Supporting your KS2 child s learning in multiplication and division

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1 Our school-home agreed mathematics strategies Supporting your KS2 child s learning in multiplication and division Information for Parents and Carers to dip in and out of when necessary Key vocabulary for multiplication Key vocabulary for division multiply product times share equally divide groups of lots of equal groups of lots of altogether repeated addition divisible by divided into This booklet is adapted from maths frameworks, internet resources, but mainly contains original content so that it is in line with the agreed math strategies taught at The New Forest CofE (VA) Primary School, Landford, Nomansland and Hamptworth CMorland Hyperlinks to the BBC website are valid at the time of launching this document please also use the Links section from our school website. 1

2 Multiplying What is the best way to do multiplication? When parents and grandparents were at school we were all taught long multiplication. It is still the standard efficient method, but is not the easiest for primary school children to master. At KS2 we start thinking about multiplication in terms of arrays - arrangements of objects in rows and columns. Then they move onto the Grid Multiplication method. When they are ready they will be shown long multiplication. However, it is very common for children to prefer grid method and stick to that. Neither grid or long multiplication method are any better than the other. This booklet explains each method, as well as the mental maths targets that are set to children in KS2, commonly known as times tables. Mental Maths Targets for Multiplication and Division- At KS2 your child WILL have a mental maths target for each week/term. This target may be a specific times table to learn or they may be asked to practise division facts e.g 5x2=10 so 10 5=2. Once your child has secured their rapid recall of multiplication facts and division facts for all numbers up to 10x10; they will be asked to start on targets involving multiplying/dividing by 10,100,1000. This develops to decimals and metric measurement conversions e.g. 224ml in litres (divide by 1000) = 0.224l. Other targets will follow for them. Times Tables Children start learning to count in 10 s in Y1 and next come the 2x, 5x. Each group of children will be tested in the best way for them. By the summer of Yr4 and throughout Yr 5/6 the children will be tested in mock tests of the national test (SATS). This is to make sure they have can do x quickly. Each upper KS2 child will have a booklet of rapid recall facts to work through. It looks like this: Overall Learning Objective: - to be able to rapidly recall multiplication facts (times tables) and the matching division calculation. Each child should work at your own level and challenge yourselves - it is not a competition with your classmates! To start with you will be tested on the times tables you know, to see which colour level you are for each set of facts. Once you have met a target you will receive a target achieved sticker in that box. If you have not yet met your target, but are progressing well, you will receive an on target sticker 7x 1x7 = = 1 2x7 = = 2 3x7 = = 3 4x7 = = 4 5x7 = = 5 6x7 = = 6 7x7 = = 7 8x7 = = 8 9x7 = = 7 10x7= = 10 Bronze Silver 23/9 2

3 To achieve Diamond level for each set of facts you need to correctly know all the division facts within 10 seconds and multiplication answers within 5 seconds. To achieve Gold level for each set of facts you need to correctly know all the multiplication facts in any order answering each question within 10 seconds To achieve Silver level for each level of facts you need to correctly know all the multiplication facts in a set order e.g. 1x, 2x, 3xwithin 10 seconds. To achieve Bronze level for each level of facts you need to correctly know 8/10 of the multiplication facts in a set order e.g. 1x, 2x, 3x Learning times tables is really important. However, developing the written multiplication method is important too. Getting hung up on times table accuracy when some facts are proving tricky to master, may slow down a child s progress with the method and damage their overall confidence. So when you are doing written x methods please get them to use a multiplication grid of the times table facts if it is required Multiplying and dividing by 10 and 100 PARENTS TIP Below are some illustrations from BBC Bitesize. Remember NOT to say that decimal point moves it doesn t! The digits in the number move (in the same order) left/right in the columns of the place value grid. If you divide the digits move right, left if you multiply. How many places they move depends upon the multiple of 10 that they are being multiplied or dividied by. 0 zero is called a placeholder. Using the wrong kind of language can really confuse a child! To multiply a number by 10, move the digits one place to the left, putting in a zero as a placeholder if necessary.58 x 10 = 580 3

4 To multiply a number by 100, move the digits two places to the left, putting in a zero as a placeholder if necessary. 58 x 100 = 5800 To divide a number by 10, move the digits one place to the right, putting in a zero as a placeholder if necessary = 0.43 To divide a number by 100, move the digits two places to the right, adding zeros if necessary = With numbers such as 20,40,90 or 300,600,700 multiply or divide using times table knowledge first and then by the 10 or 100. To do 24 20, you could divide 24 by 2 and then divide that answer by = = 1.2 To do 22 x 300, you could multiply 22 by 3 and then multiply that answer by x 3 = x 100 = 6600 Your child will also need to develop their speed with sums like: 33 x 20 Use the knowledge they have first: 33 x 2 THEN do x 10 = 66 x 10 = 660 = 22 x 300 is the same as doing 22x3 x 100 = 66 x 100 = To divide by numbers such as 20, divide by the 2 first and then by the = = 1.2 4

