Paging Doctor Math: Shrinking Dollar Task

I find using these task very valuable as an assessment piece to make sure students can apply what they are doing within a unit, but even more worthwhile when the task comes much later than the unit was presented. If students can apply the information later down the road and can explain thinking in detail, chances are what you went through the first time around stuck. I also like using tasks to introduce new concepts, but that wasn't the case this time around.

For this week's 7th grade task, I found a @ddmeyer task from his spreadsheet of tasks and added a few questions. I also took the answer video and put that at the beginning. The answer video did not have any numbers, but I thought it showed the students an excellent graphic of what this shrinking process would look like.

Here is what I presented to my students:

Modified Task

I think the biggest struggle for my students was the difference between percent growth/percent decrease, and the percentage remaining. To attempt to alleviate this problem, I emphasized that the growth or reduction should not include the original amount. We drew a few pictures to show this concept. I also related this to their own heights. We discussed what taking off an extra 100% would mean in this process as well. This wasn't prevalent with all my students, but it was the biggest problem.

I also had a few students confused with the wording of question six. If you can think of a better way to state that questions, please leave it in the comments. My goal was for them to see that while the sides decreased by 25%, the area actually decreased by 43% to 44% each time the dollar was shrunk on the copier.

As you will notice from the student work, most of my students use a ratio table method to work with all percent problems. I decided to present this as an option a few years ago because this method works for any proportion or percent situation, and the students understand what everything means. In the past I had student who would have to ask if they multiplied or divided in a percent scenario, but using this type of visual has alleviated that problem. Eventually, I have some students move on to other easier method that they figure out based on the ratio tables. In this task, I noticed a few students multiplied by .75 to find the 25% reduction. Other students spammed the divide 4 and multiply by 3 buttons on the calculator to simulate changing the whole to 25% and then 75% making the calculations quicker.

Here are the standards that I felt the task involved. I have also included the student work. One of the students commented that they saw a Despicable Me where they scanned their butt on the copy machine and could we try that next? I think we will stick with the dollar bills!

7.RP.A.3

7.EE.A.2

7.EE.B.3

My prep work I carry around on my iPad to help discussion with various groups and individuals...

I thought I would add this picture...a 7th grader trying to draw 5 millimeters with a meter stick...genius! This is why I love teaching middle school students...

Previous Posts with Student Work

Tile Floor Task

Penny Cube Task

Are the Thunder Playoff Bound?

Toothpick Task

Man Versus Squirrel

In-N-Out Burger

Dr. Clayton M. Edwards

Ed. D. Curriculum and Instruction (UNI)

Yager Exemplary Teaching Award 2014

Awarded Outstanding Doctoral Dissertation at the University of Northern Iowa 2014

MA Middle Level Mathematics (UNI)

Middle School Mathematics Instructor

Grundy Center Middle School