 16 24 32 40 48

Grid Method

13 x 7

10 3 7 70 21

70 + 21 = 91

Number line

+ 70 +21

10 x 7 3 x 7 0 70 91 13 x 7 = 91

Mental Strategies required to multiply successfully    u Recall all multiplication facts to 10 × 10; (2, 5, 10 to start) u Partition numbers into multiples of one hundred, ten and one; u Apply multiplication facts e.g. 2 × 50, 5 x 20, 2 x 500 or 5 × 200 using the related fact 2 × 5 and their knowledge of place value; u Double numbers to 10, 20 u Multiply by 10 u Add two or more single-digit numbers mentally;

Vocabulary Lots of, groups of, ‘x’, times, multiply, multiplied by Multiple of Once, twice, three times… ten times… Times as (big, long, wide… and so on) Repeated addition Array, row, column Double One each, two each, three each… Group in pairs, threes… tens

Number sentence

Record, draw, show me, jottings

Division

Resources to help children with division

½ ½

Sharing objects

Share these six biscuits between three teddies. How many biscuits does each teddy get each?

Linking with halving and quartering shapes

Splitting into equal groups/parts

½ ½

¼ ¼ ¼ ¼

Using tens and units to solve division problems

48

48 ÷ 2 = 24

Division as grouping

Can you group these cookies into groups of 3? How much does each one get?

Division as grouping – Repeated Addition

15 ÷ 3 = 5

+ 3 + 3 + 3 + 3 + 3 0 3 6 9 12 15

Arrays as a tool for solving answers

18 ÷ 6 = 3 18 ÷ 3 = 6

Link with multiplication

Remainders

13 ÷ 4 = 3r1

13 ÷ 4 = 3r1

+ 4 + 4 + 4 +1 0 4 8 12 13

Remainders: Rounding up or rounding down

6 children fit around a picnic bench. How many benches will I need for 26 children?

Cinema tickets cost £6 each. How many tickets can I buy if I have got £26?

Solving division problems

How many boxes of 6 eggs do I have if I have 36 eggs altogether?

Notation: 36 ÷ 6 =

Array:

Using known facts (grouping) : I know that 6 x 6 = 36, so 36 ÷ 6 = 6

Jottings: 6 12 18 24 30 36

Counting on by chunking

10x7 = 70 4x7 = 28 r 2 10 4 0 70 98 100

Vocabulary Share, share equally One each, two each, three each… Group in pairs, threes… tens Equal groups ÷, divide, division, divided by, divided into Halve, quarter, ½, ¼, One each, two each, three each… Group in pairs, threes… tens Left, left over, remainder Grouping and chunking

Number sentence

Record, draw, show me, jottings

Mental Strategies required to divide successfully     u Understand and use the vocabulary of division u Partition two-digit and three-digit numbers into multiples of 100, 10 and 1 in different ways; u Halves of numbers to 20 u Begin to recall multiplication and division facts to for 2, 5, and 10 times tables. E.g. I know 3 x 10 is 30 so 30 ÷ 3 = 10 and 30 ÷ 10 = 3 u Know how to find a remainder working mentally – for example, find the remainder when 48 is divided by 5; u Begin to know and use multiplication and division as inverse operations. u Understand division as grouping (using repeated addition)

Any questions?

There will be a maths page

on the website soon.

It will contain:

• this presentation

• the booklet for parents,

• our calculation policy,

• details of Rainbow Passports

• links to websites with great maths games