Year 5 Term 2 Unit 9 Day 1

L.O.1 To be able to add and subtract any pair of two-digit numbers

30+40 Write the answer in your books.

Q. How did you work that out? We can get the answer using: the number fact 3 + 4 and then applying place value x 10 We can use a similar method for subtraction LOOK…. 50 – 20 The number fact is 5 – 2 And the place value is x 10

Try these using the same method where possible: 80 – 50 70 + 40 34 + 54 75 – 40 46 + 52 58 – 25 80+ 40

In your book write synonyms for: + -

L.O.2 To be able to add or subtract the nearest multiple of 10 ,100 or 1000 then adjust.

Round these numbers: 1. To the nearest 10 34 27 78 66 55 34 27 78 66 55 2. To the nearest 100 167 761 354 855 21 3. To the nearest 1000 2435 7328 4982 6525 7721 Write in your books how much we had to adjust each number by.

We can use rounding as a strategy for addition and subtraction. 93 – 69 Thus: What multiple of 10 is nearest to 69? What is 93 – 70? Have we subtracted more or less than 69? How should we adjust the answer to make it correct?

This can be shown on a number line. Our sum is: 93 – 69 = ( 93 – 70 ) + 1 = 23 + 1 = 24 This can be shown on a number line. +1 -70 23 24 93

This can be shown on a number line. Our sum is now: 93 – 69 = ( 93 – 70 ) + 1 = 23 + 1 = 24 This can be shown on a number line. -70 + 1 23 24 93

We are going to try this: 368 + 51. 368 + 51 = (368 + 50) + 1 368 + 51 = (368 + 50) + 1 = 418 + 1 = 419 Draw the number line in your books. +50 +1 368 418 419

Try this: 286 – 97 = (286 – 100) + 3 = 186 + 3 = 189 We need a volunteer to draw the number line!

Try this: 5250 – 1998 = (5250 – 2000) + 2 = 3250 + 2 = 3252 We need a volunteer to draw the number line

Try this 458 + 199 = (458 + 200) – 1 = 658 – 1 = 657 We need a volunteer to draw the number line

include the written sum and the number line. Do these : include the written sum and the number line. All groups: + Spheres + Prisms 289 – 98 756 – 197 2348 – 1996 645 + 69 572 + 196 5932 + 2995 584 – 97 615 - 498 3688 - 1994 1267 + 88 1546 + 997 5482 + 1988

Look at these: 73 + 26 182 – 95 6003 – 5994 56 – 29 73 + 200 583 – 71 For which of these would you use the rounding and adjusting strategy? Q . How would you tackle the other questions?

By the end of the lesson the children should be able to: For example, work out mentally that: 274 + 96 = 370 as 274 + 100 – 4 = 374 – 4 = 370 and 4005 – 1997 = 2008 as 4005 – 2000 + 3

Year 5 Term 2 Unit 9 Day 2

L.O.1 To be able to recall addition and subtraction facts for each number to 20 and extending to multiples of 10.

Write the answer in your books to the following: 15 – 7 12 + 8 9 + 8 3 + 4 7 + 6 11 + 11 14 – 5 12 – 4 6 + 13 8 – 5 17 + 6 19 – 10

Q. What strategies can we use for quick recall? We can : 1. double and subtract or add e.g. 6 + 7 = 6 + 6 +1 2. round up or down and subtract or add the difference e.g. 8 + 12 = 8 + 10 + 2 Subtract even numbers by halving it and subtracting it twice e.g. 16 – 4 = 16 – 2 - 2

We can use the same strategies with multiples of 10. Do these in your book: 70 + 60 10 +20 140 – 50 190 – 100 Can you see the similarities?

Q. Did you see the similarities? Q. What strategies did you use?

L.O.2 To be able to add several numbers.

40 + 90 + 60 + 50 Copy these numbers into your book as they are here and calculate the total. Q. How did you find the total?

To find the total we can; 1. look for numbers that sum 100 60 + 40 2. start with the largest number first 90 + 60 +

Q. What strategies did you use? Now try these: 60 + 70 + 20 + 80 + 20 + 30 + 80 + 70 50 + 60 + 30 + 80 + 40 + 90 + 40 + 50 Q. What strategies did you use?

Look at this calculation: 63 + 15 + 35 Q. What strategies do you use?

To find the total we can; 1. look for unit pairs that make 10 35 + 15 2. start with the largest number first 63 + 35

Copy these numbers into your book and add them up. 1 + 2 + 3 + 4 + 5 + 5+ 6 + 7 + 8 + 9 Copy these numbers into your book and add them up. Remember to use pairing strategy.

The answer is 50.

Q. How many pairs of numbers sum to 10? 1 + 2 + 3 + 4 + 5 + 5+ 6 + 7 + 8 + 9 = 5 X 10

Look at this calculation: 4 + 4 + 3 + 5 Q. What multiplication is this equivalent to?

To find the answer we must first do the calculation using our addition strategies. 4 + 4 + 3 + 5 = 16 16 is the equivalent to 4 X 4 Q Who got this right?

