In light of the Olympics, I found this activity on proportional reasoning: http://mathalicious.com/lessons/on-your-mark
I'm rather bummed that we just finished our unit on proportions because this would have been a really fun thing to incorporate! The activity poses the question: Do taller Olympic sprinters have an unfair advantage?
First students calculate how far each sprinter would run if he ran a distance proportional to his height (using the tallest runner to set the ratio). Using this information, they are asked to calculate how long it would take for each sprinter to run his new distance. Based on these calculations the students are asked to find the new winning order. Will the medals still be awarded in the same order? The answer is no! The original gold medalist will now earn bronze.
Next students use the second tallest runner to set the ratio. Does this effect the original winning order? The revised winning order? Students will find that both revised winning orders are the same. This is a great point to talk about what it means to be proportional.
The final task is to look compare a scatterplot showing actual time vs. height results to one showing the proportional results. Students use these to discuss whether races should be reorganized by height. In looking at the data, students may conclude that reorganizing would not be fair to taller runners. In other words, there seems to be no good solution. Someone will always be at a disadvantage.
I like this activity because it could be used to introduce proportionality or can be used as an extension to the lesson. Student interest in the topic will help with engagement. I also like that you can extend this discussion to other sports (ie. swimming, wrestling).
I'm rather bummed that we just finished our unit on proportions because this would have been a really fun thing to incorporate! The activity poses the question: Do taller Olympic sprinters have an unfair advantage?
First students calculate how far each sprinter would run if he ran a distance proportional to his height (using the tallest runner to set the ratio). Using this information, they are asked to calculate how long it would take for each sprinter to run his new distance. Based on these calculations the students are asked to find the new winning order. Will the medals still be awarded in the same order? The answer is no! The original gold medalist will now earn bronze.
Next students use the second tallest runner to set the ratio. Does this effect the original winning order? The revised winning order? Students will find that both revised winning orders are the same. This is a great point to talk about what it means to be proportional.
The final task is to look compare a scatterplot showing actual time vs. height results to one showing the proportional results. Students use these to discuss whether races should be reorganized by height. In looking at the data, students may conclude that reorganizing would not be fair to taller runners. In other words, there seems to be no good solution. Someone will always be at a disadvantage.
I like this activity because it could be used to introduce proportionality or can be used as an extension to the lesson. Student interest in the topic will help with engagement. I also like that you can extend this discussion to other sports (ie. swimming, wrestling).
I like the idea behind this. One, it pulls in current events, if you time it right. Second it pulls in the idea of fairness, and could lead to an interesting debate. Of course this gets at the idea of proportionality, then you could discus if speed is really proportional to height. What other factors might come into play to not be proportional? The scientist in me would like to hear the kids respond.
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