Multiple Representations Sums, Differences and Products

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SWBAT use multiple representations to express the relationships in the constant sum and difference problems.

Big Idea

What information can you glean from a graph, a data table or a function rule? Students use graphing technology to examine different representations and to explain what each representation shows.


30 minutes

It has been both a surprise and a delight for me to realize that simply by providing students with different representations of the same problem they have already been working on, you can get them to think about the problem in different ways. At first, I would have thought that this warm-up would be too easy. To me creating one representation from the others is very straight-forward. After trying this approach in my class, I now realize that for my students it provides a new cognitive challenge and a new way for them to think.

During the class, my students initially thought that each of the three representations I gave them related to the same problem. After I clarified that these were three different problems, the lesson got much more interesting. I gave the students thirty minutes to figure out as much missing information about each function as they could. 

On this day, the transition from the warm-up to the investigation was fluid. Once students accomplished the warm-up, they transitioned directly to the main investigation.


40 minutes


10 minutes

This is a great chance for reflection:

  • What did you learn today?


  • How does looking at the multiple representations of each problem help you understand the problem?


  • What is still confusing for you?


  • Out of all the representations, which one helps you understand the most: data tables, graphs, or equations?


Choose some questions that you think will help your students reflect (or let them choose) and give them time to write about their answers.