Back Through Ten

In this activity, students will gain experience at bridging through 10 or near multiples of 10 as a mental strategy for subtraction. The activity encourages students to visualise the process and use part-whole thinking, using the same principle as in the activity on page 11 of the student booklet but this time visualising a number line.
You may wish to discuss with the students how to use brackets to separate the two steps when they are recording their answers.
Ask questions to clarify the students’ thinking as they move from the visual number line model to the mental operation. For example, “What number do you take away to reach the nearest multiple of 10?”
An alternative model, the Make Tens board, may also be used in the same way as it is on page 11.
For example:
16 – 7 = (16 – 6) – 1

Alternative mental strategies for question 3 are suggested in the Answers section.

Answers to Activity

1. a. 7
Working: 15 – 8 = (15 – 5) – 3
= 10 – 3
= 7
b. 7
Working: 16 – 9 = (16 – 6) – 3
= 10 – 3
= 7
c. 17
Working: 24 – 7 = (24 – 4) – 3
= 20 – 3
= 17
d. 89
Working: 98 – 9 = (98 – 8) – 1
= 90 – 1
= 8
2. a. 16 – 7 = (16 – 6) – 1
= 10 – 1
= 9
b. 12 – 5 = (12 – 2) – 3
= 10 – 3
= 7
c. 13 – 8 = (13 – 3) – 5
= 10 – 5
= 5
d. 26 – 8 = (26 – 6) – 2
= 20 – 2
= 18
e. 22 – 5 = (22 – 2) – 3
= 20 – 3
= 17
f. 27 – 9 = (27 – 7) – 2
= 20 – 2
= 18
g. 82 – 7 = (82 – 2) – 5
= 80 – 5
= 75
h. 143 – 8 = (143 – 3) – 5
= 140 – 5
= 135
i. 904 – 6 = (904 – 4) – 2
= 900 – 2
= 898
j. 1 746 – 8 = (1 746 – 6) – 2
= 1 740 – 2
= 1 738
k. 1 000 014 – 7 = (1 000 014 – 4) – 3
= 1 000 010 – 3
= 1 000 007
l. 5 961 – 8 = (5 961 – 1) – 7
= 5 960 – 7
= 5 953
3. Answers will vary. You could:

• count back (not a very efficient method)

• split into 5 and a bit more, for example, for 13 – 8: (13 – 5) – 3

• use relationship to addition, for example:12 – 5 = 5 + 7 – 5

• subtract 10 and then adjust, for example: 143 – 8 = 143 – 10 + 2

• round, then subtract, for example: 82 – 7 = 80 – 5.