standard_description: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
problem_activity: Warm-up
The purpose of this warm-up is to elicit methods students are already using to organize their understanding of different outcomes. In this lesson, students are asked to use different structures to think about the outcomes of experiments that involve multiple steps, so this activity should give you an idea of how students are approaching the problem on their own.
Launch
Arrange students in groups of 2. Tell students they should organize their work so it can be understood by others. Give students 1 minute of quiet think time, 3 minutes for partner discussion, and follow up with a whole-class discussion.
Student Facing
How many different meals are possible if each meal includes one main course, one side dish, and one drink?
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "main courses"}, {"_attributes": {"scope": "col"}, "_value": "side dishes"}, {"_attributes": {"scope": "col"}, "_value": "drinks"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "grilled chicken"}, {"_value": "salad"}, {"_value": "milk"}]}, {"td": [{"_value": "turkey sandwich"}, {"_value": "applesauce"}, {"_value": "juice"}]}, {"td": [{"_value": "pasta salad"}, {"_value": "\u2014"}, {"_value": "water"}]}]}]}]}
Student Response
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Activity Synthesis
Select several groups to share their methods for organizing their thoughts about the different meals that are possible.
Consider these questions for the discussion:
“How did you know you counted all of the different possible meals?”
“How did you know you didn’t repeat any meals?”


aligns: no