Stepping Out

This activity focuses on addition strategies. A good place to start is to have the students compare Piri’s and Tom’s strategies. Both are trying to find an easy way to add. The difference is that Piri sees that 8 and 2 are compatible because they make 10, while Tom chooses to round to a tidy number and then do an adjustment to allow for the rounding. Hannah uses place value knowledge to split the addends and then adds the tens before the ones.
These examples of different strategies show part–whole thinking in addition that indicates the transition between stages 5 (early additive) and 6 (advanced additive) of the Number Framework.
The students should use a calculator only to check their answers, otherwise there will be no opportunity for strategy development.
It’s important in teaching strategy development that you don’t tell the students to learn a particular strategy and apply it. The strategies they choose will depend on the numbers that they are working with: there is no one strategy that is best for all situations. The students must “buy into” a strategy because they see it makes sense. You can encourage this by sharing your strategies and those of students without directing the students to use a particular one. Some suitable questions are: “Where
did you begin?” “What was it about the numbers that helped you choose that strategy?” “Can you use a diagram (or equipment) to explain the steps in your thinking?” “Is there another efficient way to do it?”
For question 4, the students need to realise that Tom does not have to visit the pool (although this may add to the time in 4b) and he needs to return home. The students will probably use a trialand- improvement strategy to test out all possibilities, so encourage them to work co-operatively, in problem-solving groups of four students, by dividing up the different routes to check between them. They should all check the “best” route for themselves before you ask them to share their calculation strategy.

Answers to Activity

1. 54 min
2. First Piri’s house and then Mira’s house
3. To get to 2 friends’ houses before the swimming pool, Mira must take one of the following routes:
• Mira’s to Tom’s to Brad’s to the swimming pool: 14 + 18 + 33 = 65 min
• Mira’s to Tom’s to Emeli’s to the swimming pool: 14 + 21 + 23 = 58 min
• Mira’s to Emeli’s to Tom’s to the swimming pool: 19 + 21 + 19 = 59 min
• Mira’s to Emeli’s to Piri’s to the swimming pool: 19 + 16 + 13 = 48 min
• Mira’s to Piri’s to Emeli’s to the swimming pool: 23 + 16 + 23 = 62 min
• Mira’s to Piri’s to Hannah’s to the swimming pool: 23 + 18 + 22 = 63 min
4. a. 113 min. (Tom’s to Mira’s to Emeli’s to Piri’s to Hannah’s to Brad’s and home or the same route in reverse)
b. 161 min. (The slowest possible route, which can be done in reverse, is: Tom’s to Emeli’s to Mira’s to Piri’s to Hannah’s to Brad’s to the swimming pool and home.)
5. Answers will vary.