To solve this problem which compares different rates of usage, students should be encouraged to use a graph or a table. Both of these approaches produce the conceptual knowledge that is required to solve more complicated algebraic problems.
The problem is typical of many real world problems such as investment problems, where there are different rates of return, and travel problems where different methods of travel cost different amounts.
Mr Morrison and his daughter Rose each get a bottle of QwikQure Cough Medicine from the pharmacy. Mr Morrison’s bottle has 300ml and he has to take 10ml every 3 hours. Rose has a smaller bottle with 90ml and she has to take 5ml every 6 hours. They have to take the medicine between the hours of 7am and 7pm.
Who will use up their medicine first?
- Pose the problem to the class and show 2 bottles labelled according to the problem.
- Have the students think about how they might solve the problem before asking them to work on the problems in pairs.
- As the students solve the problem, ask questions that focus their thinking on the strategy they are using:
How are you solving the problem?
Why did you decide to solve it that way?
What can you tell me about what you have found out?
How are you going to record your solution?
Do you think that you can convince others that you have found the solution? What will you say?
- Share solutions and also discuss:
Why does Rose have the smallest dosage?
How large is 10ml? How many doses would go into a cup/glass/soft drink can?
How realistic is this problem? What are typical doses of cough medicine?
Extension to the problem
Mrs Morrison has some cough medicine. She must take 10ml every 4 hours. If her bottle lasts as long as her husband’s, how much medicine does her bottle hold?
Other Contexts for the Problem
Walking different distances at different speeds
Use of other resources such as money
Use a graph with the horizontal axis marked from 7am to 7pm in hours for about 7 days. Mr Morrison will then use all his medicine up on the sixth day at 7pm. Rose will do the same.
Solution to the extension
Mrs Morrison will use up 40ml per day (4 doses of 10 ml each). If the bottle lasts six days as her husband’s did, then she will have a bottle of 40 ´ 6 = 240 ml.