Objectives By the end of the lesson students will: Be able to multiply and divide whole numbers without using a calculator. Be able to multiply and divide numbers with decimals without using a calculator.

Multiplication

Multiplication of Numbers Ending in Zero E.g. 20 x 40 = 2x4 = 8 plus 2 zeros on the end = 800 500 X 60 = 5x6 = 30 plus 3 zeros = 30000 15 x 3000 = 15 X 3 = 45 plus 3 zeros = 45000

You try! Complete as many of the following in 10 minutes: 20 x 300

Traditional Multiplication Eg. 3 7 5 X 2 6

You try it! Try to complete as many of the following as possible using traditional multiplication in 10 minutes: 24 x 45 38 x 54 26 x 88 45 x 12 234 x 566 344 x 523 345 x 28 345 x 405

Lattice Multiplication http://www.youtube.com/watch?v=gS6TfWUv97I

You try it ! Complete as many of the following as possible using lattice multiplication. You have 10 minutes. 24 x 45 56 x 48 55 x 675 246 x 245 345 x 213 433 x 567 554 x 3246

Halving and Doubling E.G. Half one side and double the other to make an easier sum: 16 X 26 = 8 X 52 = 4 X 104 = 2 X 208 = 1 X 416 This system works well for multiples of 4

Grid Multiplication http://www.youtube.com/watch?v=7_2fiYzEf8A

You try it Complete as many as possible of the following using grid multiplication. You have 10 minutes. 24 x 65 772 x 34 445 x 565 556 x 224 667 x 234 892 x 428 2345 x 123 1156 x 227 7781 x 332

Weeks: Months: Years What are the multiplication factors? Weeks Months Months Year Week Year

Salary Carol earns £8.50 an hour. She works a 37 hour week. How much does Carol earn a week? How much does she earn in a month? How much does she earn in a year?

Materials A pack of 50 bricks costs £15 How much would you have to spend to buy: 150 bricks? 600 bricks? 1800 bricks?

Materials A standard house brick measures 215mm by 102.5mm by 65mm. You want to build a wall that is 10m long. How many bricks will be in each row? You have worked out that you need 30 rows of bricks, how many bricks, in total, will you need?

Activity Complete the activity sheets at appropriate level.

Multiplication and Division Decimals Multiplication and Division

Expected Knowledge… 4.5 + 3.6 6.5 - 4.4 Put these in order (largest first): 7.2, 9.01. 7.25, 21.3 Round this to the nearest tenth: 7.8542

Multiplication and division

First place decimal multiplication Sometimes it is useful to talk it through in your head For example 4 × 0.7 4 times 7 tenths equals 28 tenths So 4 × 0.7 = 2.8

Try these Talk these through in your head or with your partner then write down your answer 0.5 × 3 = 9 × 0.2 = 0.4 × 8 = Answers 1.5 1.8 3.2

You may need to write like this 3.4 × 4 = 6.3 × 8 = T U . t 3 . 4 × 1 4 1 .6 T U . t 3 . 4 × 1 4 6 T U . t 3 . 4 × 4 T U . t 6 . 3 × 2 8 5 .4 T U . t 6 . 3 × 8 T U . t 6 . 3 × 2 8 4

You may need to write like this 13.4 × 2 = 22.3 × 5 = T U . t 1 3 . 4 × 2 6 .8 T U . t 1 3 . 4 × 2 T U . t 1 3 . 4 × 2 6 8 T U . t 1 3 . 4 × 2 6 .8 T U . t 1 3 . 4 × 2 6 8 H T U . t 2 . 3 1 ×1 5 .5 H T U . t 2 . 3 × 5 H T U . t 2 . 3 ×1 5 H T U . t 2 . 3 1 ×1 5

First Place division Sometimes it helps to talk it out 0.6 ÷ 2 Six tenths divided by 2 gives 3 tenths So 0.6 ÷ 2 = 0.3 Sometimes we write it like this

Using extra zeros We should not end up with a remainder in decimals Sometimes we need to use extra zeros and keep dividing E.g. 23.5 ÷ 4

Decimals × 10 and ÷ 10 Multiplying by ten moves all the figures one place to the left Dividing by ten moves all the figures one place to the right 0.4 × 10 =i 5.6 = 10 =s 62.3 × 10 =e 23 ÷ 10 =e 277 ÷ 10 =y 34.5 ÷ 10 =o 2.2 ÷ 10 =u

How to divide by a decimal by considering equivalent calculations Dividing by a decimal How to divide by a decimal by considering equivalent calculations

Example 1 Calculate 0.36 ÷ 0.02 Step 1: Write it as a fraction 𝟎.𝟑𝟔 𝟎.𝟎𝟐 Step 1: Write it as a fraction Step 2: Find an equivalent fraction with a whole number denominator x100 𝟎.𝟑𝟔 𝟎.𝟎𝟐 = 𝟑𝟔 𝟐 x100 Step 3: Complete the division 𝟑𝟔÷𝟐=𝟏𝟖

Example 2 Calculate 0.765 ÷ 0.005 Step 1: Write it as a fraction 𝟎.𝟕𝟔𝟓 𝟎.𝟎𝟎𝟓 Step 1: Write it as a fraction Step 2: Find an equivalent fraction with a whole number denominator x1000 𝟎.𝟕𝟔𝟓 𝟎.𝟎𝟎𝟓 = 𝟕𝟔𝟓 𝟓 x1000 Step 3: Complete the division 𝟕𝟔𝟓÷𝟓=𝟏𝟓𝟑

Note that only the DENOMINATOR needs to be a whole number. Example 3 Calculate 0.0216 ÷ 0.9 𝟎.𝟎𝟐𝟏𝟔 𝟎.𝟗 Step 1: Write it as a fraction Step 2: Find an equivalent fraction with a whole number denominator x10 𝟎.𝟎𝟐𝟏𝟔 𝟎.𝟗 = 𝟎.𝟐𝟏𝟔 𝟗 x10 Step 3: Complete the division 𝟎.𝟐𝟏𝟔÷𝟗=𝟎.𝟎𝟐𝟒

Homework Complete the exam questions on negative and positive numbers and decimals Use MyMaths links on boodle to consolidate learning