Recording Multiplication Calculations A guide to the progression and written methods for Multiplication used at: Verwood CE VA First School Trinity First School Hillside First School Emmanuel CE VA Middle School

The following is designed to help pupils and parents understand the written methods for multiplication used in all of the First Schools and onward through the Middle School in Verwood at Key Stage 1 and Key Stage 2 (from reception to year 6). It is important to realise that the methods shown in this document might not be what parents were taught while they were at school, but they are common methods used today in the teaching of Mathematics. This presentation starts off with the methods taught in reception and year 1 and progresses through to the multiplication methods and some examples of multiplication problems that your child can expect to come across in years 5 and 6.

Early multiplication (R) Begin to count in 2’s Counting pairs of objects such as pairs of socks and shoes Using vocabulary lots of, groups of, sets of.

Early multiplication (1) Counting in steps of 2’s, 5’s and 10’s. Including groups of objects and money. How many spots are there altogether? Doubling numbers up to 10. 2+2=4 7+7=14

Early multiplication (1) Use sets of objects. 2 sets of 3 Begin to use repeated addition including using a number line. 3+3+3+3=12 +3 +3 +3 +3 Vocabulary: Double, multiply by, times, lots of, sets of.

Early multiplication (2) Use arrays including using counters. 3 Counting in 3’s and 4’s Chanting tables. 2’s, 3’s, 4’s, 5’s and 10’s Fact families e.g. 3x5=15, 5x3=15, 15÷3 =5, 15÷5 =3 or 4x5=20, 5x4=20, 20÷4 =5, 20÷5 =4

Once a pupil has grasped the basics, they are ready to move on to a more formal written method for multiplication. These methods are taught as a progression and the pupil will need to have an understanding of place value in order to progress

Grid Method – involving a single digit number This relies on knowledge of times tables and an ability to multiply in tens. The 2 digit number is partitioned and the multiplication is completed in two steps as follows: E.g 23 x 8 x 20 3 8 Pupils need to calculate: 8 x 20 = 160 and 8 x 3 = 24 and fill them into the grid as shown 160 24 Finally they need to add the numbers in the grid to get the final answer (see addition powerpoint for method) 160 + 24 = 184 Answer = 184

The Grid Method then progresses to multiplications involving two 2-digit numbers e.g 45 x 16 = x 40 5 10 6 The grid is set out similsrly to the previous question with each number partitioned according to its place value 400 50 240 30 Insert each multiplication into the grid like before 400 240 50 30 720 1 Finally, add all the numbers inside the grid together to get the answer ANSWER = 720 +

Following the grid method, pupils would progress on to formal long multiplication with a single digit number. This again requires a good grasp of times tables and place value E.g 46 x 7 4 6 x 7 2 4 First you multiply the 7 by the 6 (the digit furthest to the right) which gives 42. You put the 2 in the units column and carry the ‘4’ over to the next column and put it at the bottom 3 2 Next, you multiply the 7 by the 4 to get 28 and then remember to add on the ‘4’ you carried across to get 32. You write this in the tens and hundreds column ANSWER = 322

Following this pupils would progress on to long Multiplication with 2 digit numbers. A knowledge of place value is again crucial for this. e.g 57 x 36 Like before start by multiplying the 6 by the 7 and then the 5 – remembering to carry across any digits (marked in blue). This gives 342 5 7 x 3 6 3 4 2 1 7 1 0 2 0 5 2 4 Before you multiply by the ‘3’ you need to remember that it is in the ‘tens’ column so you need to put a ‘0’ (in red) on the end of the next row down before you start your multiplying. 2 1 Then you multiply the 3 by the 7 and then the 5 like before to get 1710 Finally you add the 342 and the 1710 using column addition to get the answer 2052

Once pupils are able to multiply whole numbers using these methods they will progress on to multiplying decimals. It is possible to multiply decimals using either the grid method or the formal long multiplication method. In our experience we have found that some pupils will struggle with these methods when using decimals so we encourage the use of the Geolosia method (sometimes called Napiers bones). Chances are, as a parent, you may not have seen it before. The good thing about this method is that it is virtually identical no matter what type of numbers you are multiplying

Using Geolosia to multiply two whole numbers together e. g 46 x 78 Set out the digits as shown with a box in the middle 4 6 x 7 8 Next, put horizontal and vertical lines inside the box as shown 2 4 8 2 3 4 2 8 Next, put in diagonal lines as shown – always top right to bottom left – one small box at a time – extend slightly at the ends Now the grid is set up (this is the same for all geolosia questions) you now need to fill in the boxes by doing times tables as shown – always write the tens unit in the top left triangle of the box and the unit in the bottom right 6 x 7 = 42 and 4 x 7 = 28 4 x 8 = 32 and 6 x 8 = 48

The final step is to add all the numbers inside the box in their diagonal rows. 7 8 Always start at the bottom right corner There is only ever one number here so it simply drops in to place as shown 2 4 3 1 8 2 3 4 5 2 8 In the next diagonal row you add together the 2, 4 and 2 which gives 8 as shown 8 8 In the next column up you add together the 4, 8 and 3 as shown to get 15 You write the 5 as shown and carry the tens unit up to the next coulmn as shown Next you add the 2 to the 1 that you carried over to get 3 as shown Finally you read round the digits on the outside to get the answer as shown. ANSWER = 3588

Using Geolosia to multiply a whole number and a decimal together e. g 4.6 x 78 . 4 6 x 7 8 It doesn’t matter if you put the decimal number at the top or the side of the grid – you set it up as before and do the question as before 3 2 4 8 2 3 4 5 2 . 8 8 8 For this type of question you simply need to decide where to put the decimal at the end If the decimal number is at the TOP of the grid as shown then the decimal point simply ‘drops like a stone’ in to place as shown This gives us the answer 358.8

e. g 4.6 x 78 7 8 x 4 6 2 3 . 3 8 2 4 4 5 If you put the decimal number at the side instead then the decimal point ‘rolls down the hill’ in to place instead as shown 2 . 8 8 8 This still gives us the answer 358.8

The final type of question is when you multiply two decimal numbers together e. g 4.6 x 7.8 . Similar to all the other questions, the set up and method is the same, its only at the end when you need to figure out where to put the decimal point in the answer is there something new to do 4 6 x 7 8 3 2 4 . 8 2 3 4 . 5 2 8 8 8 The decimal point at the side moves across and the one at the top moves down until they meet. Then you follow the diagonal grid line from that point to see where you put the decimal in the answer This gives us the answer 35.88