Introduction to Multiplication Mathematics Introduction to Multiplication

The aim of this powerpoint is to teach you the 2 to 12 times tables as well as highlight some key facts and patterns. EITHER Take notes as you go along, include some examples and write down any questions and your answers (which you can mark as you go along) and complete the MyMaths lessons quoted! OR At the end of the powerpoint, printout the notes called Calc5a

What is multiplication? Instead of repeatedly adding the same amount each time we use multiplication (whose symbol is: ×). E.g. 5 + 5 + 5 + 5 = 4 lots of 5 = 4 × 5 E.g. 7 + 7 + 7 = 3 lots of 7 = 3 × 7 E.g. 2 + 2 + 2 + 2 + 2 + 2 = 6 lots of 2 = 6 × 2

Multiplication is commutative When multiplying, it doesn’t matter which order the numbers are in. E.g. 5 × 8 is worth the same as 8 × 5 This is helpful if you know your 5 times table but are not so good at your 8 times table!

Terms which tell you to multiply Words that tell you to multiply are as follows: ‘lots of’ ‘times’ ‘multiply’ ‘product’ The word ‘of’ also tells you to multiply particularly when the calculation involves fractions. Other special terms are… Double which tells you to multiply by 2 Treble or triple which tells you to multiply by 3 Quadruple which tells you to multiply by 4 Adding the suffix ‘fold’ also tells you to multiply E.g. ‘It increased tenfold’ means it was multiplied by 10.

Learning your tables The best way to learn your tables is by rote… This is repeating them out loud, over and over to yourself again and again, until your brain simply remembers them. The order we recommend you learning them is as follows: 2 then 10 then 5 THEN 3 then 4 THEN 11 then 9 THEN 6, 7, 8 and finally 12 There are lots of resources and websites that can help you to learn your tables.

Multiplication Grid BEFORE you continue with this powerpoint... Save and complete a 12 by 12 multiplication grid (a document called: Mult12.xlsx) WITHOUT using a calculator IMPORTANT: Please TIME how long it takes you to complete the whole grid. Write the date and time (along with the number 1 on the back of your grid). You will be asked to repeat this several times over the next few lessons to see if you improve your time. Continue this powerpoint only AFTER you’ve complete your timed grid…

Two Times Table Here is your 2 times table… 1 × 2 = 2 2 × 2 = 4 3 × 2 = 6 4 × 2 = 8 5 × 2 = 10 6 × 2 = 12 7 × 2 = 14 8 × 2 = 16 9 × 2 = 18 10 × 2 = 20 11 × 2 = 22 12 × 2 = 24

All the numbers in the two times table are EVEN They all end in 0, 2, 4, 6 or 8 They can all be halved exactly to give a whole number answer. If numbers end in 1, 3, 5, 7 or 9 they are ODD If you need practice at this table, work through the MyMaths lesson called 2 Times Table found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables02&taskID=1353

Ten Times Table Here is your 10 times table… 1 × 10 = 10 2 × 10 = 20 3 × 10 = 30 4 × 10 = 40 5 × 10 = 50 6 × 10 = 60 7 × 10 = 70 8 × 10 = 80 9 × 10 = 90 10 × 10 = 100 11 × 10 = 110 12 × 10 = 120

All the numbers in the ten times table are EVEN and they all end in 0. They can all be halved exactly to give a whole number answer. If you multiply ANY whole number by 10, you can write it out with a zero on the end for the answer. (Watch out – this trick does NOT work for decimals!) E.g. 512 × 10 = 5120

Five Times Table Here is your 5 times table… 1 × 5 = 5 2 × 5 = 10 3 × 5 = 15 4 × 5 = 20 5 × 5 = 25 6 × 5 = 30 7 × 5 = 35 8 × 5 = 40 9 × 5 = 45 10 × 5 = 50 11 × 5 = 55 12 × 5 = 60

All the numbers in the five times table end in 5 or 0. Some are odd and some are even. If EITHER of the numbers in the multiplication are even, then the answer will be even. If BOTH numbers in the multiplication are odd, then the answer will be odd. The numbers in the 5 times table are HALF of the numbers in the 10 times table… E.g. 8 × 5 is half of 8 × 10 (i.e. ½ of 80 ) = 40

Three Times Table Here is your 3 times table… 1 × 3 = 3 2 × 3 = 6 3 × 3 = 9 4 × 3 = 12 5 × 3 = 15 6 × 3 = 18 7 × 3 = 21 8 × 3 = 24 9 × 3 = 27 10 × 3 = 30 11 × 3 = 33 12 × 3 = 36

14 is NOT in the 3 times table so neither is 45032! Did you know that if a number is in the 3 times table, its digits will also add to a total that is in the 3 times table? E.g. Is 45032 in the 3 times table? Check: 4 + 5 + 0 + 3 + 2 = 14 14 is NOT in the 3 times table so neither is 45032! If you need practice, work through the MyMaths lesson called 3 Times Table found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables03&taskID=1357

Four Times Table Here is your 4 times table… 1 × 4 = 4 2 × 4 = 8 3 × 4 = 12 4 × 4 = 16 5 × 4 = 20 6 × 4 = 24 7 × 4 = 28 8 × 4 = 32 9 × 4 = 36 10 × 4 = 40 11 × 4 = 44 12 × 4 = 48

As 4 is an even number, ALL the numbers in the four times table are even (so they can all be halved exactly to give a whole number answer). The numbers in the 4 times table are DOUBLE the numbers in the 2 times table… E.g. 8 × 4 is double 8 × 2, i.e. double 16 = 32

Eleven Times Table Here is your 11 times table… 1 × 11 = 11 2 × 11 = 22 3 × 11 = 33 4 × 11 = 44 5 × 11 = 55 6 × 11 = 66 7 × 11 = 77 8 × 11 = 88 9 × 11 = 99 10 × 11 = 110 11 × 11 = 121 12 × 11 = 132

Did you notice that up to 9 x 11 = 99, the tens and units digits are the same? The numbers in the 11 times table are the numbers in the 10 times and 1 times tables added together… E.g. 8 × 11 is (8 × 10) + (8 × 1) 80 + 8 = 88 Ask your teacher (or read through the Calc5a notes carefully) to demonstrate the quick method for multiplying any 2-digit number by 11!

