1. 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.

2. Multiplication

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

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

5. Traditional Multiplication
Eg. 3 7 5 X 2 6

6. You try it!
Try to complete as many of the following as possible using traditional multiplication in 10 minutes: 24 x x x x x x x x 405

7. Lattice Multiplication

8. You try it !
Complete as many of the following as possible using lattice multiplication. You have 10 minutes. 24 x x x x x x x 3246

9. 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

10. Grid Multiplication

11. You try it
Complete as many as possible of the following using grid multiplication. You have 10 minutes. 24 x x x x x x x x x 332

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

13. 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?

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

15. 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?

16. Activity
Complete the activity sheets at appropriate level.

17. Multiplication and Division
Decimals
Multiplication and Division

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

19. Multiplication and division

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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 ÷ 4

26. 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

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

28. 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

29. 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

30. Note that only the DENOMINATOR needs to be a whole number.
Example 3
Calculate ÷ 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

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