This is a level 4 measurement and number activity from the Figure It Out theme series.
Click on the image to enlarge it. Click again to close. Download PDF (337 KB)
convert between time units
solve problems involving time, distance, and stroke rate
FIO, Levels 3-4, Theme: Sport, Waka Ama, page 17
To start the activity, the students could simulate a stroke rate of 40 strokes per minute to get some feel for how fast that is. They could change sides every 10 strokes. One student could call the stroke, using words to set the approximate pace: “1 001 stroke, 1 001 stroke, 1 001 stroke, 1 001 stroke, … 1 001 stroke, change, 1 001 stroke, 1 001 stroke, …” This will help the students to model the questions.
To answer question 1a, the students might draw a diagram like this:
So the crew took approximately 100 strokes.
The students can use this information to answer question 1b. If the crew took 100 strokes and changed sides every 10 strokes, they changed sides 100 ÷ 10 = 10 times. Alternatively, they may reason that 40 strokes per minute means four side changes, so 100 strokes means 10 side changes.
A higher stroke rate results in a faster boat speed only if the crew is able to maintain the same power output per stroke. This is difficult to do, and often a faster stroke rate means that each stroke is less powerful. Also, a faster stroke rate may mean that the crew are tired and are not well co-ordinated, so the boat may actually go slower. Question 2 continues this idea by looking at how tiredness over a longer distance results in lower average speed.
Questions 3a and 3b are difficult because they involve the concept of average speed.
The students may need the following scaffolding questions to help them. (They could also use double number lines.)
For question 3a:
“How many minutes altogether is 2 hours and 4 minutes?” (You may need to explain to the students that 2:04:06 means 2 hours, 4 minutes, and 6 seconds.)
“How many minutes would the crew have taken to cover one-third of the distance?”
“How many kilometres was one-third of the distance?”
“How long would it have taken them to cover 1 kilometre?”
For question 3b:
“How many minutes did the women take to cover each 11 kilometres? Compare that to the time taken for the men to cover 10 kilometres.”
“How long would the men take to cover 11 kilometres?”
“Which crew was fastest?
Answers to Activity
1. a. 100–113 strokes
b. 10–11 times
c. Answers will vary. A higher stroke rate usually means faster, but this depends on
how much power the paddlers create with each stroke.
2. Answers will vary. The crew members would need to pace themselves over the longer distance so that they do not run out of energy. This means that they would go more slowly overall.
3. a. 4.14 minutes per kilometre (rounded to 2 d.p.)
Speed would vary depending on wind direction, points at which there are crew
changeovers, and so on. A well-trained crew would try to pace itself so that it keeps up a consistent speed.
b. The women’s average was 5.31 minutes per kilometre (to 2 d.p.), so the men’s waka ama was faster.