Stencilrama

Est. Class Sessions: 3

Developing the Lesson

Part 1. Liz and Diana's Stencil Border Data

Introduce Stencilrama Context. Refer students to the Stencilrama pages in the Student Guide. These pages begin by describing the process of making a border using stencils. Two girls in a classroom choose a design for a stencil, cut the stencil, and take turns using the stencil to start their border. The class wants to make borders of different lengths, so they decide to investigate how the number of times they use a stencil affects the length of the border. They collect data and record it in a data table. As you read, demonstrate how to make a stencil using the sample stencil. See Materials Preparation.

Discuss the variables in the investigation using Questions 1–4 in the Student Guide to prepare them to draw a picture of this investigation. Use Question 1 to discuss what variables the two girls compared in their data table: the Number of Stencils (N) and the Length of the Border (L). Question 2 asks what stayed the same or which variables are fixed as the girls made the border. In order to look for the relationship between the number of stencils in the border and the length of the border, the size and shape of the stencil must stay the same, there must not be any space between the stencils, and the orientation of the cards (either vertical or horizontal) must be the same each time. See Figure 3. Each time the girls colored in a stencil, they placed the index card vertically and marked the paper at the edge of the stencil.

Use Question 3 to discuss the procedure the girls used to collect the needed data. They made a border with 5 stencils, then measured the distance between their marks to find the length of one, two, four, and five stencils. Ask students how they can use this data to figure out how many stencils would be in a border used to decorate the top of the board (Question 4).

Ask:

What will you need to measure? (The length of the top of the board.)
Let's suppose the top of the board is 60 inches. How can you use Liz and Diana's data to figure out how many stencils are in that border? (Strategies will vary. I know there are 5 stencils in a 10-inch border, so I need those 5 stencils 6 times to make a 60-inch border. The 60-inch border would have 30 stencils.)
How many stencils are needed to make a 12-inch border? (According to the data, each stencil adds 2 inches to the length of the border. If there are 5 stencils in a 10-inch border, there are 6 stencils in a 12-inch border. I skip counted by two for each stencil until I got to 12 inches.)

Solve Problems Using Data. Ask students to work with a partner to answer and discuss strategies for solving Questions 5–8. As students are working, identify student strategies to discuss with the entire class. Look for a variety of strategies. Some students will skip count and others will reason from the information in the data table. See Figure 4 for some examples. Give each student materials needed to prepare a display of their strategy.

Discuss Questions 5–8 by asking the identified students to display their strategy for the class. Leave these strategies displayed around the classroom for the remainder of the lesson.

Ask:

Who would like to summarize [student name]'s strategy?
Do you think this strategy is efficient?

Apply Strategies. Follow up by asking students to use one of the strategies shared while discussing Questions 5–8 to solve Question 9 in the Student Guide.

Ask:

Did you use a different strategy than you used to solve Questions 5–8?
Did you and your partner use the same strategy?
Work with your partner to try another strategy to solve Question 9.
Why is it a good idea to have more than one strategy? (If you have another strategy you have a way to check if your answer is reasonable; some strategies are a better fit for a given problem.)

Ask a few students to share their strategy for solving Question 9 to prepare students to answer Question 10. In Question 10, students are asked to determine the number of stencils needed to make a border that is 51 inches in length. This is problematic because 51 inches is not evenly divisible by 2. Some students may decide that they need 25 stencils because 26 stencils would make a border that is 52 inches and therefore too long. Other students might argue that half of a stencil is 1 inch so a border of 251/2 stencils would make a border 51 inches long, the length of the board. Students are inevitably going to encounter similar situations when they are measuring the length of real locations in a classroom.

Some students may be distracted by the aesthetic and detail of creating the stencil and border. Ask students to keep the stencil design simple. You may also choose to have students simply trace the stencil outline to keep the activity moving and focused on the problem solving, and color the border pattern after the lesson.