Fast Walker & Painted Cube

Fast Walker

Last week, I wrote briefly about “fast walker,” an activity I created on a whim so that we could go outside and enjoy the weather. It involved having students time how long it would take them to make a lap of the 400m track. We came back inside, they found their rate and we did some graphing of total distance traveled vs. time.

When we came back on Monday, I wanted to add to this activity.  I gave them the following question:


I didn’t give them much direction on this, so most simply found the head start in time. This is the easier question and I was hoping for the distance. After they found the time, I told them to find the distance of the head start you would need in metres.


The students found how long it would take the runner to run 400 metres and then used that POI to find the initial value for their equation. For my rate of around 1.33 m/s, I would need around a 266.66 metre head start. Good review here of partial vs. direct.

Next it was on to some area and perimeter questions. I asked them the following two questions.


Solving for the radius in the first question was a bit tricky but they did a great job!

Since we were graphing distance-time, I decided it would be a great opportunity to review distance-time graphs and graphing stories. I gave them 4 graphs to review.


For an activity that was just suppose to be a way to get outside for a bit, it actually turned into a great activity covering quite a few expectations in the course. Nothing like math and a spark break all in one.

Painted Cube

We do a variation of this activity in our MHF 4U course. Students completed the following chart. Most built the cubes using cubilinks to find the number of cubes with paint on them.


Once they had the chart, we tried to come up with the general rule for each column for any side length n. I was impressed by how many students went straight to finding the differences to see if there was some type of a pattern. They found the first 3 quite easy and we had to look at finding the last two together.


We then graphed the 4 relationships and compared the graphs (linear vs. non-linear) etc.


There were some great questions here that would be great to dive into with an enriched class (domain, etc.)

A great activity to review linear and no-linear relations, first differences, graphing and equations.

This week we will be having a performance task. The plan is to allow students a period to work with their VRG to complete some higher order thinking questions. They will then have to complete an individual assessment the following day that has a similar flavour to the questions they were working on in a group.

It is also OAME this week, so 4 of us will be travelling to Kingston for some math education. It’s always great to hear the amazing things going on in other boards.



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