# Creating a perplexing math task with disequilibrium

Last week our district 6-12 math teachers spent the day learning to create math tasks with teacher Zach Herrmann, Evanston Township High School. We experienced three perplexing, high school geometry tasks and observed Herrmann’s delivery before being given time to create our own tasks.

Our sixth grade PLC developed a task based on students discovering that the altitude, not the slanted edge, is used to find the area of  parallelograms, trapezoids, obtuse and equilateral triangles.

Which figure has the greatest area is actually a trick question. Each polygon has an area of 10 inches sq. The altitude of each figure is 1 inch.

This is a small group task. If the students need help, a representative can ask a question. We want to develop perseverance and resourcefulness so we’ve decided to use the line, “You may use any tools available in the classroom.” We want the students to discover for themselves how the ruler, graph paper, etc. can assist them. We also wanted to create disequilibrium so we positioned each figure so that the base is not necessarily on the bottom.

I really want a polished look so I don’t want to upload a file with hand drawn figures. I’m still learning Sketchpad and I’m having trouble getting the correct size when I paste the figures into Word. As soon as I tackle the problem, I’ll repost.

## 2 thoughts on “Creating a perplexing math task with disequilibrium”

1. Telannia says:

Hey, Mrs. Doom! I saw your post on edmodo and couldn’t wait to read. I love the task and the requirement to have students think about their tools to use. You are doing so many of the mathematical practices in common core. I like the group and individual requirements stated in the task. The exit question is also great at helping give you insight into what students do and do not know. I am assuming that students will at least have a working definition of area before they complete the task. I would be curious how many students will use squares to help the determine the area.

Let me first say my suggestions may be wrong because I am a little tired. I know if I don’t answer today, I won’t get back to it. The first thing is a small thing on page 2. It doesn’t look like your program connected the third vertex. The second is on the last page. Two of the shapes seem to be labeled wrong. I only glanced but they are labeled 5 and 1. Again, I only glanced but the shapes seemed to be a rectangle and parallelogram which both are just multiplying base and height. If you have English language learners, maybe you can provide sentence starters to help them with the writing aspect.

I am curious if you have Zach Herrman’s handouts from your training. I would love to see them. I would have killed to be in your training. I have heard great things about Evanston Township High School.

1. Thanks, Tellania for catching the typos and lack of vertex. You were not tired, you were being very polite! I was having a heck of a time printing the figures from Sketchpad. The shapes seem to want to spill over onto the second page, even when I move it to another part of the screen. I’m still learning Sketchpad, so I thought about placing the figures into Word. Well, the images were being resized so I ended up drawing a rectangle in Word and resizing the shapes to the rectangle’s dimensions.

On Monday, I’ll scan the tasks and send them to you via edmodo.