1. Lesson Objective Be able to add, subtract multiply and divide whole and decimal numbers without a calculator 1)What is 23 × 367? Use this result to answer 2.3 x 36.7 0.23 x 3.67 2.3 x 3670 2)Find: a) 0.3 x 0.2b) 2.7 x 1.2 c) 3567 ÷ 4d) 4837 ÷ 12 e) 23.6 ÷ 0.03

2. Given that 12.4 × 4.3 = 53.32 Find the value of: a) 124 × 4.3 b) 62 × 8.6 c) 53.32 ÷ 31 d) 124 × 430

3. GROUP A Challenge: 15 mins How many can you answer correctly? 1) 12 x 17 2) 23 x 345 3) 1.2 x 0.3 4) 0.2 x 0.4 5) 0.6 x 0.7 6) 83710 ÷ 2 7) 2364 ÷ 4 8) 17622 ÷ 3 9) 487 ÷ 11 10) 8361 ÷ 7 11) 0.6 ÷ 0.3 12) 12 ÷ 0.2 13) 20 ÷ 0.15 14) 0.9 ÷ 0.15 15) 1.2 ÷ 0.01 16) 24 x 0.12 17) 0.5 x 19 18) 2.5 ÷ 2.5 19) 0.7 ÷ 20 20) 1.4 ÷ 30 GROUP B Challenge: 15 mins How many can you answer correctly? 1) 12 x 17 2) 23 x 345 3) 1.2 x 0.3 4) 0.2 x 0.4 5) 0.6 x 0.7 6) 83710 ÷ 2 7) 2364 ÷ 4 8) 17622 ÷ 3 9) 487 ÷ 11 10) 8361 ÷ 7 11) 0.6 ÷ 0.3 12) 12 ÷ 0.2 13) 20 ÷ 0.15 14) 0.9 ÷ 0.15 15) 1.2 ÷ 0.01 16) 24 x 0.12 17) 0.5 x 19 18) 2.5 ÷ 2.5 19) 0.7 ÷ 20 20) 1.4 ÷ 30 GROUP C Challenge: 15 mins How many can you answer correctly? 1) 12 x 17 2) 23 x 345 3) 1.2 x 0.3 4) 0.2 x 0.4 5) 0.6 x 0.7 6) 83710 ÷ 2 7) 2364 ÷ 4 8) 17622 ÷ 3 9) 487 ÷ 11 10) 8361 ÷ 7 11) 0.6 ÷ 0.3 12) 12 ÷ 0.2 13) 20 ÷ 0.15 14) 0.9 ÷ 0.15 15) 1.2 ÷ 0.01 16) 24 x 0.12 17) 0.5 x 19 18) 2.5 ÷ 2.5 19) 0.7 ÷ 20 20) 1.4 ÷ 30 GROUP D Challenge: 15 mins How many can you answer correctly? 1) 12 x 17 2) 23 x 345 3) 1.2 x 0.3 4) 0.2 x 0.4 5) 0.6 x 0.7 6) 83710 ÷ 2 7) 2364 ÷ 4 8) 17622 ÷ 3 9) 487 ÷ 11 10) 8361 ÷ 7 11) 0.6 ÷ 0.3 12) 12 ÷ 0.2 13) 20 ÷ 0.15 14) 0.9 ÷ 0.15 15) 1.2 ÷ 0.01 16) 24 x 0.12 17) 0.5 x 19 18) 2.5 ÷ 2.5 19) 0.7 ÷ 20 20) 1.4 ÷ 30

4. When multiplying: Eg 2.5 × 0.05 When dividing: Eg 0.62 ÷ 0.05

5. Do these without a calculator: 1) 0.5 × 42) 0.3 × 0.23) 12.4 × 0.1 4) 1.2 × 0.125) 0.4 × 0.086) 0.3 2 7) 2.4 × 5.18) 6.2 ÷ 0.19) 0.4 ÷ 0.2 10) 1.2 ÷ 0.4 11) 24 ÷ 0.45 12) 0.06 ÷ 0.30 13) 12.4 ÷ 0.25 14) 0.2 ÷ 0.02 15) 4.32 ÷ 0.4

6. A supermarket sells jars of coffee of the same brand in two different sizes. Which jar gives the better value for money? You must show your working. Answer................................................. (Total 3 marks)

8. Being a nice, kind maths teacher Mr B decides to give his Year 10 class some sweets: In the class there are 16 girls and 10 boys. Mr B gives the girls 23 sweets and the boys 15 sweets, who gets the best deal? Show your working!! How many different ways can you answer this question?

9. Lesson Objective: Know how to find the reciprocal of a number

10. Eg. Find the reciprocal of these numbers 1)62) 3 / 4 3) 0.4

11. Find the reciprocals of these numbers: 1) 82) 2 / 9 3) 3 / 4 4) 0.8 5) 5 / 8 6) 1 / 7 7) 128) 1 3 / 4 9) 2 1 / 3 10) 0.125 11) 0.5 12) 0.3333… 13) 4 2 / 7 14) - 2 / 3 15) -0.25 16) x 17) x – 3 18) 2.4 19) 4.25 20) -2.02 21) x / y 22) 1.4 23) 0.42 24) π

12. Decimals Worksheet – Problem Solving

13. Lesson Objective: Learn about limiting sequences and practise our Fraction and Decimal skills.

14. Limiting Sequences Consider the sequence: 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ………………… What will this add up to?

15. 012345 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 6 789 10 Number of Fractions in the sequence Total so far Number of Fractions in the sequence so far Total 10.5 20.75 30.9375 40.96875 50.984375 60.992188 70.996094 80.998047 90.99023 100.999512

16. Will the sequence ever reach 1?

17. Imagine a frog 1m away from a wall. It always jumps half way to the wall. 1/21/2 1/41/4 1/81/8 1 / 16 Then the distance jumped will be = 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + …… WALL

18. What about: 1 / 3 + 1 / 9 + 1 / 27 + 1 / 81 + ………………… Or 1 / 4 + 1 / 16 + 1 / 64 + 1 / 256 + ………………… What would the sequence look like that starts with 1 / 5 ? Can you find a general result for any starting fraction in the form 1 /n ? In general we say that: 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ………………… has a limiting value of 1. Meaning that it gets closer to 1 as the number of terms in the sequence increases.

19. Litou’s Mean Value Theorem Start with 2 numbers. Eg 15 and 9 We are going to use these to generate a sequence. The 10 and the 6 are the first two numbers in the sequence. 15, 9,....., …., …., …., …., …., …., …. Find the next number in the sequence by calculating the mean of the previous 2. Calculate the next eight numbers in the sequence. You may write them as decimals to 2 d.p. What happens to the sequence? Is there any way of predicting this result? Try Starting with 2 different numbers does your result still work?