Special Guests In Grade 10

Today we had the pleasure of welcoming Dr. Peter Taylor and several graduate students from Queen’s University, and RabbitMath to come and do some problems with us.

In grade 9 and 10 the problem we did was a neat one which showed a way of representing a line using a parameter. Students drew the line segment between the points (1,0) and (5,5).

the journey from point to point took 1 minute. The next task was to determine where the halfway point would be? Where you’d be after 0.5 minutes, t=1/2, and the also where you’d be when t=1/4, or t=4/5.

There were great discussions happening in the groups, and students were pushed to justify their conclusions and explain their thinking.

Next we brought in a parameter t, and we were able to express the point on the line for any value of t with the following equation.

We turned to desmos and built a model

we used B=(1,0) and F=(5,5)

then we defined the line to be B+t(F-B) where t is a parameter

then we put a point on the line that could be animated with a slider. Q=B+T(F-B) where the capital T is controlled with a slider between 0 and 1.

We made another line as well, and added a slider dot on that one too.

The final part was to make a line that joined the sliding dots together. We were exploring when that new line segment was vertical and when it was horizontal.

Here is the desmos result. It was pretty cool!

Students and teachers learned a great deal from this experience, and it was fun to do something totally different. We are thankful to our visitors for bringing good questions to share with us, and the support as we explored the math.