Do you know why the gears on your bike make it easier to steadily climb a hill or swiftly speed down the other side? There’s math embedded in the explanation, and if your child has a bicycle, you can start getting mathy with it.
Begin by simply pointing out the gears. Every bicycle has at least two – one in the front and one in the back. They’re called the chain wheel and the free wheel. The number of teeth on each gear matter. Count them. Compare those two numbers. Are they the same? Which is larger? Which is smaller? By a lot? By a little? Why in the world would they be different?
The first two questions are objective, meaning there is a clear and correct answer that will be the same for everyone. Comparing numbers is a skill that students are actively taught in early elementary school. The second two questions are subjective. They depend on your point of view and, as long as you can explain your answer, your answer can differ from someone else’s and still be correct. Students should be actively taught how to do this, too, but that will vary from school to school. That final question is a great one to leave hanging for your child to wonder about. If you know the answer, don’t say it! If you don’t know that answer, all the better.
If you’re child is showing interest, you can ask some more questions:
When the front gear makes one full rotation, does the rear gear also make one full rotation?
How far does your bike move with one full circle of the pedals (the front gear)? (Not including coasting.) Is the answer different if you have a bike that is larger or smaller? How does wheel size make it easier or harder to ride your bike? (My kids just sized up in their bikes, and it takes a lot more effort for me to keep up with them!)
Now explore a bike that has multiple gears (a bike that can shift gears.) Gears that shift provide the opportunity to explore ratios. A ratio is a comparison of two numbers and it can be expressed as a fraction (1 to 2 can be written 1/2 or 1:2.) Explore gear ratios with a kid who enjoys her bike, and she may not even notice that she’s working with fractions.
Investigate gear ratios by first counting up the teeth on all your gears. Then compare ratios of the chain wheel (front gear) to the free wheel (rear gear). If your kid is feeling scientific and experimental, have her write down all the possible gear combinations. If she has 3 front gears and 5 rear gears, there will be 15 possible gear combinations. Now she can pedal through each one, feel them, and consider some more questions: Which gear combinations make it easier to pedal? Which make it harder to pedal? Which help you get uphill more easily and which help you speed downhill more swiftly? Why? Why does a higher gear ratio like 4/1 (44 teeth up front compared to 11 teeth in back is a ratio of 44/11 or, simplified, 4/1) make it so that you fly downhill but struggle uphill??
As always, it really doesn’t matter if you, the parent, know the answers to these questions. (Though if you’d like, you can start here: How Bicycles Work.) What really matters is that you ask the questions and then give some space for your kid think at her own pace. Once you get the hang of it, it will be easy. Kind of like riding a bike.
Mathematically speaking…the bicycle is a cornucopia of math and science topics. It is a full STEM…even STEAM…experience if you spend some time with it. The ratio of gears, the radius of wheels, momentum, mass, inertia, potential energy…it’s fantastic! And then there is the beauty, elegance, and simplicity of the design of a bike. You could even teach quite a bit about local and world cultures through the topic of bicycles…oh this IS getting exciting now! Have fun! (And don’t forget to spend some time just riding that bicycle, too!)
mathy moments 
Leave a Reply