Teaching Numeracy in Key Stage 2

In this area of numeracy we look at: Properties of Shape Properties of position and movement Measures

Properties of Shape regular irregular horizontal parallel It is important for children to be familiar with 2D and 3D shapes in key stage two. We introduce some new vocabulary and encourage children to use the new vocabulary whenever we are working with shape. The vocabulary is built upon throughout key stage two but will include terms such as: regular irregular horizontal parallel perpendicular vertices congruent vertical reflective symmetry

YEAR 3 AND 4 We think about how to CLASSIFY 3D and 2D shapes using mathematical properties. We look at recognising RIGHT ANGLES in shapes in different orientations and angles which are smaller (ACUTE) or bigger (OBTUSE) than right angles. We look at recognising EQUILATERAL and RIGHT-ANGLED triangles We think about whether shapes have any lines of SYMMETRY or not and begin to use this information when describing shapes. We begin to recognise NETS of familiar shapes and make 3D models by linking given faces or edges.

YEAR 5 AND 6 We think about RECOGNISING and NAMING most QUADRILATERALS e.g. trapezium, parallelogram, rhombus. We think more about triangles and introduce ISOSCELES and SCALENE triangles. We think about VISUALISING shapes and recognising them in different ORIENTATIONS. We continue to think about CLASSIFYING, including classifying quadrilaterals using their properties We think about calculating ‘missing’ angles and drawing and measuring angles.

Properties of Position and Movement In this area of numeracy we look at recognising shapes in different orientations, reflecting and translating shapes and describing position and movement. reflect symmetry left oblique clockwise quarter turn right rotate anticlockwise

We think about recognising shapes in different ORIENTATIONS. We look at REFLECTING and TRANSLATING shapes in a vertical or horizontal mirror line and begin to reflect simple shapes in a mirror line presented 45 degrees. Describe position and movement using terms such as LEFT/RIGHT, CLOCKWISE/ANTICLOCKWISE, QUARTER TURN/900 We begin to ROTATE a simple shape or object about its CENTRE or a VERTEX. In upper key stage two we start to think about translating shapes horizontally and vertically.

Measures We think about using standard and non-standard units of LENGTH, CAPACITY and MASS. This includes measuring and drawing lines to the nearest half cm and then to within 2mm. We look at reading simple SCALES initially and then move on to more complex scales. We practise standard units of TIME, we begin with reading a 12 HOUR clock and then onto 24 HOUR clocks and calculating time durations that initially don’t go over the hour but then move onto durations that go over the hour. We begin to understand PERIMETER as a measure of length and AREA as a measure of surface. Initially we might calculate area of shapes by counting squares and then we move onto using standard units such as cm2 and m2. We look at recognising ANGLES as a measure of turn and knowing that a full turn is 360o We look at CONVERSION of measure, for example cm to m and move on to solving problems involving the conversion of units.

Addition methods plus add More than the sum of altogether increase total

Addition Key vocabulary used: add, increase, total, altogether, the sum of, more than, plus. Thorough knowledge of this vocabulary is essential in KS2 because children will more likely be given worded problems to solve and they have to work out which operation to use. e.g. Peter was given £10 for his birthday and he put this into his saving account which contained £25. What is the sum of his savings now?

USING A NUMBER LINE 37 + 9 = +6 +3 37 40 46 We go to the nearest 10 and then add the rest on. For this method, the children will need a thorough knowledge of multiples of 10.

PARTITIONING – 2 digit 37 + 29 = Children are taught to partition the tens and the units. First they add the tens separately. 30 + 20 = 50 Then they add the units separately. 7 + 9 = 16 Then they add them together to get the answers: 50 + 16 = 66 So 37 + 29 = 66

PARTITIONING – 3 digit 237 + 129 = Children are taught to partition the hundreds,tens and the units. First they add the hundreds separately: 200 + 100 = 300 Then they add the tens separately: 30 + 20 = 50 Finally they add the units separately: 7 + 9 = 16 Then they add them together to get the answers: 300 + 50 + 16= 366 So 237 + 129 = 366

COLUMN ADDITION For this calculation the children would need to have an awareness of place value in order for them to place the numbers in the correct columns to carry out the calculation. T U 53 + 34 __87__ HT U 253 + 134_ __ 387_ Decimals HT U.t h 2 5 3.4 1 + 1 3 4.2 2 3 8 7. 63

COLUMN ADDITION AND CARRYING T U 5 7 + 3 4 9 1 HT U 2 5 7 + 1 6 4 4 2 1 1 1 1

USING THE INVERSE OPERATION TO CHECK ANSWERS Children are encouraged to do this in the majority of numeracy lessons in order to get into a good habit of checking answers. e.g. 37 + 9 = 46 Inverse to check: 46 – 9 = 37

Subtraction Decrease Take away Minus Deduct Less than Subtract Find the difference Subtraction

Subtract hundreds, tens and units using a number line. Year 3 Subtract hundreds, tens and units using a number line. 85 – 32 = ? 1. 53 55 85 2. 32 40 80 85 Inverse operation! - 30 - 30 - 2 - 2 + 40 + 8 + 5 18

2 56 15 - 1 3 7 67,134 17 8 - 3, 6 9 5 Column method Year 3 Year 4 H T U 2 56 15 - 1 3 7 1 2 8 Year 4 T H T U 67,134 17 8 - 3, 6 9 5 3, 7 8 3 Children need to understand how to exchange: 1 ten for 10 units (10 = 10 x 1) 1 hundred for 10 tens (100 = 10 x 10) 1 thousand for 10 hundreds (1000 = 10 x 100)

