mathematics multiplication – mental methods. the aim of this powerpoint is to teach you further...

MATHEMATICSMultiplication – Mental Methods

• The aim of this powerpoint is to teach you further techniques for multiplying numbers mentally.

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 work through the MyMaths lessons listed.

OR

• At the end of the powerpoint, printout the notes called Calc5b

Doubling• Start with the units and move to the left.• Double each digit but be careful, if any answer comes to

10 or more you will have to carry 1 and add that on to the next doubled digit.

• E.g. 2 × 134 double 4 (units) 8

double 3 (tens) 6

double 1 (hundred) 2 = 268

• E.g. 248 × 2 double 8 (units) 16 6 carry 1

double 4 (tens) 8 + carry 1 9

double 2 (hundreds) 4 = 496

Practice Doubling

• Work through pages 1 to 5 of the MyMaths lesson called Doubling and Halving found at:

• http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/doubles&taskID=1023

• If you need more practice, use the doubling mix ‘n’ match cards or the doubling double-sided cards – you can find the document to save, print out and cut up on the VLE website.

Multiplying by 4 or by 8• If you are good at doubling then you can use this to help

to multiply by 4 or multiply by 8!

• Multiplying by 4 is doubling TWICE• E.g. 231 × 4

231 doubled 462 doubled = 924

• Multiplying by 8 is doubling THRICE (i.e. three times)• E.g. 23 × 8

23 doubled 46 doubled 92 doubled = 184

Practice Multiplying by 4 and 8

• Work through the following MyMaths lessons:

• 4 Times Table found at:• http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables04&taskID=1358

• 8 Times Table found at:• http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables08&taskID=1362

• If you need more practice, complete the ‘Multiplying by 4’ and the ‘Multiplying by 8’ spider diagram sheets – you can find these documents to save/print out on the VLE website.

Multiplying by 10 – Whole Numbers• This trick ONLY works for whole numbers NOT decimals!• Put a zero on the end of the number you are multiplying

by 10.

• E.g. 8 × 10 = 80

• E.g. 52 × 10 = 520

• E.g. 10 × 704 = 7040

Multiplying by 100 – Whole Numbers• This trick ONLY works for whole numbers NOT decimals!• Put two zeros on the end of the number you are

multiplying by 100.

• E.g. 8 × 100 = 800

• E.g. 52 × 100 = 5200

• E.g. 100 × 704 = 70400

Multiplying any number by 10, 100…• When we are multiplying by 10, we are increasing every part of

the number tenfold which moves each digit one column to the left (to see this in whole numbers you have to put a zero in the units column!)

• When we are multiplying by 100, we are increasing every part of the number a hundredfold which moves each digit two columns to the left (which is seen in whole numbers by putting two zeros in the tens and units columns!).

• When we are multiplying by any power of 10 (e.g. 1000, 10000, 100000 and so on), however many zeros comes after the 1 tells you by how many columns the digits in the original value will move to the left.

Effect on Integers & Decimals• The effect of moving digits in whole numbers to the left

means that the columns on the right become empty and we have to write extra zeros on the end.

• E.g. 73 × 1000 =

• With decimals the digits simply move to the left (or the decimal point looks like it moves to the right!).

• E.g. 0.476 × 100 =

TTh Th H T U 7 3 (original value) 7 3 0 (x 10) 7 3 0 0 (x 100) 7 3 0 0 0 (x 1000)

3 zeros after the 1 so move digits 3 columns to the left

73000

H T U . tth hth

0 . 4 7 6 (original value) 4 . 7 6 (x 10) 4 7 . 6 (x 100)2 zeros after the 1 so move

digits 2 columns to the left

47.6

Practice Multiplying by 10 and 100

• Work through pages 1 to 5 of the MyMaths lesson called Multiplying by 10 and 100 found at:

• http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/multiplyby10&taskID=1027

• Work through pages 1 to 3 of the MyMaths lesson called Multiply Decimals by 10 and 100 found at:

• http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=decimals/decimalx10x100&taskID=1013

• Save and complete the ByTen-S0a.xlsx worksheet.

Multiplying by 20• This trick ONLY works for whole numbers NOT decimals!• Double the value then put a zero on the end of the

number.

