I found this task on @robertkaplinsky's site (which has numerous free and engaging resources). The focus is largely on creating an equation to find out how much a burger would cost no matter the number of hamburger patties and slices of cheese. I decided to take this in a a slightly different direction (although in hindsight I might as well have added the equation creation as well). I wanted to see if my 7th grade students could find the individual prices of a hamburger patty, a slice of cheese, and everything else lumped together (bun and toppings)...sort of an introduction to solving systems of equations in a more organic way. I realize this is an 8th grade topic, but what I teach can shift around from year to year and I wanted to see how this would go should I have 8th graders again.

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Here is the information I presented to my 7th graders, and I have included the specific questions below:

1. What is the individual cost of one hamburger patty, one slice of cheese, and everything else together (bun and toppings)?

2. How much does the 100 by 100 cost?

3. What is the individual calorie amount for one hamburger patty, one slice of cheese, and everything else together (bun and toppings)?

4. How many calories are in the 100 by 100?

5. About how many days worth of food would you ingest if you ate the 100 by 100?

Here is how the individual prices broke down for each sandwich for the slice of cheese (.25), the patty (.65), and the bun and toppings combined (.85).

Double-Double .25 .25 .65 .65 .85 .85 = $2.65

Cheeseburger .25 .65 .85 = $1.75

Hamburger .65 .85 = $.150

Many of my students took to this right away. For those who did not, I posed these questions to get them started...

"What is the difference between a cheeseburger and a hamburger?"

"What is the price difference between a cheeseburger and a hamburger?"

*Walk Away*

For the most part, these students (or groups of students) did a traditional multi-step elimination problem with more context, but without the expectation of being locked into a specific method someone teaches.

Students found many ways to compare these sandwiches in order to attain the prices for the individual parts. Student work examples below...enjoy!

This student was not finished, but I thought the first part was exceptional... |

Dr. Clayton M. Edwards

Assistant Professor of Curriculum and Instruction

Middle Level Program Coordinator

University of Northern Iowa
Schindler Education Center/Nielsen Field House

Middle Level Major Requirements

National Council of Teachers of Mathematics Editorial Panel

Curriculum VitaMiddle Level Major Requirements

National Council of Teachers of Mathematics Editorial Panel

This is an interesting take on the problem. I don't recall seeing anyone ever approach it this way. What I love is the quantity and quality of the student explanations. Specifically many students integrated the context into their mathematical explanation. Really nice to read. I will be linking to this from the lesson when I find some free time.

ReplyDeleteThank you for the comments and kind words! My students love these tasks and I attempt to push a high level of mathematical understanding so they actually understand and don't fake understand. I really appreciate people like you who make these outstanding materials available. I'm currently trying to figure out a few different ways to use the Ms. Pac-Man task...we'll see what I come up with. Keep up the good work!

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