Joe the Goldfish

Est. Class Sessions: 1

Developing the Lesson

Discuss Constraints of the Raincoat Problem. Organize students into design teams of 2 or 3 students. Refer students to and introduce the problem on the Joe the Goldfish page in the Student Guide. Tell students that they will work with a design team to design and make a raincoat for Joe.

The size of the group does matter. If groups are too big, some students have difficulty staying engaged. If groups are too small, there may be too many tasks or not enough people to contribute to the task. For this problem, student pairs or groups of three have been effective.

Elicit responses to Question 1 and then ask students to discuss Questions 2–6 with their design team members. The answers to most of these questions should be left to the discretion of each design team. You may want to stress that an important part of this activity is for the design team to work together to make these decisions, design a raincoat for Joe, and show how to find the area of the raincoat. Be sure students know where to find the tools they will need.

Design Teams Solve the Raincoat Problem. Display the Math Practices page from the Student Guide Reference section. Tell students the class will revisit and discuss the Math Practices expectations after students have solved the problem and had a chance to write an explanation.

Distribute copies of the A Raincoat for Joe the Goldfish and the Centimeter Grid Paper Assessment Masters to each design team of students. Give students time to work on the problem.

Discuss Math Practices Expectations. Discuss each Math Practices Expectation taking notes on a display of the Math Practices Notes Master. The notes should help students understand what to look for when evaluating work from another group or revising their own. See Figure 1 for possible student-generated notes.

Ask:

What did you include in your work to show you know the problem? (Possible response: I showed a coat design and the area of the coat.)
What did you include in your work to show your strategy? (Possible response: I showed how I counted the square centimeters and described any shortcuts that I used.)
How did you check and show if your response was reasonable? (Possible response: I described how two group members counted the square centimeters and compared their answers.)
How did you show any mistakes or changes in your solution? (Possible response: I described the changes or mistakes and how I fixed them.)
What else did you include in your explanation? (Possible response: I described what the design team agreed upon, the coat design, and how the area of the coat was found.)
What labels should you include in your explanation? (square centimeters, Joe's coat, area of the coat)

Review Student Work. Choose and display a student work sample to model how to provide feedback and to clarify the Math Practices Expectations as they relate to this problem. Figures 2–5 show sample sets of work and sample feedback notes for two different students to help you facilitate this discussion. Masters for display are also available for the student work in these figures.

Give students a few minutes to look at the student work sample and then provide feedback on a display of the A Raincoat for Joe the Goldfish Feedback Box Master.

Ask:

How did [student/team name] go about solving this problem?

Do you think [student/team name] knows the problem?

What guided [student/team name]'s design?

Tell how [student/team name] checked if their answer was reasonable?

What feedback would you provide [student name]?

Based on [student name]'s work, what changes would you make to your solution?

Use student responses on the A Raincoat for Joe the Goldfish Assessment Master and the corresponding Feedback Box in the Teacher Guide to assess students' abilities to find the area of shapes with curved sides [E3] and use all the Math Practices [MPE 1–6].