1. Patterns and Algebra Balancing Number Sentences
Outcome
PAS3.1b Records, analyses and describes geometric and number patterns that involve one operation using tables and words
Indicators
completes number sentences that involve more than one operation by calculating missing values.
balances number sentences.
identifies the equal sign to mean “the same as” as opposed to an instruction to complete a sum.
Board of Studies NSW (2002). Mathematics K-6: Syllabus. Sydney: BOS

2. What can I put in the basket to make the equal arm balance level?12
10 + 2
3 x 4
24 ÷ 2
5 x 2

3. 12
10 + 2

4. 12
10 + 2
24 x 1

5. Well done! Both sides equal 12. You made the balance level!
10 + 2
24 x 1
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Next Question

6. 12
3 x 4

7. 12
3 x 4
24 x 1

8. Well done! Both sides equal 12. You made the balance level!
3 x 4
24 x 1
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9. 12
24 ÷ 2

10. 12
24 ÷ 2
24 x 1

11. Well done! Both sides equal 12. You made the balance level!
24 ÷ 2
24 x 1
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12. 12
5 x 2

13. 5 x 2 12

14. 12
5 x 2

15. 12
5 x 2

16. Good try, but the balance is not level.
This is because 5 x 2 is less than 12. 12
5 x 2
5 x 2 = 10
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17. Let’s try another one...

18. What can I put in the basket to make the balance level?
24 x 1
25 - 4
30 - 6
20 + 4

19. 24 x 1
20 + 4

20. 24 x 1
20 + 4
24 x 1

21. Well done! Both sides equal 24. You made the balance level!
24 x 1
20 + 4
24 x 1
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22. 24 x 1
30 - 6

23. 24 x 1
30 - 6
24 x 1

24. Well done! Both sides equal 24. You made the balance level!
24 x 1
30 - 6
24 x 1
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25. 24 x 1

26. 24 x 1
24 x 1

27. Well done! Both sides equal 24. You made the balance level!
24 x 1
24 x 1
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28. 24 x 1
25 - 4

29. 25 - 4
24 x 1

30. 24 x 1
25 - 4

31. 24 x 1
25 - 4

32. Good try, but the balance is not level.
This is because 25 – 4 is less than 24 x 1
24 x 1
25 - 4
= 21
24 x 1 = 24
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33. Let’s try one more before we make it trickier...

34. What can I put in the basket to make the balance level?
18 x 2
39 - 3
40 - 2
36 ÷ 1

35. 18 x 2
36 ÷ 1

36. 36 ÷ 1
18 x 2
24 x 1

37. Well done! Both sides equal 36. You made the balance level!
36 ÷ 1
18 x 2
24 x 1
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38. 18 x 2

39.
18 x 2
24 x 1

40. Well done! Both sides equal 36. You made the balance level!
18 x 2
24 x 1
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Next Question

41. 18 x 2
39 - 3

42. 39 - 3
18 x 2
24 x 1

43. Well done! Both sides equal 36. You made the balance level!
39 - 3
18 x 2
24 x 1
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44. 18 x 2
40 - 2

45. 18 x 2
40 - 2

46. 40 - 2
18 x 2

47. 40 - 2
18 x 2

48. Good try, but the balance is not level.
This is because 40 – 2 is greater than 18 x 2
40 - 2
18 x 2
18 x 2 = 36
= 38
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49. What would happen if we took the equal arm balance away?
15 - 5
7 + 3
Click here

50. What do we need to put in the middle for this to make sense?
15 - 5
7 + 3

51. We need to put an equals sign in the middle=
15 - 5
7 + 3
The equals sign tells us that what is on the left side, is the same as what is on the right side.

52. 7 + 3
15 - 5 =
This is called a ‘balanced number sentence’. They can be written without the boxes and it would look like this
15 – 5 = 7 + 3

53. Now it’s your turn! Can you make these number sentences balance?

54. Click on the box that will make this number sentence balance.
16 – 5 =
19 + 7
9 + 2 21

55. 16 – 5 =
11 = 11
That’s right! 16 – 5 is and is 11 so this number sentence is balanced
9 + 2
Next Question

56. Good try, but 21 is not equal to 11.
16 – 5 = 21
11 = 21
Good try, but 21 is not equal to 11.
Try Again

57. Good try, but 19 – 7 is 12. 12 is not equal to 11.
16 – 5 =
19 - 7
11 = 12
Good try, but 19 – 7 is is not equal to 11.
Try Again

58. Can you make a balanced number sentence with any of these boxes?
49 - 7
56 - 9

59. 7 x 6 =
42 = 42
That’s right! 7 x 6 is and is 42 so this number sentence is balanced
49 - 7
Next Question

60. Good try, but 4 x 11 is 44. 44 is not equal to 42.
42 = 44
Good try, but 4 x 11 is is not equal to 42.
Try Again

61. Good try, but 56 - 9 is 47. 47 is not equal to 42.
7 x 6 =
56 - 9
42 = 47
Good try, but is is not equal to 42.
Try Again

62. Two of these boxes will balance this number sentence. Can you find them?
64 ÷ 2 =
36 - 3
4 x 8

63. Click here to go back and find the other correct answer
64 ÷ 2 =
32 = 32
That’s right! 64 ÷ 2 is and is 32 so this number sentence is balanced
Click here to go back and find the other correct answer
NEXT

64. Click here to go back and find the other correct answer
64 ÷ 2 =
32 = 32
That’s right! 64 ÷ 2 is and 4 x 8 is 32 so this number sentence is balanced
4 x 8
Click here to go back and find the other correct answer
NEXT

65. Good try, but 36 – 3 is 33. 33 is not equal to 32.
64 ÷ 2 =
32 = 33
Good try, but 36 – 3 is is not equal to 32.
Try Again

66. Congratulations! You just learnt how to balance number sentences

67. Here are some things to remember:
The equals sign (=) means ‘the same as’
What is on the left side of an equals sign must be the same as what is on the right side e.g = 2 x 6