Yes, adding or subtracting the same number from each entry in a magic square will preserve the magic property, where all rows, columns and diagonals sum to the same number. This is because adding or subtracting a constant to each term in a sum does not change the total. So the underlying structure and relationships that make the square "magic" are maintained regardless of what constant is added or subtracted from each entry.

1. Year 7 Term 1
Room 1

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

3. 30+40
Write the answer in your books.

4. 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

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

6. In your book write synonyms for:
+ -

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

8. Round these numbers:
1. To the nearest 10
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.

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

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

11. 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

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

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

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

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

16. 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

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

18. 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

19. Year 5 Term 2 Unit 9
Day 2

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

21. 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

22. 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
3. Subtract even numbers by halving it and
subtracting it twice
e.g. 16 – 4 = 16 – 2 - 2

23. 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?

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

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

26. 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?

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

28. 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?

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

30. 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

31. 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.

32. The answer is 50.

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

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

35. 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?

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

37. 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

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

39. 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

40. 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

41. 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

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

43. 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.

44. Year 5 Term 2 Unit 9
Day 3

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

46. 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.

47. 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

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

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

50. 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?

51. 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.

52. 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

53. The answers are:
25 2.5
49 4.9
87 8.7

54. 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.

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

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

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

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

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

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

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

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

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

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

65. 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

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

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

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

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

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

71. 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

72. 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

73. 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

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

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

76. 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

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

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

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

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

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

82. 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.