5 PARENTS TIP Please make sure you are not saying add a zero as in fact we are not adding anything! We all know that for 60x40 we do 6x4=24, but the way to phrase it is to say: because each number is ten times bigger we have to take that into account. We can count the number of placeholders 0 in the original and check that we have included them e.g Remember this booklet is to tell you how we do it at school so you can hopefully help at home. Multiplying/Dividing by 4,8,16,32 Make sure the problem is LOOKED at carefully. If the number you are being asked to multiply or divide by is 4,8,16,32 then you can double and double again (4x) OR double, double, double (8x), double, double, double, double (16x) To divide it is halve, halve ( 4) etc. This only works for numbers in the 4, 8, 16, 32, 64 sequence. Arrays We start written multiplication strategies talking about rows and columns in arrays. The children will count how many objects in the column and how many rows there are down. Initially they will need to count every object. Then they realize that they can count in multiples and get the same answer e.g.3,6,9,12,15,18,21 Obviously at this point their knowledge of multiplication facts plays a big part in increasing success with larger multiplication problems. Arrays can be used when setting out problems such as 3x7= 21. Just like the iced bun example. OR you can use arrays to help with bigger problems: e.g. 13 x 6 (10x6=60) + (3x6=18) = 78 From this the child learns to set out a grid and understands the relative sizes of the grid boxes 5

6 12x7= Partition the 12 into a 10 and 2. Mark off on the grid 10 columns and then 2 columns and count down the 7 rows x7=70 2x7=14 7 Then we add the two answers together = 84 Switching from arrays to grid multiplication once the child understands the idea of what multiplication is then the actual array can be dropped and the grid retained x7=70 2x7=14..until they eventually do not even need such large grids and can move onto smaller versions. Introducing 2digit numbers x 2 digit numbers e.g. 17x 13 x x x3 30 7x x3 21 Use chosen addition method to add the amounts together so 17x13=221 6

7 For 3 digit numbers 3 columns will be needed etc. Decimals can be handled in the same way: 28.6x14= x x x x x4 80 8x x so 28.6x14=400.4 Long multiplication the standard traditional method (or that s what they taught us when I went to school ) is taught to children in Year 5 and 6 once they have mastered the grid method and understand the process and place value of multiplication. Like in the grid method we multiply by the units and the tens separately, then add the two rows together. The following is taken from BBC Bitesize KS3: To calculate : First, multiply by 7 (units): 158 x Then add a zero on the right-hand side of the next row. This is because we want to multiply by 60 (6 tens), which is the same as multiplying by 10 and by 6. Now multiply by 6: 158 x Now add your two rows together, and write your answer. 158 x So the answer is Obviously in school we would break this teaching down further and explain that 7x8 is 56 so the six is recorded and the fifty carried over. Then 7x5 is 35 (representing 7x50 = 350 so the the fifty we carried are added together) and now four hundred has been carried over and 0 recorded under the total line for this column. 7x1=7 (representing 7x100=700) so now we add the four hundred that was carried over to this 700 and get 1100, hence the 1106 is showing under the total line. As with all these standard efficient methods that were traditionally taught, it is tricky to explain and relies upon a lot of previous knowledge and understanding of place value of number. 7

8 Dividing What is the best way to divide? Children are introduced to the concept of sharing very early on in their education and will continue to group and divide into lots well into Year 4, using visual images (grouping sweets, animals etc) and apparatus. The first written method they are introduced to is an extension of this grouping work. It will involve counting in multiples along a number line. Dividing on a number line division is taught by using the inverse operation of repeatedly counting multiples. To do 42 3 I can count on in 3s So the answer is how many groups of 3 are there in 42 = 14 groups Introducing chunking - Then the child quickly realizes that they can make bigger chunks of multiples to get towards the target number. In this case the target number is 42. It s easier and quicker to jump 3 x 10 in one jump. 3x10 3x1 3x1 3x1 3x So I took 14 chunks ( ) so 42 3 = 14 They can then begin to cope with remainders as left-overs that don t fit into these groups/chunks. Remainders means: How many 5s are there in 82? Count on in 5s on my numberline (10 lots of 5) (6 lots of 5) (2 left not enough to make a group of 5) 5x10=50 6x5=30 X X Ten 5s are 50 and six 5s are 30. On my number line that takes me to 80. I only have 2 more, so I can t do a jump of 5. I have 2 left, and I marked them with a X, not a jump. That means I have done 16 jumps of 5, with 2 left. I can call 2 left remainder 2 so 82 5 = 16 r 2 8

