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L.O.1 To be able to count in steps of equal size.

L.O.1 To be able to count in steps of equal size.

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L.O.1 To be able to count in steps of equal size.

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  1. L.O.1 To be able to count in steps of equal size.

  2. We are going to count in even time. We’ll do 2’s, 20’s, 3’s, 30’s, 5’s, 50’s, and 0.5’s

  3. L.O.2 To be able to use closely related facts: multiplying by multiples of ten and adjusting.

  4. Mr. Buttons has 20 children in his class. He orders reward stickers for the term. He estimates that each child will earn 14 stickers – one each week. How many stickers does he need to order? Q. What calculation do we need to carry out to answer this question?

  5. The calculation is 14 x 20 Remember…..14 x 2 = 28 so 14 x 20 = 280 The 20 from the 28 has become 200 and the 8 has become 80. so 14 x 20 = 280 stickers!

  6. Q. How could we work out a similar problem if there were 21 children in the class? Q. Should we start all over again or can we use any information we already have?

  7. We can use the answer to 14 x 20 and record : 14 x 21 = ( 14 x 20 ) + ( 14 x 1 ) = 280 + 14 = 294 stickers.

  8. Q. What if there were only 19 children present? Q. How could we use the information we have to help us?

  9. We could use the answer to 14 x 20 and record: 14 x 19 = ( 14 x 20 ) – ( 14 x 1 ) = 280 - 14 = 266 stickers.

  10. Do the sums from the accompanying sheets in your book. Set out your work properly and neatly.

  11. = X 41 is the same as ( X 40 ) + You are going to insert some numbers in this equation and use calculators to see if it is true. Q. Do you think both calculations will always be the same for any number you choose.

  12. = X 41 is the same as ( X 40 ) + With your partner write a word problem for which the above would be a solution.

  13. By the end of the lesson children should be able to: Understand how to calculate in multiples of 10 and how to adjust for numbers close to multiples of 10: Multiply a number by 19 or 21, multiply it by 20 and add or subtract the number.

  14. L.O.1 To be able to count on in steps of equal sizes

  15. We are going to count in even time. We’ll do 4’s, 5’s, 6’s, and 7’s

  16. Q. How does counting in 4’s help us count in 8’s?

  17. How does counting in 3’s help us count in 6’s? • How does counting in 6’s help us count in 12’s? • How does counting in 7’s help us count in 14’s?

  18. L.O.2 To be able to use closely related facts for deriving multiplication and division facts

  19. 12 x 3 = 36 Q. Which number sentences can we derive from this one?

  20. 12 x 6 = 72 120 x 3 = 360 36 ÷ 12 = 3 36 ÷ 3 = 12 120 x 3 = 360 24 x 3 = 72 12 x 3 = 36 120 x 3 = 360 13 x 3 = 39 1.2 x 3 = 3.6 360 ÷ 30 = 12

  21. With a partner draw a web map for this number sentence. Use a ruler! Find as many associated facts as you can. 9 x 5 = 45

  22. Now try these with a partner: Prisms : 14 x 4, 16 x 5, 19 x 9, 23 x 7. Spheres: 12 x 6, 14 x 7, 15 x 9. Tetrahedra: 12 x 5, 13 x 8, 11 x 7. When you have finished check other pairs’ work. 10 minutes

  23. Now is the time to review the number strategies we have used over the last two days. 11 x 4 = 44 What closely related facts can you tell me?

  24. Q. Can you explain what you did to get the new facts? Write the following neatly in your books: 1. Adding and subtracting… 12 x 4 = 48, 11 x 4 = 44, 11 x 5 = 55 2. Making multiples of 10 11 x 40 = 440, 110 x 40 = 440, 110 x 40 = 4400. 3. Doubling 11 x 8 = 88, 22 x 4 = 88, 11 x 16 = 176 4. Making decimals 1.1 x 4 = 4.4, 11 x 0.4 = 4.4. 5. Finding inverses 44 ÷ 4 = 11, 44 ÷ 11 = 4, 176 ÷ 16 = 11

  25. For homework write four closely related facts to the number sum 13 x 6 = 78 for each of the 5 headings.

  26. By the end of the lesson children should be able to: Use related facts Halve an even number in the calculation, find the product, then double it Answer questions like: given that 14 x 11 = 154 what is 11 x 14, 154 ÷ 11 or 140 x 11

  27. L.O.1 To be able to count on and back in steps of equal size To be able to identify related number facts and calculate differences

  28. We are going to count from 0 in steps of 7 using a pendulum.

  29. We know 56 ÷ 7 = 8 Write down what other multiplication and division facts we know.

  30. We know that 7 x 8 = 56 8 x 7 = 56 56 ÷ 8 = 7 Let’s count on….

  31. Now let’s count back from 36 in 3’s If we stop at 0 write down what the next number will be?

  32. It should be - 3 Q. How far away from 6 is - 12?

  33. Copy into your books: The difference between -12 and 6 is 18. -12 -6 0 6

  34. We are going to count on and back in 4’s. As we do we shall stop to generate and write down facts and identify differences.

  35. L.O.2 To be able to use closely related facts (partitioning) and factors – when completing a mental multiplication.

  36. 15 x 12 Work with your table to find two methods to solve this problem. 3 minutes

  37. Q. Can we rewrite 15 x 12 as (15 x 10) + (15 x 2) ? Here we have partitioned the 12. Q. Can we rewrite it in another way?

  38. Loooook….. 15 x 12 = 12 x 15 so we could partition the 15 and write : 12 x 15 = (12 x 10) + (12 x 5)

  39. We can use factors to multiply. Write in your book the factor pairs for 15 and 12. 15 = 12 = 15 = 12 = 12 =

  40. Q. How can I write the calculation 15 x 12 using the information we had on the board?

  41. 15 x 12 =1 x 15 x 3 x 4 = 15 x 12 =1 x 15 x 2 x 6 = Are there any more ways? With your table write as many as you can think of. Is the answer always the same?

  42. Let’s try again: 35 x 8 Write the factor pairs for 35 and for 8 35 = 8 = 35 = 8 =

  43. 35 x 8 = 5 x 7 x 4 x 2 Q. Can we rearrange the numbers to make the calculation easier ? How?

  44. 35 x 8 = 5 x 2 x 4 x 7 = 10 x 28 = 280 Replacing each number in a multiplication calculation with its factors can often make a calculation easier.

  45. 14 x 15 Q. How can we write this calculation using the factors of 14 and 15?

  46. 14 X 15 Can be written as: 2 x 7 x 3 x 5 Q. How does this help us carry out the calculation mentally? Q. What are the important factors to look for? Why?

  47. 14 x 15 Can be written as 2 x 5 x 3 x 7 = 10 x 21 = 210 Notice……. we have put the factors 2and 5 first in our calculation!

  48. Work with a partner to answer these multiplications by using factors. Set them out sensibly. Tetrahedra: 15 x 16; 15 x 24; 15 x 26; 45 x 6 Spheres: (also) 45 x 12; 45 x 18; 35 x 12 Prisms: (also) 35 x 16; 35 x 18; 35 x 48 10 minutes

  49. 25 x 32 Q. How could we work out this calculation using: a) partitioning and b) factorising. Q. Which method do you prefer? Q. Would you use the same method every time?

  50. Remember: Partitioning is reliable and works for any pairs of numbers. Factorising works best when one of the numbers is a multiple of 5