Field Day Blunder! – A Multiplication Performance Task

How many of you have ever used the Georgia framework lessons? If you haven’t you should really take a look at them. Some of them are fantastic and all of them are free! Click here to go see the frameworks for elementary math.

This math lesson is in unit 2 on page 156 and is title Field Day Blunder. Essentially the problem is this:

Mrs. Nelson’s third grade class was very excited about the upcoming field day events. Each third grade class was given a helmet and sacks for the upcoming sack race. Once the sack race was complete, Mrs. Nelson’s class moved on to the next race. As the students rushed to the next event, they left all of their helmets and sacks in a big pile. Christopher and Megan were left to match the helm ets with the sacks. Some of the sacks were for 2 people, and some were for 3 people. There were 24 helmets in all. Christopher and Megan were able to match all of the helmets to their sacks. How many 2-and 3-person sacks could there be?
I give students 24 foam tiles to represent the helmets. I also use index cards for the sacks. A full 3×5 inch index card is for three people/helmets and an index card cut in half is for 2 people/helmets.
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With my low groups we solve the problem for all 2 person sacks first. Then I have them solve it for all 3 person sacks. If they have time I ask them to solve a third way which would be a combination of 2 and 3 person sacks. With my higher groups I explain the manipulatives I have given them, read the problem, and just watch them solve the problem. Some of them chose to do mixed sacks the first time and some don’t. It is interesting to watch how some kids are very organized in their solving and others are scattered all over their work space and others. I require all students to find two ways to solve, draw the picture on their paper, and write matching multiplication sentences.
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I have had students ask if they could “invent” a 4 person sack and solve some more ways. I ask them to write that they invented a new sack which holds 4 people and then to solve that way. I love to watch students work on these types of problems and know that they are being challenged with the abundant amounts of correct answers.
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