9 Chunking Method Year 5 and 6 will develop any grouping and chunking knowledge from the number line into a vertical method: 82 5 = Right so my target number is 82 5x10= 50 5x 6= remainder 2 As the numbers become bigger this chunking method can speed up the process from the earlier work a number line = 9x50 = 450 9x20= (246 left to go) 9x20= 180 9x 5= (21 left) 9x 2= (3 left) 97 remainder 3 By keeping the work in neat columns it makes adding up easy to do using column addition. Division (Traditional method) Short and Long Short division is sometimes referred to as the bus stop method. Along with long division they are both methods similar what they taught me when I went to school for most parents and grandparents. They are valid methods which some children prefer to use. However, they are no better or worse than the chunking method of repeated addition of multiples. You can find good descriptions on various websites including BBC Bitesize KS3 as it tends to be a method that is consolidated by children during KS3. The following has been taken from the BBC Skillwise (the adult education version of Bitesize) which is available for free and is designed for adults returning to maths after a long period away from the classroom. 9

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12 Tackling Word Problems and real life challenges a) It is always recommended that the question is read a few times first so that it is understood. Highlight any words and values/numbers that are significant. Are there several stages to the problem? b) Then the operation (s) that is needed has to be decided on. c) Calculate the answer approximately, so you know roughly what the answer should be e.g. for the calculation above 876 9= you could do 9x100 is 900 so the answer has to less than 100 but not much less as 9 x 50 is 450. d) Carry out the calculation step by step remembering to do all the stages of a multi-step problem. e) Is the answer close to your approximation? Does it MAKE SENSE? f) Check your calculation, if you can do the inverse (the opposite) to work backwards. g) Finally record the answer and make sure it is in the right unit or context for the original question. Hyperlinks to BBC material will take you through to the games section of the BBC s KS2 maths resources. Under the read section of each area of maths is a guide on how to solve problems, explanation of vocabulary. So which method should I teach my child? Multiplication and Division Key Stage 1 or catch up in KS2: The ideas of multiplication and division begin with counting patterns and contexts involving equal groups. These can be introduced wherever equal groupings are involved. At first, results will use phrases like lots of or shared between. Rhymes and stories can be used which involve counting in twos or fives ( One, two, three, four, five, once I caught a fish alive ), or counting forwards or backwards in different intervals from a given starting number. These help to develop familiarity with number patterns and sequences. Practical activities can be asking questions such as How many pencils do I need if everyone has to have 2? and I have 12 pencils to share equally among the three of you; how many will you each have? Begin by using actual objects, with the activities recorded using a mixture of pictures, tally marks and symbols. 12

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14 Years 3 and 4 It is important for children to understand, as soon as possible, the commutative rule of multiplication (i.e. 4 7 is the same as 7 4), although they do not need to know the name of the rule! This will not only halve the number of facts to be memorized, but will help them to decide on the most efficient way to calculate. Children also need to understand that every multiplication fact has two corresponding division facts, for example if they know that 5 3 = 15, they also know that 15 3 = 5 and that 15 5 = 3. Written recording of related facts will help children to make connections they will need when calculating. Written recording will focus on: gaining a good understanding of the meanings of the operations and the different ways they can be symbolised; recognising that multiplication and division are inverse (opposite) operations to each other; learning multiplication and related division facts; making connections between numbers, e.g. 36 is a multiple of 3 and of 6 and of 9 and of 12; 16 is double 8; developing and refining written methods for multiplying and dividing two-digit numbers by a single digit. Years 5 and 6 In years 5 and 6, informal written calculations for multiplication and division will depend on the numbers involved and the ways they are connected. Standard methods of multiplication and division will be developed progressively however it is most important that at all stages children understand the methods they are using. Some children will need to use a long written form of calculation for a longer period of time than others. Children should check their answers, preferably using a different method, for example the inverse operation. The written recording in years 5 and 6 will focus on: making appropriate choices from a flexible range of strategies; relating known facts to larger numbers and to decimals; establishing clear and efficient ways to record working Not all written work will involve larger numbers, as smaller numbers continue to be used to reinforce number relationships and rules that help when calculating. Your child s teacher will be able to explain which method they should be using. Your child will know their own way We hope this booklet has been useful please tell us if there is something we can do to improve it. If in doubt please ASK! 14