Problem Solving with Guests

Today we had the pleasure of hosting several mathy people from Queen’s. They came with some rich tasks to present to a grade 11 class and a grade 10 class

The first one was a question about maximizing area of a fenced field located against a long barn.

Students worked on different ways to model the problem, with a picture, and variables, and equations. They had different strategies for finding the vertex, some completed the square, some found the axis of symmetry, some used the quadratic formula and found roots and then the axis of symmetry.

It was great to see how actively groups collaborated together to solve the problem. The next challenge was a bit trickier. We needed to find the rectangle inscribed within a certain parabola with the maximum perimeter.

Students had challenges knowing where to start, and how to proceed. Many of them struggled with calling the length and width of the rectangle x and y, so that brought in 2 conflicting definitions of x. By labelling the width of the rectangle as “w” we were able to build an equation for w in terms of x and use that in the other equations.

Here’s some examples of works in progress. It was neat to see some groups base their perimeter calculations on different things: some counted x as the distance from the origin. Others counted the horizontal distance from the axis of symmetry to the edge of the rectangle.

We had a lot of struggle, but kept working through the struggle and made some progress before the end of class.