# Would you solve this problem using the distributive property?

Let’s consider revamping this 7th grade problem as a task where the students plan a variety show:

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Your group is planning the annual variety show, and you need to make some recommendations about how the time should be spent. The principal insists on 20 acts and the show typically lasts 2 hours.

You must also consider the following:

- The combined set-up and take down for each act
- Introducing each act by the host of the show

Provide 3 scenarios that will make the best use of the time. Justify your thinking.

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Caveat: It is implied that the students should consider how long each act should be. Should I make it explicit and list it with the considerations?

If I present the problem this way I think the students will begin to recognize the “considerations” as variables. A problem that has multiple solutions lends itself nicely to variables and the distributive property.

Am I leaving anything out?

Maybe it would be TOO explicit, but I might change the phrase “You must also consider the following” by simply expanding that phrase to “You must consider the time taken for the following”

I cannot imagine that the original prompt would make many 7th graders ‘consider’ the distributive property.

Thanks for the feedback. Perhaps I’ll try it one way with one class and the second way with my other standard class. Then see which method works best. I appreciate your help!

Mary – I like the open-endedness of your task and that you ask students to provide multiple scenarios.

I would be interested to hear about the activity later simply because I don’t envision my students thinking about using the distributive property in the problem.

I’m wondering if any of the students will feel compelled to request more time from the principal … 2 hours is a very short time for 20 acts.

I

havechanged the focus from the original problem. I’ve moved the task away from solve using the distributive property to teasing out how to plan an event like this and what the distributive property would look like in this situation. If the students immediately recognize that a 3 minute act has used up all the available time, would a 2 minute act be reasonable given the other variables involved?Your comments are sooo appreciated! Now I’m thinking the students could watch segments from The Voice, or America’s Got Talent to get an idea of how long an act should be. Maybe they’ll ask to act-it-out by pretending to be in a talent show. Then they would time the act, intro, and setup/take down.

At the end of the lesson the students explore the distributive property in this situation and see how groups allocated their time based on the distributive property.

I really have turned the problem into more of an investigation. The original problem lacked any purpose for using the distributive property. I was trying to make it more meaningful.

Please continue to share your thoughts. And yes, two hours is a very short time for 20 acts. The students could either request more time from the principal or , if brave, ask to cut the number of acts.

Two hours can be short, or on the other hand, it could feel like FOREVER depending on the quality of talent :)

Thanks for your feedback. It has caused me to think of other possibilities.