Set Expectations for Communicating Your Solution Strategies. Advise students that they are going to share and discuss their solutions to Explore Questions 5 and 6. Ask a student to share her solution and explanation to Question 5. Refer to Math Practices Expectation 1 on the Math Practices page in the Student Guide Reference section. See Figure 6.
- What is Question 5 asking you to find out? (Question 5 is asking me to predict the heights of different fourth-graders using the data our class collected about height and arm span.)
- Did [student name] show that she knows the problem and the important information?
- How do you know? What did she show or say?
Referring students to Expectation 5 on the Math Practices page, ask:
- How did [student name] predict the heights of the different fourth-graders? (Some possible responses: she used our class graph; she found an arm span of 53 inches and went up to the cluster of data and found the height to be about the same as the arm span; she showed on the data table that the arm span and height are about the same, so the height of the new fourth-grader is about 53 inches.)
- Did she show how she arrived at the solution? Are there any steps missing?
- Did she show how she used the graph or table? (Possible responses: she showed how she traced her finger on the graph; she drew dotted lines on her graph, showing how she used the graph; she made notes on the table; she described the pattern she saw in the numbers.)
- Would someone who has never seen this problem be able to understand what she did from her explanation?
- Can you understand her thinking?
- Can you suggest any improvements to her explanation?
Ask students to look at their own responses to Question 5 and decide if they made clear that they knew the problem and showed how they answered it. Encourage students to revise their work based on Problem Solving Expectations 1 and 5 and the class discussion.
Pairs Review Work. Now ask student pairs to swap answers to Question 6 and review each other's answers using Math Practices Expectations 1 and 5 and the following questions.
- What is the problem my partner answered? (Where on the graph will the first-graders and the kangaroo data go using the graphed data in the problem?)
- How did my partner solve this problem?
- What improvements should be made to make my partner's explanation clearer?
While students are reviewing their partners' work, circulate through the room looking for student solutions to share and discuss with the rest of the class. Look for student work that meets the Math Practices Expectations and work that has room for improvement. Review and revise those selected pieces of student work as a class.
Observe the Peer Review of Question 6 to assess students' abilities to identify the important information in a problem [MPE1] and show their work [MPE5].
Give students a copy of the Arm Span vs. Height Feedback Box Assessment Master to attach to their lab packets. Ask students to review the Expectations on the Feedback Box to see that they have met those expectations.
Use the Arm Span vs. Height Feedback Box to document progress on the following expectations:
- E5.
- Make a point graph using ordered pairs.
- E7.
- Read a table or graph to find information about a data set.
- E8.
- Model real-world situations with bar and point graphs.
- E9.
- Make predictions and generalizations about a data set using a median.
- E10.
- Make predictions and generalizations about a data set using a data table and graph.
See Figure 7 for sample Feedback Box.
The Workshop in Lesson 6 provides targeted practice.
Distribute and assign the More Arm Span vs. Height Data Assessment Master. Ask students to respond to the Journal Prompt as they complete their work. When appropriate, discuss in small groups and then as a class.
Use the More Arm Span vs. Height Data Assessment Master with the Feedback Box to document progress on the following expectations:
- E6.
- Find the median of a data set represented in a table, graph, or line plot.
- E7.
- Read a table or graph to find information about a data set.
- E8.
- Model real-world situations with bar and point graphs.
- E9.
- Make predictions and generalizations about a data set using a median.
- E10.
- Make predictions and generalizations about a data set using a data table and graph.
See Figure 7 for sample Feedback Box.
The Workshop in Lesson 6 provides targeted practice.
Challenge students to complete the Journal Prompt describing where data for an orangutan's arm span and height would lie on a graph in relation to the class graph. Ask students to find information on orangutan's arm span and height and check their prediction.
An orangutan is about as tall as a tall fourth-grader but its arms are longer, sometimes reaching an arm span of 80 inches or more. If you measured the height and arm span of an orangutan and plotted the data on your class graph, would the point be to the right or left, above or below your class cluster? Explain your answer.