Year 5 & 6 Year 6 then move onto using hundreds of thousands Decimals Subtracting two 2 digit numbers – Mentally Subtracting two 3 digit numbers or more – Column method Year 6 then move onto using hundreds of thousands Units Decimals 38 ∙ 4 – 14 ∙ 26 = 38 ∙ 40 - 14 ∙ 46= T U ∙ t h 3 8 ∙ 34 10 - 1 4 ∙ 2 6 2 4 ∙ 1 4 Money Jack bought a television which cost £238 ∙ 49. He had £359 ∙ 00 to spend, how much money does he have left? H T U ∙ t h £ 3 5 89 ∙ 910 10 - £ 2 3 8 ∙ 4 9 £ 1 2 0 ∙ 5 1 20

Multiplication Facts In Key Stage 2 we concentrate on the key vocabulary used in these calculations. Words such as: product, groups of, lots, multiples of, times, multiply. Times tables are extremely important and must be learnt thoroughly because they will be using multiplication facts in most areas of mathematics e.g. working out division, percentages, ratio, fractions (reducing fractions), working out area etc.

EXAMPLES OF SOLVING MULTIPLICATION CALCULATIONS In early Key Stage 2, children will continue to use partitioning (splitting the number into tens and units or hundreds, tens and units) and the grid method to secure their working out. The children will progress through KS2 to use column for multiplication and must have a secure knowledge of place value in order to do this. Short Multiplication (one digit multiplier) 23 x 6 = 23 123 6 x 6 x 138 7 3 8 ¹ ¹ Long Multiplication (2 or 3 digit multiplier) 46 4 . 5 8 27 x 64 = 13 x 2 4 x 1 3 8 1 8 . 3 2 ¹ + ² ³ + 4 6 0__ ¹ 9 ¹ 1. 6 0 5 9 8 109 . 9 2 6 20 120 3 18 138 60 4 20 1200 80 1280 7 420 28 448 1728

Multiplication Worded Problems Find the product of 31 and 8 Multiply 0.4 by 10 There are 16 biscuits in a packet. There are 5 packets. How many biscuits are there? A shelf holds 15 videos. How many videos can 15 shelves hold? How many hours are there in a week? What is 5 groups of 0.6? There are 17 oak trees is a wood. There are 8 times as many beech trees. How many beech trees are there in the wood? 300 people watch a film on Thursday. The audience on Friday is 1.6 times larger. How many people watch the film on Friday?

DIVISION In Key Stage 2 we concentrate on the key vocabulary used in these calculations. Words such as: share, group, lots of, groups of, divide, multiples of, divisible. Division and multiplication are linked because one is the inverse (opposite) of the other. In order for children to be secure in division, they must know their multiplication facts thoroughly. 24

Year 3 and 4 0 x 4 = 0 1 x 4 = 4 2 x 4 = 8 3 x 4 = 12 4 x 4 = 16 5 x 4 = 20 6 x 4 = 24 7 x 4 = 28 8 x 4 = 32 9 x 4 = 36 10 x 4 = 40 11 x 4 = 44 12 x 4 = 48 12 ÷ 4 = 3 15 ÷ 4 = 3 r 3 28 ÷ 4 = 7 33 ÷ 4 = 8 r 1 40 ÷ 4 = 10 46 ÷ 4 = 11 r 2 In Year 3, division continues to be in the form of a concrete visual representation e.g. 16 sweets shared by 2 people – the children will draw 2 circles and share out the sweets evenly. 25

Year 3 and 4 0 x 6 = 0 1 x 6 = 6 2 x 6 = 12 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 6 x 6 = 36 7 x 6 = 42 8 x 6 = 48 9 x 6 = 54 10 x 6 = 60 11 x 6 = 66 12 x 6 = 72 85 ÷ 6 = 1 4 r 1 6 8 5 2 456 ÷ 6 = 7 6 6 4 5 6 4 3 In Year 3 and 4 children should learn all multiplication tables up to x by 12. 26

Year 5 and 6 0 3 8 4 3, 456 ÷ 9 = Solving problems by rounding remainders up or down. How many £12 tickets can I buy with £187? 15 remainder 7 15 tickets can be bought. 9 3, 4 536 3 7 0 1, 8 1 5 r 6 14, 526 ÷ 8 = 8 1 4, 5 2 6 94 ÷ 4 = 83 ÷ 5 = 2 3 r 2 4 Giving the remainder as a fraction 4 9 14 1 6 . 6 Giving the remainder as a decimal 5 8 33 .30 Five friends travel by coach. Their tickets cost £78 altogether. How much does one ticket cost? £ 1 5 . 6 0 5 £ 7 8 . 0 0 2 3 27

Year 5 and 6 3 4 578 ÷ 17 = 17 5 7 8 (17 x 10) 10 1 7 0 - 4 0 8 1 ( 17 x 20) 3 20 3 4 0 - 0 6 8 ( 17 x 4) 4 0 6 8 - 0 0 0 Lloyd saves £ 35 a week. How long will it take him to save £ 840? 28

HELPFUL TIPS TO HELP YOUR CHILDREN To learn multiplication and division facts To practise mental maths with every day situations e.g. going to the supermarket and working out how much items would cost altogether or working out change. Practise using a wide range of mathematical vocabulary regularly Practise telling the time on an analogue clock and must know what the time on a digital clock would be on an analogue clock To practise word problems by using the steps to solve them. To help themselves by highlighting the key words and phrases which indicate the operation they will need to use and to solve the problem. To use visual representation (drawings, jottings, diagrams) to help them work out the problem.

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