Introduce the problems on the Professor Peabody Invents a Ball page in the Student Guide. Use the expectations outlined on the Math Practices page in the Student Guide Reference section and the discussion prompts below to set problem-specific expectations. Record notes from this class conversation on a display of the Math Practices Notes Master. See Figure 1 for possible student generated notes.
- What are you being asked to find out? (Find the bounce height when given the drop height and find the drop height when given the bounce height.)
- What are some possible strategies? (Find the pattern in the data table and extend it, make and use a graph.)
- How will you check for reasonableness? (Use a second strategy to check the answer, compare answer to known patterns in the data.)
- How can you use the data table to explain your answer? (Show the data table and add the new data to fit the pattern.)
- How can you use a graph to show your thinking? (Include dotted lines on the graph to show the drop heights and bounce heights.)
- What labels should you use? (cm, drop height, bounce height)
Students should understand that they are free to devise their own strategies and use any of the tools they normally use in class such as rulers, graph paper, and calculators. Be sure these tools are made available.
Have students solve the problems on the Professor Peabody Invents a Ball page. If they work in pairs, each student writes up his or her own strategy and solution.
- Ask students to underline what the problem is asking. For example, students would underline “what height was the drop height?”
- If students are having trouble describing and finding the pattern, ask students to draw a new data table with a drop height of 75 included in the table. This should help students see the patterns in the data table.
- Encourage students to tell a partner what they did to solve a problem before they record a solution.
- Display the class-generated Math Practices Notes while students are working.
- Revise student sample work as a class. Use Maria's Work shown in Figures 6 and 7.
Figures 2–7 show sample student responses.
