Wheels Galore

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Purpose

This is a level 3 number activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.
A PDF of the student activity is included.

Achievement Objectives
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
Student Activity

Click on the image to enlarge it. Click again to close. Download PDF (270 KB)

Specific Learning Outcomes

solve story problems

write own story problems

Required Resource Materials
FIO, Level 3, Number, Book 3, Wheels Galore, page 19

A classmate

Activity

This activity involves the use of multiplication and division skills and doubling and halving.
The students need to extract from the sentences the mathematics required to solve the problems. Many students have difficulty with this because the skills needed for reading and understanding informational text are different from those needed for normal reading. Encourage the students to ask themselves questions about the information, such as: “What does this tell me?” “What do I have to find?” “How should I solve this?” “Is there enough, not enough, or too much information?”
“Can I draw a picture of the information given?”
The activity gives information about various types of cycles, and from the information given, the students have to extract the correct number of cycles and/or riders. These types of problems are usually solved through a trial-and-improvement strategy. So that the students don’t lose sight of the information provided from question to question, ask them to lay it all out in a table. For example, in question 2, the students are asked how many tandems there are if there are 23 riders and a total of 14 mountain bikes and tandems in a group. The trial-and-improvement table could help.

table.

By listing the possible combinations in the table, the students can see that there are 9 tandems in the race. Students who are having difficulty could use materials such as different-coloured cubes or counters to model each situation.
For question 3, you may need to explain what “half as many” means. Again, the students can use a table to help with this.
In question 4, the students may forget to add the wheels of the trailer and the wheels of the car to find the total.
When the students are making up their own problems in question 5, have them put the data into a table, check their answers, and then extract the information from the table to write the problem. For example, the table could be:

table.

The related problem might be: “Quinten saw that there were 45 people, including unicycle, mountain bike, and tandem racers, in the round-the-lake race. He counted 65 wheels. How many of each type of cycle were in the race?”
The students can improve their problem-solving skills by revisiting the activities and solving them using different strategies, such as working backwards. The students will probably benefit more from solving a problem 5 different ways than solving 5 different problems the same way.

Answers to Activity

1. 78 wheels
2. 9 tandems (and 5 mountain bikes)
3. 4 tandems (and 2 unicycles)
4. 17 wheels (includes trailer [2 wheels] and car [4 wheels]). (Light trailers only have 2 wheels, but if you thought that the trailer had 4 wheels, then your answer would be 19 wheels.)
5. Problems will vary.

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Level Three