Those who know me know that my interest and knowledge about sport is almost nil. So the fact that I’m writing a second post involving sport, when I just wrote one last week about soccer, amazes even me! **But that’s just the thing about maths education – it’s so important to engage kids through what interests them, even if it doesn’t interest you**.

My husband is a cyclist, and by that I mean the full deal – fancy bike, lycra, everything. So lately my evenings have been spent watching other men in lycra cycling through some of the most beautiful landscapes in France. And while I’m watching and occasionally showing interest, it occurred to me that there’s quite a bit of mathematics available to engage with.

Do you have kids who enjoy riding their bikes? Do they ever like to race each other or their friends? Do you have kids in the neighbourhood who like to build jump ramps? Or is there a keen cyclist in your house? If you answered yes to any of these, then I think I have some ways you can integrate some maths education into your discussion and activities.

**The Climbs – Slopes, Gradients and Trigonometry**

The most powerful mathematics we have to help us understand and navigate our world is Calculus. And the very foundation of calculus is the understanding of changing slopes and gradients. And that’s what the Tour is all about.

As you can see on the picture above, a point on the route has an 18% incline. This means that for every 1 metre of horizontal distance (what we call the “run”), the slope rises by 18 cm (the “rise). When we divide the rise by the run, we get a gradient.

You can also see that the average gradient for this section of 3.5 km is 9.5%. How did they work this out?

**The total rise is 914 m – 580 m = 334 m**

**Divide this by the run of 3500 m = 0.095**

**Multiply this by 100 to get a percentage of 9.5%.**

If your kids find these climbs fascinating, there’s plenty of charts like this available on the official website for each stage. Just check out this one!

Exploring these with your child and discussing the different slopes and difficulties of the climb is a great introduction to these all important foundational ideals in calculus.

To extend this further we can start to take a look at the angle of incline, rather than the percentage gradient. This involves angle measure and even the use of trigonometry.

Do your kids enjoy building ramps to jump their bikes off? I know the kids in our neighbourhood used to assemble down at the park and watch the older boys create a ramp using dirt and planks of wood to jump their bikes off. And I’ve seen kids doing this for years on a vacant block near my mum’s house. Why not get your kids involved in a bit of maths while they’re at it? Each time they build up the ramp, they could calculate the percentage incline and keep track of which incline gives the best overall jump. They could also measure or calculate the angle of incline too.

From the base of the ramp they could measure the angle the base makes with the ground, using a regular protractor. No doubt this will be a bit tricky due to the small size of the protractor. An easier way is to calculate the angle using trigonometry. Your kids might be too young to explore trigonometry in detail, but they’ll be excited by the prospect of using some advanced mathematics and some new buttons on their calculator.

Once we know the gradient of the incline, for example, it was 0.095 in the example above, we can then take the inverse or arc tangent of this value to find the angle. We get 5.43 degrees. This page shows another example with a diagram.

**The Pace – Speed, Time and Distance**

Of course the other major component of the Tour is all about the speed and time taken to cover the significant distances of each stage. The Year 7 Australian Curriculum for maths requires students to have a good understanding of the interaction between speed, distance and time, including the interpretation of distance-time graphs.

If watching the Tour has your child a little more excited about riding their bike fast, why not help them calculate their speeds?

Choose a safe and quiet straight section of footpath or cyclepath in your area and start by measuring its length. This is a great activity to teach your child to do and will require you finding the measuring tape or getting yourself a trundle wheel

Next you’ll need a stopwatch of your phone to time your child as they race the length of the route you’ve measured.

Now it’s time to calculate their speed together. **To do this divide the distance by the time taken**. If you measured the distance in metres and the time is seconds, then their speed will be in metres/second. You might also want to convert this to kilometres/hour, the units of speed the professional cyclists use.

To do this you can first convert the distance to kilometres by **dividing by 1000**. Then convert the seconds to hours by **dividing the seconds by 3600** (60 seconds x 60 minutes = 3600 seconds in an hour). **Divide the distance in km by the time in hours to calculate the speed in km/h.**

Perhaps your kids can race each other on this route, or you could all have a go as a family. You kids might even want to complete this “time trial” regularly to see if they are improving their speed and skill on their bike. Together, you can record and graph their speeds and make it a small project.

As I said at the beginning, if you can engage your child’s interaction with maths through something they already enjoy doing, then their learning will be all the more powerful and effective.

What do your kids love to do? Do you need our help in finding a way to connect some maths to one of their favourite activities? Please let us know in the comments 🙂

**Photo credit: swambo / Foter / Creative Commons Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0)**