Nine Times Table Here is your 9 times table… 1 × 9 = 9 2 × 9 = 18 1 × 9 = 9 2 × 9 = 18 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 7 × 9 = 63 8 × 9 = 72 9 × 9 = 81 10 × 9 = 90 11 × 9 = 99 12 × 9 = 108

Did you notice that as the tens values increase by 1, the units values decrease by 1 and that up to ’90’, the two digits add up to 9? Like the 3 times table, when you add the digits of any number together, if their total is in the 9 times table so is the original number! The numbers in the 9 times table are the difference between the numbers in the 10 times and 1 times tables… E.g. 7 × 9 is (7 × 10) – (7 × 1) 70 – 7 = 63 Ask your teacher (or read through the Calc5a notes) to show you the ‘fingers’ method for the 9 times table!

Six Times Table Here is your 6 times table… 1 × 6 = 6 2 × 6 = 12 1 × 6 = 6 2 × 6 = 12 3 × 6 = 18 4 × 6 = 24 5 × 6 = 30 6 × 6 = 36 7 × 6 = 42 8 × 6 = 48 9 × 6 = 54 10 × 6 = 60 11 × 6 = 66 12 × 6 = 72

As 6 is an even number, ALL the numbers in the four times table are even (so they can all be halved exactly to give a whole number answer). The numbers in the 6 times table are DOUBLE the numbers in the 3 times table… E.g. 8 × 6 is double 8 × 3 double 24 = 48 If you need practice, work through the MyMaths lesson called 6 Times Table found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables06&taskID=1359

Seven Times Table Here is your 7 times table… 1 × 7 = 7 2 × 7 = 14 1 × 7 = 7 2 × 7 = 14 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35 6 × 7 = 42 7 × 7 = 49 8 × 7 = 56 9 × 7 = 63 10 × 7 = 70 11 × 7 = 77 12 × 7 = 84

I’m afraid that the 7 times table does not have any patterns in it – you will need to learn it by rote or use all your knowledge of all the other tables to work out its values. If you need practice, work through the MyMaths lesson called 7 Times Table found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables07&taskID=1361

Are you good at doubling (i. e Are you good at doubling (i.e. multiplying by 2) and can you multiply by 5 easily? The numbers in the 7 times table are either the numbers in the 5 and 2 times tables added together… E.g. 6 × 7 is (6 × 5) + (6 × 2) 30 + 12 = 42 OR the difference between the numbers in the 10 and 3 times tables… E.g. 6 × 7 is (6 × 10) – (6 × 3) 60 – 18 = 42

Eight Times Table Here is your 8 times table… 1 × 8 = 8 2 × 8 = 16 1 × 8 = 8 2 × 8 = 16 3 × 8 = 24 4 × 8 = 32 5 × 8 = 40 6 × 8 = 48 7 × 8 = 56 8 × 8 = 64 9 × 8 = 72 10 × 8 = 80 11 × 8 = 88 12 × 8 = 96

As 8 is an even number, ALL the numbers in the four times table are even (so they can all be halved exactly to give a whole number answer). The numbers in the 8 times table are DOUBLE the numbers in the 4 times table which are in turn, double the numbers in the 2 times table… E.g. 7 × 8 is double 7 × 4 which is… double double 7 × 2 double double 14  double 28 = 56 The numbers in the 8 times table are the difference between the numbers in the 10 and 2 times tables… E.g. 7 × 8 is (7 × 10) – (7 × 2) 70 – 14 = 56

Twelve Times Table Here is your 12 times table… 1 × 12 = 12 2 × 12 = 24 3 × 12 = 36 4 × 12 = 48 5 × 12 = 60 6 × 12 = 72 7 × 12 = 84 8 × 12 = 96 9 × 12 = 108 10 × 12 = 120 11 × 12 = 132 12 × 12 = 144

As 12 is an even number, ALL the numbers in the 12 times table are even (so they can all be halved exactly to give a whole number answer). The numbers in the 12 times table are DOUBLE the numbers in the 6 times table which in turn are double the numbers in the 3 times table… E.g. 8 × 12 is double 8 × 6 which is… double double 8 × 3 double double 24  double 49 = 96 The numbers in the 12 times table are the numbers in the 10 times and 2 times tables added together… E.g. 8 × 12 is (8 × 10) + (8 × 2) 80 + 16 = 96

What next? If you haven’t made any notes or copied any examples, questions and answers out during this presentation, print out the notes called Calc5a. Read through them and make sure you answer any questions. To practice your tables, in addition to the MyMaths lessons already listed throughout this powerpoint, please work through the following ones too… Mixed Tables 2,5,10 found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTablesBronze&taskID=1356 Mixed Tables 3,4,6 found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTablesSilver&taskID=1360 Mixed Tables 7,8,9 found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTablesGold&taskID=1364 Mixed Tables 2 to 12 found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTablesDiamond&taskID=1367 Now move on to the Calc5b-MentalM powerpoint