Recently I gave my grade 6's the following task (fyi: they have been working on patterns, rules, tables, and graphs since school started):
Ms. is going on vacation and needs to rent a car while
she is there. There are two different car rental companies at the airport. Fast
Cars charges $45 a day to rent cars, while Cheap Cars charges $15 a
day plus $0.75 for every mile you drive.
Which company should
Ms. rent a car from to get a better deal?
I split the class in to pairs, gave them the remainder of class (35-40 minutes) and basically said, "have at it!" which they did not like. They wanted more information, they wanted answers to their questions (where are you going? for how many days? how many miles will you drive?), they wanted help and were unhappy that I told them that they needed to talk things out with their partner and come up with a strategy on how they planned to solve the problem.
As I walked around the room I was amazed at what I saw! Each group was doing something different, had started a different way, taken a different approach, thinking of scenarios, creating charts, jotting down numbers, and working together to take a stab at something they thought was impossible to solve. There was a whole lot of thinking going on in the room - you could see it in their work, you could hear it around the room (and probably down the hall since they are a fairly loud class) - it was everywhere!
Their homework this day was to do the following:
Write a one paragraph argument on which company I should use and why.
Next class I plan on having them share their arguments in small groups (possibly using a protocol) which will then lead to a full class discussion and a debrief on the task. I'm really interested in seeing what they come up with and how the follow up class goes!
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This problem was modified from the CMP 2 Series (I believe it was from the Grade 7 books).