Tiring teamwork
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Compare positions of objects moving at different rates.
Tiring teamwork
Achievement objectives
NA5-4: Use rates and ratios.
Description of mathematics
Number framework links
Use this activity to help students learn to solve problems with the use of fractions, proportions, and ratios (stages 7 and 8).
Required materials
- Figure it out, Level 3+, Proportional Reasoning, "Tiring teamwork", page 21
See Materials that come with this resource to download:
- Tiring teamwork activity (.pdf)
- Tiring teamwork CM (.pdf)
Activity
This problem-solving activity requires students to work out how long it would take walkers walking at different speeds to lap each other. Give your students every chance to solve the problems themselves, working in pairs or groups of no more than four. There are at least three strategies that they could use: a circular diagram, a double strip diagram, and a table.
The student book suggests using a circular diagram with counters to represent the walkers. Alternatively, students could mark a copy of the copymaster, using a pencil. A teaching clock face would serve the same purpose as long as the hands can be moved independently to represent the two walkers.
If they use a circular diagram, students may find it easier to focus on where the slower walker is when the fastest walker completes a lap rather than plot minute-by-minute progress as suggested in the student book.
In Question 1, Kelvin takes 6 minutes and Ian 8 minutes, so where would Ian be when Kelvin has completed a circuit? Expressed differently, if Ian takes 8 minutes to do 1 lap, where is he after 6 minutes? After 6 minutes, he has completed 6/8 or 3/4 of a lap. After 12 minutes, Kelvin has completed 2 laps and Ian 2 x 3/4 = 1 1/2 laps.
After 24 minutes, Kelvin will have completed 4 laps and Ian 4 x 3/4 = 3 laps, so at that point, Kelvin is exactly 1 lap ahead of Ian.
The Answers section shows how the same information can be pictured using a double strip diagram.
Using the third suggested strategy, a table for question 1 could look like this:
|
Kelvin (min) |
Ian (min) |
Lap 1 |
6 |
8 |
Lap 2 |
12 |
16 |
Lap 3 |
18 |
24 |
Lap 4 |
24 |
32 |
The table shows that, after 24 minutes, Kelvin has completed 4 laps and Ian 3.
The table for Question 2 shows that, after 40 minutes, Ian has completed 5 laps and Kate 4.
|
Kate (min) |
Ian (min) |
Lap 1 |
10 |
8 |
Lap 2 |
20 |
16 |
Lap 3 |
30 |
24 |
Lap 4 |
40 |
32 |
Lap 5 |
50 |
40 |
The table for Question 3 shows that, after 30 minutes, Kelvin has completed 5 laps and Kate 3. This means that Kelvin is now 2 laps ahead, so he must have lapped Kate at the 15 minute point:
|
Kelvin (min) |
Kate (min) |
Lap 1 |
6 |
10 |
Lap 2 |
12 |
20 |
Lap 3 |
18 |
30 |
Lap 4 |
24 |
40 |
Lap 5 |
30 |
50 |
1.
24 min. A double strip diagram shows that it takes this long for Kelvin to get 1 complete lap ahead of Ian (4 laps to 3):
2.
40 min. After this time, Ian is 1 complete lap ahead of Kate (5 laps to 4):
3.
15 min. This is a little harder to see on a strip diagram, but after 30 min, Kelvin is exactly 2 laps ahead of Kate (5 laps to 3), so after 15 min, he must be exactly 1 lap ahead (2 1/2 laps to 1 1/2 ).
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