Q. How can we represent the following as a multiplication? 18 + 20 + 22

To find the answer we must first do the calculation using our addition strategies. 18 + 20 + 22 When we look at the numbers we can see that 18 and 22 make 40 ; a multiple of 20 20 is also a multiple of 20 That means that there are 3 multiples of 20 so 60 is the equivalent to 20 X 3

Let’s look at this one 48 + 49 + 50 + 51 + 52 Q. What strategies could we use to find the sum?

To find the total we can; 1. look for numbers that sum 100 48 +52 2. start with the largest number first 52 + 51 + 3. look for multiples 50 4. look for unit pairs of 10 51 + 49

Showing your method, do the following in your books: 18 + 19 + 20 + 21 + 22 26 + 28 + 30 + 32 + 34 64 + 66 + 70 + 74 + 76 83 + 85 + 90 + 97 + 95

Q. What strategies did you use to find the answers? Q. Which strategy do you think is best for this calculation? 18 + 19 + 20 + 21 + 22

Copy this into your books 20 2 49 23 86 17 64 50 60 38 21 7 40 16 62 42

In your books write down sets of numbers from the table that you can total using all the addition strategies we have looked at today.

Year 5 Term 2 Unit 9 Day 3

L.O.1 To be able to add near doubles including decimals.

Look at this calculation 35 + 36 Q What strategy could you use to find the sum? Look at the numbers, they are near doubles of each other.

To calculate the sum we simply have to double one of the numbers and adjust the answer. E.g. 35 + 36 = (35 x 2) +1 70 + 1 = 71 OR 35 + 36 = (36 x 2) -1 72 – 1 = 71

Try these using one or all of the near doubling strategies: 41 + 42 = 85 + 82 = 53 + 50 = 11 + 15 =

17 + 16 and 1.7 + 1.6 Now work out these calculations Q. How did you work them out?

To find the sum of 16 + 17 we double and adjust the numbers. 16 x 2 = 32 32 + 1 = 33 If 16 is the same as 1.6 x 10 and 17 is the same as 1.7 Q. How can this help us work out 1.6 + 1.7?

The answer is simple. If 16 +17 = 33 then 1.6 + 1.7 = 3.3 We have divided 33 by 10 OR moved the decimal point one place to the left.

In your books work out the following using the same method 12 + 13 1.2 + 1.3 25 + 24 2.5 +2.4 44 + 43 4.4 + 4.3 TiP : do the whole numbers first

The answers are: 25 2.5 49 4.9 87 8.7

L.O.2 To be able to add several numbers using a variety of strategies for mental addition. To solve mathematical problems or puzzles, recognise and explain patterns and relationships.

Look at this table 13 18 11 12 14 16 17 10 15

What is the total for this column and this row? 13 18 11 12 14 16 17 10 15

What do you notice about the totals? 13 18 11 12 14 16 17 10 15

Yes. They all add up to 42!! 13 18 11 12 14 16 17 10 15

Are there any other patterns? 13 18 11 12 14 16 17 10 15

Look at these numbers 13 18 11 12 14 16 17 10 15

This known as a 3 x 3 magic square. 13 18 11 12 14 16 17 10 15

Q What do you think would happen if we subtract 7 from each number? Would it still be a magic square?

Let’s check. What is the ‘magic’ total for the square now? 6 11 4 5 7 9 10 3 8

Yes. It is 21.How could we have predicted this happening? 6 11 4 5 7 9 10 3 8

Would the square still be magic if we aded or subtracted ANY number from each square? 13 18 11 12 14 16 17 10 15

It would have to be the same number from each square. 13 18 11 12 14 16 17 10 15

Let’s look at the number patterns with some different numbers.

Q What do you notice about the answers we have found each square that we have tried?

Each answer we have had has been a multiple of 3! 13 18 11 12 14 16 17 10 15

The total we found (42) is 14 X 3. 13 18 11 12 14 16 17 10 15

Remember when we subtracted 7 from each number Remember when we subtracted 7 from each number? The total (21) is 3 x 7…MAGIC 6 11 4 5 7 9 10 3 8

What is the sum of the first row and column? 17 10 15 4 14 5 16 11 8 19 6 13 7 12 9 18

It is 46. Is this a multiple of 4? 17 10 15 4 14 5 16 11 8 19 6 13 7 12 9 18

No. It isn’t. 17 10 15 4 14 5 16 11 8 19 6 13 7 12 9 18

Do all the rows and columns total 46? 17 10 15 4 14 5 16 11 8 19 6 13 7 12 9 18

Yes they do. Can you find any sets of 4 numbers that total 46? 17 10 15 4 14 5 16 11 8 19 6 13 7 12 9 18

Let’s have a look at some. 17 10 15 4 14 5 16 11 8 19 6 13 7 12 9 18

This is made up of 4 magic squares put together. 17 10 15 4 14 5 16 11 8 19 6 13 7 12 9 18

Do these numbers add up to 46? 17 10 15 4 14 5 16 11 8 19 6 13 7 12 9 18

Q Will every diagonal of 4 total 46? On your on sheet highlight 4 diagonals and test.

Let’s look at some of your answers. 17 10 15 4 14 5 16 11 8 19 6 13 7 12 9 18

L.O.2 To be able to add several numbers using a variety of strategies for mental addition. To solve mathematical problems or puzzles, recognise and explain patterns and relationships.