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Lesson Objective Be able to add, subtract multiply and divide whole and decimal

Lesson Objective Be able to add, subtract multiply and divide whole and decimal numbers without a calculator. What is 23 × 367? Use this result to answer 2.3 x 36.7 0.23 x 3.67 2.3 x 3670 Find: a) 0.3 x 0.2 b ) 2.7 x 1.2

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Lesson Objective Be able to add, subtract multiply and divide whole and decimal

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  1. Lesson Objective Be able to add, subtract multiply and divide whole and decimal numbers without a calculator • What is 23 × 367? • Use this result to answer 2.3 x 36.7 • 0.23 x 3.67 • 2.3 x 3670 • Find: • a) 0.3 x 0.2 b) 2.7 x 1.2 • c) 3567 ÷ 4 d) 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 • 0.2 x 0.4 • 5) 0.6 x 0.7 • 83710 ÷ 2 • 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 • 0.2 x 0.4 • 5) 0.6 x 0.7 • 83710 ÷ 2 • 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 • 0.2 x 0.4 • 5) 0.6 x 0.7 • 83710 ÷ 2 • 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 • 0.2 x 0.4 • 5) 0.6 x 0.7 • 83710 ÷ 2 • 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: • 0.5 × 4 2) 0.3 × 0.2 3) 12.4 × 0.1 • 1.2 × 0.12 5) 0.4 × 0.08 6) 0.32 • 2.4 × 5.1 8) 6.2 ÷ 0.1 9) 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)

  7. 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?

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

  9. Eg. Find the reciprocal of these numbers • 6 2) 3/4 3) 0.4

  10. Find the reciprocals of these numbers: • 8 2) 2/9 3) 3/4 4) 0.8 • 5/8 6) 1/7 7) 12 8) 13/4 • 21/3 10) 0.125 11) 0.5 12) 0.3333… • 42/7 14) -2/3 15) -0.25 16) x • x – 3 18) 2.4 19) 4.25 20) -2.02 • 21) x/y 22) 1.4 23) 0.42 24) π

  11. Decimals Worksheet – Problem Solving

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

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

  14. Total so far 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 10 Number of Fractions in the sequence

  15. Will the sequence ever reach 1?

  16. Will the sequence ever reach 1? Imagine a frog 1m away from a wall. It always jumps half way to the wall. WALL 1/2 1/4 1/8 1/16 Then the distance jumped will be = 1/2 + 1/4 + 1/8 + 1/16 + ……

  17. 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. 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?

  18. 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?

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