Lesson 1

A Three Hat Day

Est. Class Sessions: 1

Summarizing the Lesson

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Student work samples have been provided, but analyzing work done by your students is preferred. Ask for students' permission before using their work. This will ease their anxiety.

After students have finished, discuss the solution and ask several students to display and share their method, particularly those who used a systematic approach. Have several students who used a variety of representations display their work showing the six possible combinations for the order of the three hats. Include representations using drawings, number symbols, color symbols, and letter symbols. See Figure 6. If all of these representations were not shared, demonstrate how to solve the problem systematically eliciting input from students as you record different combinations.

Include questions such as the following as you discuss students' solutions:

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  • What did you find to be helpful in solving the problem?
  • Did you try a strategy and then not like it? How did you change your strategy to make it more effective?
  • Did you ever get confused? What helped?
  • Was one strategy or method easy to use? Difficult? Describe it.
  • Why is it important to record your work?

Display the Work Samples Master. Remind students of Math Practices Expectation 5, Show my work. Explain that these are samples of two students' work on the Three Hat Combinations page.

Ask:

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  • What do you notice about Emily's work?
  • What do you notice about Diana's work?
  • Is it easier to understand Diana's thinking or Emily's thinking? Why do you think so?

Students may notice that Emily's work is disorganized and messy. Emily changes the symbols she uses to represent the hats. It is difficult to see if she has used a hat combination more than once.

Diana's approach is more systematic. It is organized and you can clearly see that she used letters to represent the different type of hats. It is easy to see that she didn't repeat any of the combinations, and that she has six different ways to order the hats.

Conclude the lesson by asking:

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  • Do you think Emily's method could be improved so that it is more efficient?
  • What advice would you give to Emily so that she could do a better job solving the problem and showing her work? (Possible response: Record her work carefully and neatly; choose only one set of symbols to use.)
Adventure Book:
Student Activity Book:
Master:
Possilble representations of the six combinations of three hats
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