Boo the Blob

Est. Class Sessions: 1

Developing the Lesson

Compare the Shapes Made with Six Tiles. Give each student six square-inch tiles and refer them to the Boo the Blob page in the Student Guide. Introduce the context by reading Question 1 and by displaying the shapes Mara made with the six square-inch tiles. Give students a few minutes to make a shape with the six square-inch tiles and then ask students to discuss Question 2 with a partner. Add student-created shapes to the shapes already displayed and work with students to write a class response to Question 2. Students should notice that the area is always the same even though the shapes are different. Some students may notice that the distance around each shape (perimeter) is different but that observation is beyond the expectations of this lesson.

Find the Area of Boo the Blob. Challenge students to find the area of Boo the Blob in square centimeters on the Boo the Blob Changes Shape pages in the Student Activity Book. Allow them to use any method but emphasize the need for accuracy. One method is for students to count square centimeters as they did in the previous lesson. They should find the area for the entire blob, including its mouth and eyes.

There are a variety of ways to collect large amounts of data to find the median. However you manage to collect and organize the class data, students should be able to see all the data collected, see the data in order, and the order should stay intact so that the data can easily be revisited. Here are some possible solutions:

Collect approximate areas in a list. First lightly cross out the highest and lowest measurements. Then cross out the second highest and second lowest measurements. Continue to cross out one measurement from each end of the data until you are left with one value—the middle value.
Have students write their approximate areas on a self-adhesive note and post them in a line in order from smallest to largest. When finding the median, move the highest and lowest out of the original line of data.
Have students write their approximate areas on index cards large enough for others to read. Holding the index cards, students line up from smallest to largest. When finding the median, have the student holding the largest area and the lowest area sit down until the median is found.

Averages. The meaning of “average” is slightly different in ordinary English than in mathematical English. In ordinary English, average usually means the “add-up-all-the-numbers-and-divide average” that we all learned in school. Mathematicians call this number the mean. Mathematicians also recognize other averages, or measures of central tendency. One type of average accessible to young students is the median, or middle value. Primary students can understand the middle value in terms of being the “fairest” among several trials. We specifically used three trials in this activity because it makes finding the median easy.

Compare students' results for the area of the shape labeled “Boo.” List all the answers from smallest to largest on a display. Record each student's measurement, including duplicates. They should cluster around 20 square centimeters—the approximate area of the shape. Most answers will probably fall between 19 and 21 square centimeters. Since this method for finding the area of curved shapes does not give exact answers, expect some measurement error in the results. Let students give reasons for the different numbers.

Here are some sample questions to guide discussion:

Is there only one right answer?
How can you decide which answers are reasonable and which are not?
Why is it a good idea to check your answer against those of other students?
When should you try to recheck your answers?

Explain that we should expect to get results that differ a little bit. Scientists address this by making multiple trials when they do an experiment. They then deter- mine representative—or average—values for the data. Since there are different measurements for the shape, the class needs to decide on a good representative value. Have students share their ideas on how to agree on one representative measurement for Boo the Blob.

Tell students that the middle measurement is a good representative value. Remind them that the class's measurements have been collected and recorded in order from smallest to largest. Demonstrate how to find the median or the middle measurement. See the TIMS Tip for strategies to collect and find the median of the students' measurements. If the list has an even number of measurements, two will be in the middle of the data. The median is the value halfway between these two numbers. For example, if the two values are 19 square centimeters and 20 square centimeters, the median is 191/2 square centimeters.

Find the Area of the Mystery Blobs. Once students have agreed on Boo's approximate area, the class can form groups of three to measure the mystery blobs in search of the disguised Boo. Encourage students to count square centimeters as accurately as possible so they will be able to identify Boo correctly.

Have each student record his or her own measurements for the area of Shapes A, B, and C in the Shape vs. Area data table on the Boo the Blob Changes Shape pages.

Ask groups to discuss the following:

Did all three members of your group get the same area for each shape? Why or why not? (No, we estimated the pieces a little differently.)
How might your group agree on one measurement for the area of each shape? (Find the median value.)

Demonstrate Finding the Median Area. Ask group members to share their data and record it on their data tables. Then ask one group to share their data for Shape A as asked in Question 1. List the three measurements from smallest to largest on the board.

Ask:

How do I find the median or middle measurement? (Toss out the high and low measurements.)

Ask the remaining groups to discuss and answer Questions 1 and 2 with their group members. Circulate among the students to verify that students are identifying the median appropriately. Once students are confident with finding the median, have them repeat this procedure to find the median area of the other shapes and record it in the table as directed in Question 3. The last row in the table will be completed later in the lesson (Question 6). Discuss and share the median area of each shape.

Check to see that students have not confused the median with the second measurement. Sometimes the median might have occurred in the second trial; however, this will not always be the case. If students have difficulty identifying the median, randomly list measurements in groups of three on the board. Use a number line to help them identify the median for each group of three.

Blob A has an area of 25 square centimeters; Blob C has an area of approximately 16–17 square centimeters; Blob B, which has an area of approximately 20 square centimeters, is Boo.

Decide Which Shape Is Boo. Direct small groups to decide which shape is Boo (Question 4). Before students start writing their explanation, refer students to and display the Math Practices page in the Student Guide Reference section. Focus their attention on Math Practices Expectation 5, Show my work.

Make a list of student responses after you ask:

What types of words should you include in your answer to Question 4 to be sure you are showing your work? (The median area of Boo, the median area of the Shape, how these measurements compare, a description of how you decided, and a description of why you eliminated the other shapes.)

What if none of the medians of the mystery blob match Boo the Blob exactly? It is possible. The class can either decide that none of the mystery blobs are Boo or they can decide that the blob with the area closest to Boo is a Boo in disguise.

Focus attention on Math Practices Expectation 6, Use labels.

Ask:

What labels should you include in your explanation? (square centimeters)

Give students a chance to write their own explanation to Question 4. Circulate among the students and look for student work samples to share with the class.

Display each student work sample and use the following questions to help provide feedback and discuss expectations:

Read [student name]'s explanation. In your own words tell us how the student decided which shape was Boo.
What needs to be clearer?
What labels did he or she use?