Word Problems

In Grade 11 we’ve been working on word problems and applying our skills with quadratics.

We work in random groupings each day, so we are getting to know each other and to work well with each other. It’s not always easy to know how to solve problems. We are building our confidence in starting problems, and making a plan to get to the answer.

It was interesting to see how various groups decided to place the bridge on the graph. Some placed the y axis at one of the foundations, others placed the y axis as the axis of symmetry of the parabola. Some decided to use vertex form, and some decided to use factored form. No matter what, we all got to the same “a” value which was a neat observation to bring forward in consolidation. There can be many correct models, and many paths to get to them.

This problem was fun. We worked on this one until the end of class, and left it as a cliff hanger, and started it again the next day.

There was a lot of perseverance while working on this one. Reading and re-reading and making sense of how to use all the words was an interesting challenge. We wanted to maximize the area of the rectangle, so we need an equation for the area of the rectangle, and then we need to make sure that it is in terms of one variable, and THEN we need to find the vertex (maximum). Some groups missed that we are maximizing the rectangle. Some groups needed prompting about substitution, some needed help visualizing where the parabola is, because it’s not evident in the drawing that there is a parabola.

Today we started the class by finishing the problem. Some students had come in at lunch to try it again. We are developing more than just skills with finding the vertex, we are getting better at modelling a situation, creating equations, substituting when needed, and then finding the vertex.

It’s an impressive sight to see all 34 students engaged and working hard. It’s been a fun 2 weeks so far!