• E.g. 8 × 20 double 8 16 160

• E.g. 52 × 20 double 52 104 1040

• E.g. 20 × 704 double 704 1408 14080

Multiplying by 5 or 50 • To multiply by 5…• Multiply the value by 10 first (by putting a zero on the end) then halve

that answer OR halve the value then put a zero on the end.

• E.g. 42 × 5 ½ of 420 = 210

• E.g. 5 × 320 ½ of 320 160 1600

• To multiply by 50…• Multiply the value by 100 first (by putting two zeros on the end) then

halve that answer OR halve the value then put two zeros on the end.

• E.g. 42 × 50 ½ of 4200 = 2100

• E.g. 50 × 320 ½ of 320 160 16000

Practice Multiplying by 20, 5 or 50

• Work through the MyMaths lesson called 5 Times Table found at:

• http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables05&taskID=1354

• Use the ‘Multiples of 50’ mix ‘n’ match cards or the double-sided cards.

• Save and complete the worksheet called 5and20.xlsx

Multiplying by 11• Multiply the value by 10 first (by putting a zero on the end) then

add itself on to that answer.

• E.g. 42 × 11 420 + 42 = 462

• E.g. 11 × 320 3200 + 320 = 3520

• OR if multiplying 11 by any 2-digit number• Split the two digits and put their total in-between BUT if their

total is 10 or more, you must carry the one on…

• E.g. 42 × 11 4 2 462 (4 + 2 = 6)

• E.g. 11 × 39 3 9 429 (3 + 9 = 1 2)

Practice Multiplying by 11

• You could practice by working through the MyMaths lesson called 11 Times Table found at:

• http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables11&taskID=1365

• You could practice by playing ‘Beat the Master’ against members of your family. Instructions can be found on the VLE

• Save and complete the worksheet called 11Times.xlsx

Multiplying by 9

• Remember that the 9 times table is the difference between the 10 and 1 times tables so…

• Multiply the value by 10 first (by putting a zero on the end) then subtract itself from that answer.

• E.g. 42 × 9 420 – 42 = 378

• E.g. 9 × 320 3200 – 320 = 2880

Practice Multiplying by 9

• You could practice by working through the MyMaths lesson called 9 Times Table found at:

• http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables09&taskID=1363

• You could complete the ‘Trail 9’ grid – you can find the document to save / print out on the VLE website.

• Save and complete the worksheet called 9Times.xlsx

Multiplying by 12 or 8• To multiply by 12 add the 10 and 2 times tables together by…• Multiplying the value by 10 first (by putting a zero on the end) then

adding double itself on to that answer.

• E.g. 42 × 12 420 + 82 = 502

• E.g. 12 × 320 3200 + 640 = 3840

• To multiply by 8 subtract the 2 from the 10 times table by…• Multiplying the value by 10 first (by putting a zero on the end) then

taking double itself off that answer.

• E.g. 42 × 8 420 – 82 = 338

• E.g. 8 × 320 3200 – 640 = 2560

Practice Multiplying by 12

• You could practice by working through the MyMaths lesson called 12 Times Table found at:

• http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=MultiplyDivide/timesTables12&taskID=1366

• You could complete the ‘Trail 12’ grid – you can find the document to save / print out on the VLE website.

• Save and complete the worksheet called 12Times.xlsx

Equivalent Calculations• Equivalent multiplication calculations can be found by

multiplying one of the values and dividing the other value by the same amount. However, you should only do this if it is going to make the equivalent calculation easier to do!

• I find it easier to multiply by 2 or 10 or 100 so…

• E.g. 25 × 16 E.g. 4 × 26

100 × 4 = 400 2 × 52 = 104

• Save and complete the worksheet called EquivM1.xlsx

× 4 ÷ 4 ÷ 2 × 2

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 Calc5b. Read through them and make sure you answer any questions.

• Please ensure you have worked through all the MyMaths lessons identified throughout this powerpoint and for further practice use the additional resources (such as mix and match cards etc.) also listed.

• Please ensure you have saved and completed all the worksheets listed (and emailed them to the VLE teacher).

• Now move on to the Calc7a-IntroD powerpoint