Maths Information Evening 2017

Aims of today To gain an insight into how children’s mathematical understanding develops from R to Y6. To gain a better understanding of the methods taught in each age range. To, hopefully, make you more confident with helping you child at home.

Maths at St. Mary’s = + x % subtract more add sum factor product Here is a receipt for some shopping. How much did I spend? How much change did I get from £20?

The New Maths Curriculum Children should: Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. Reason mathematically by following a line of enquiry, identifying relationships and generalisations and developing an argument, justification or proof using mathematical language. Solve problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Number Sense! Children need to understand our number system, starting with counting numbers, building an understanding of how our numbers work and fit together. This includes exploring place value and comparing and ordering numbers then applying this understanding in different contexts.

Recalling facts It is important that children recognise number bonds, different pairs of numbers with the same total. 6 + 2 3 + 2 5 8 7 + 3 5 + 3 10 1 + 4 6 + 4 6 + 1 7 6 + 3 3 + 4 9 6 5 + 4 3 + 3

Place Value Place value is at the heart of the number system. Children must understand that digits have a value and a secure understanding of this will enable children to use and understand different calculation methods. Ten Frames

1 2 3 9

Partitioning 72 x 8 70 x 8 = 560 2 x 8 = 16 560 + 16 = 576 432 + 325 400 + 300 = 700 30 + 20 = 50 2 + 5 = 7 700 + 50 + 7 = 757 757 – 432 700 – 400 = 300 50 - 30 = 20 7 - 2 = 5 300 + 20 + 5 = 325 72 x 8 70 x 8 = 560 2 x 8 = 16 560 + 16 = 576

Understanding number Concrete calculation Partitioning

Column methods Children with a secure understanding of place value will better understand the column method for addition and subtraction. Understanding place value will help children see the relationship between the columns.

Keep Counting! Backwards and forwards in 10s, 100s, 1000s. Counting in decimals. Counting in fractions. Counting into negatives.

KS1 – Years 1 & 2 Addition Subtraction Division Multiplication

Understanding number The ‘eight-ness’ of eight. The ‘ten-ness’ of ten.

Addition Written calculations: Models & images: Mental calculations:

Written calculations: Addition Mental calculations: Written calculations: Models and images:

Subtraction Written calculations: Models & images: Mental calculations:

Written calculations: Subtraction Written calculations: Models and images: Mental calculations:

Multiplication Written calculations: Models & images: Mental calculations:

Written calculations: Multiplication Models and images: Written calculations: Mental calculations:

Division Written calculations: Models & images: Mental calculations:

Written calculations: Division Written calculations: Mental calculations: Models and images:

KS2 – Years 3, 4, 5 and 6 Addition Subtraction Division Multiplication

Understanding number Number bonds are the window to success in KS2 and it is vital that your child knows these securely as they enter this phase. By the end of Year 4, your child is expected to know all their times tables up to 12 x 12. To ensure this, we practise the tables daily and explore connections between the tables, e.g. to find 6 x 8, we know 5 x 8 is 40, so 6 x 8 is one more 8, so is 48.

Terror Tables

Addition Written calculations: Models & images: Mental calculations:

Now, have a go at this question on your whiteboards using one of the methods here, then try a different method: 128 + 76 =

Subtraction Written calculations: Models & images: Mental calculations:

Tens Ones 1 1 1 10 1 10 10 10 1 1 1 10 10 1 10 1 6 7 2 10 1 1 1 1 - 7 4

Tens Ones 1 1 1 10 1 10 1 10 10 1 10 6 7 2 1 - 7 4

Tens Ones 1 1 1 10 1 10 1 10 10 6 7 2 1 10 1 - 7 4

Tens Ones 1 1 1 10 1 10 1 10 10 6 7 2 1 - 7 4 10 1

Tens Ones 1 1 1 10 1 10 1 10 10 6 7 2 1 - 7 4 10 1 5 2

Now, have a go at this question on your whiteboards using one of the methods here, then try a different method: 68 - 27 =

Multiplication Written calculations: Models & images: Mental calculations:

Models for multiplication Fingers But these images aren’t commutative “3” “6” “9” “12” Bead Bar 3  4 4  3 Number Line 3 6 9 12

Multiplication Progression arrays grid compact

More than single digits? 18 18 8 10 10 100 80 13 13 3 30 24

Progressing towards the grid… Progressing towards expanded column… 1 0 8 1 0 1 0 0 8 0 3 3 0 2 4 Progressing towards expanded column… Now, have a go at this question on your whiteboards using one of the methods here, then try a different method: 53 x 15 =

Division Written calculations: Models & images: Mental calculations:

5 6 7 8 56  7 The array is an image for division too Either: Try some for yourself: Choose a number of counters Make an array Describe it to each other using ×’n and ÷’n language Record it in an equation using × and ÷ symbols 56  7 Either: How many 7s can I see? (grouping) Or: If I put these into 7 groups how many in each group? (sharing) The array is an image for division too 5 6 7 8

An image for 56  7 5 6 7 8 How many 7s can I see?

5 6 7 8 How many 7s can I see?

8 How many 7s can I see? 7 5 6

8 How many 7s can I see? 7 5 6

120  3 The power of the place value: counters for larger numbers 40 48

1200  3 Similarly for 100s 400 1200 3 49

Long division via chunking Children are taught to use their knowledge of x 10 or x 100 to take away large ‘Chunks’ of the number first. Knowledge of doubling/having and the 2, 4, 8 times table helps them to quickly realise they can take large numbers away in order to reach the answer quicker. The children need to track how many ‘lots of’ the number they have taken away in order to get to the final answer. e.g. 10 x 32 = 320 20 x 32 = 640 40 x 32 = 1280 80 x 32 = 2560 160x32= 5120 5600 32 The lots are added up to reach the answer 175 5120 (160 x 32) 480 320 (10 x 32) 160 160 (5 x 32)

23 x 100 = 2300 3200 2300 = 900 690 (23 x 30) = 210 115 (23 x 5) = 95 92 (23 x 4) = 3 139 r 3 3200 23

Now, have a go at this question on your whiteboards using one of the methods here, then try a different method: 853 ÷ 5 =

Resources on the School Website

Follow up evenings for specific year groups. Year 2 Maths Night – Wed 8th March Year 6 Maths Night – Thurs 9th March