Lemonade Stand

Est. Class Sessions: 2

Developing the Lesson

Part 1. Using Strategies to Develop Multiplicative Reasoning

Explore Strategies. Read the recipe for homemade lemonade on the Lemonade Stand page in the Student Guide. Tara and Peter are faced with a problem: they need to know how many lemons to buy for the number of pitchers of lemonade they plan to sell. Discuss with students how to determine the number of lemons Tara and Peter will need.

Ask:

What strategies can you use to find the number of lemons Tara and Peter will need for each pitcher of lemonade? (Possible responses may include: I can draw a picture of each pitcher and then draw the lemons I need for each. I can add 8 lemons together for each pitcher of lemonade. I can make a data table to see if I can find a pattern.)

Assign Questions 1–2 to student pairs.

After students have completed their work, ask:

What did you include in your story and picture so that others will understand your thinking? (Possible response: Our picture showed four pitchers of lemonade. We drew 8 lemons for each pitcher.)
What number sentences did you write for your picture? (Possible responses: We used addition and wrote 8 + 8 + 8 + 8 = 32. Or, we used multiplication and wrote 4 × 8 = 32.)
What do each of the numbers in the addition sentence stand for? (Possible response: The 8s tell the number of lemons needed for each pitcher of lemonade. There are four of them because Tara and Peter are making four pitchers. The 32 tells the total number of lemons they will need.)
What do each of the numbers in the multiplication sentence stand for? (Possible response: The 4 tells how many pitchers Tara and Peter are making and the 8 tells how many lemons they will need for each pitcher. The number 32 is the total number of lemons they will need.)

Identify Patterns in a Data Table and Bar Graph. Direct students to the Making Lemonade pages in the Student Activity Book. Begin by reading the short vignette about Tara and Peter's choice to use a data table to find out how many lemons they would need for different numbers of pitchers. After reading the vignette ask students to complete Question 1. They complete the Lemonade Stand data table in Question 1A. A completed table is shown in Figure 1.

In Question 1B, students look for patterns in the data table. These patterns reflect the multiplicative structure of the problem. The discussion of these patterns gives students opportunity to use words that describe multiplication.

To guide the discussion ask:

What patterns do you see in the data table? (Possible responses may include: The number of pitchers doubles each time starting with 1 pitcher. The number of lemons also doubles starting with 8 lemons. You can find the number of lemons by multiplying the number of pitchers times 8.)
What addition number sentences can you use to show the number of lemons you need for 2 pitchers of lemonade? (Possible response: You can add 8 + 8 = 16.)
When you add 8 + 8 = 16, what do each of the numbers represent? (The numbers all stand for lemons, 8 lemons + 8 lemons = 16 lemons.)
What multiplication sentence can you use to show the number of lemons you need for 4 pitchers of lemonade? (Possible response: 4 × 8 = 32)
What does each of the numbers in the number sentence 4 × 8 = 32 represent? (The four is the number of pitchers you are making and the eight is the number of lemons you need for each pitcher. The thirty-two is the total number of lemons you need for four pitchers.)

After students have had time to explore the patterns in the data table ask them to complete Questions 2A–D. These patterns can also be represented in a graph. Questions 2A–C guide students through the process of making a graph using the data in the Lemonade Stand data table. Students should use the Lemonade Stand graph that is already started on the last page of this lesson in the Student Activity Book.

Since students will later convert this bar graph to a point graph, it is important to check that their graphs are correctly labeled and scaled, as shown in Figure 2. Use the display of the Lemonade Stand Graph Master to lead a discussion that will help students assess the accuracy of their graphs.

Ask:

Are the axes scaled appropriately?
Are the lines, rather than the spaces, numbered?
Is each axis labeled with the name of the variable and a letter to stand for the variable?
Do the bars lie on the vertical lines rather than between them?
Did you use a ruler to draw the sides of each bar?
Are the bars the correct height?
Are the bars on the correct lines?

When they have completed their graphs, ask:

Describe the graph. What patterns do you see? (Possible response: The bars look like you are going up stair steps. Each bar is twice as tall as the bar before it. There are spaces that do not have any bars drawn in.)

After discussing the patterns on their graphs, ask students to use their graph or their data table to answer Question 3.

To answer Question 3 students often sketch the bar for six pitchers, making its height midway between the bar for four pitchers and the bar for eight pitchers. They can also add the height of the bar for four pitchers to the height of the bar for two pitchers. Students can also use their data tables to solve this problem by adding the number of lemons needed for two pitchers to the number of lemons needed for four pitchers (16 + 32 = 48 lemons). They can also use repeated addition, adding 8 + 8 + 8 + 8 + 8 + 8 = 48 lemons. Using these or other methods, students should find that Tara and Peter will need 48 lemons for six pitchers of lemonade.

Student Guide: 282

Answers