Stencilrama

Est. Class Sessions: 3

Developing the Lesson

Part 2. Your Stencil Data

Make a Stencil. In Question 11 in the Student Guide, students are directed to make their own stencil using the steps outlined by Liz and Diana earlier in the lesson. Share the design and stencil examples that you have gathered to inspire students. Give each student pair a 3 × 5–inch index card to make a stencil. Remind students to keep the stencil shape simple.

Draw a Picture. Using the sample stencil you prepared, model the procedure of making a border across a long piece of paper. Use a stencil five times, marking the paper at the edge of the stencil. Point out those variables that need to be kept fixed. Tell students they will compare the number of stencils and the length of the border by measuring the length in inches of one, two, four, and five stencils just as the girls did in the vignette in the Student Guide.

Ask students to describe what they are going to compare by drawing a picture on the Draw section of Stencilrama Lab page in the Student Activity Book. Students should label the variables and show the procedure for making and measuring the border. Two student drawings are shown in Figure 5. In both drawings, students clearly labeled the variables of length and number. Students also indicated they will make small marks after they use the stencil each time so they will not leave any gaps between each stencil pattern. Nick's drawing shows that he will hold his index card vertically each time he uses the stencil. Sevara's drawing shows she will always hold hers horizontally.

Review student drawings as you circulate. Check to see that students:

label the variables;
show the procedure for making and measuring the border;
indicate that the unit of measure is inches.

Make a Stencil Border. Students are now ready to make a border with their stencil. Distribute inch rulers, markers or crayons, and the long pieces of paper you prepared for each pair of students. Direct students to use their stencil to make a border of five stencil patterns. You may need to revisit Liz and Diana's procedure as described in the Student Guide.

Collect Border Length Data. After students have made their border, they are ready to measure the lengths of one, two, four, and five stencils. Ask students to record their measurements on the data table on the Stencilrama Lab pages in the Student Activity Book. There are two extra rows on the data table to give students an opportunity to collect other data if they wish. A sample data table is shown in Figure 6. The stencil used to make the border represented in this sample data table is placed on the paper vertically. The data will not always be this exact. Measurement error or stencil placement error may lead to some variation in the measurements.

In this lab students are focusing on using patterns in a data table and are not being asked to make a graph. Asking students to reason from the relationships represented in the table supports students reasoning strategies for the multiplication facts. This also gives students yet another strategy to check for reasonable responses. A line graph would be an appropriate model to represent the relationship between the number of stencils and the length of the border. Students will learn how to make, read, and analyze line graphs in Unit 10.

Assess students' abilities to measure length to the nearest inch while they are collecting border length data [E9].

Show How to Reason from Data. Students are now ready to look for patterns in their data to make predictions and solve problems. Ask students to work with their partner to complete Questions 1–5 in the Student Activity Book. Remind students to use the strategies they discussed and displayed earlier in the lesson. With these questions, students will show different reasoning strategies to find the length of a border. While students are working, determine if students oriented their stencil along the 3-inch side or the 5-inch side of the index card. As students have completed these questions, pair them up with other students who oriented the stencil the same way and ask these students to compare their solutions and reasoning strategies. Ask each group to pick their favorite strategy used in one of the problems to share with the rest of the class. As each group shares their favorite strategy compare the strategies.

Ask:

Why is this your favorite strategy?
Is this strategy similar to any of the other strategies?
How is this strategy different?
Do you think this strategy is efficient?

Solve Problems Using Data. Working with their partner once again, ask students to answer Questions 6–10 in the Student Activity Book. Circulate among the students listening for reasoning strategies and providing support to students as needed.

Ask:

Do you know the length of a border with [one] stencil? How can you use that information?
Look at your data table. Where would this data be on the table?
How could you use repeated addition to solve this problem?
How could you use multiplication to solve this problem?
How is Question 9 different than the others? (I need to find the length of a border with 10 stencils rather than the number of stencils to make a border a certain length.)
Do you have to think about this problem differently? How? (Yes, I can think addition or multiplication. For example, if I know a 1-stencil border is 5 inches long, a 10-stencil border is going to be 50 inches long. In the other problems I had to think backwards using subtraction or division.)
How could you check to see if your answer is reasonable? (Possible responses: Solve the problem another way; make the stencil border and measure; extend the data table.)

After most students have completed Questions 6–10, display the Math Practices page in the Student Guide Reference section.

Ask:

Which Math Practices did you focus on while solving Questions 6–10? (Possible responses: know the problem, find a strategy, show my work, and use labels)

Ask students to now look back over Questions 6–10 and check to see if their answer is reasonable [MPE3]. Prepare to gather students' ideas on a piece of chart paper.

Ask:

What did you do to check to see if your answer is reasonable? (Possible responses: Solve the problem another way; make the stencil border and measure; extend the data table.)
What did you do if your answer was not reasonable? (Possible response: I checked my calculations [MPE4] and then tried the problem yet another way.)

Now that students have a variety of strategies to solve multiplication and division problems ask students to answer Questions 11 and 12 with a partner. In Question 11 students are asked to determine the number of stencils needed to make a border for the front of their desk. Since student desks in a class are generally consistent, students can compare solutions and strategies to check that their answers are reasonable. In Question 12 students choose a location for a border and will need to show how they checked for reasonableness.

Remind students to use the Math Practices page in the Student Guide Reference section as they work. Provide time for students to talk about their solutions before they begin writing. See the Meeting Individual Needs boxes for strategies you can use to get students talking about their problem solutions.

To minimize congestion while students work on Question 12:

choose locations in different areas of the room;
ask some students to work on Question 12 first and then Question 11;
take students outside or to a larger room to choose a location for their border.

Vary the complexity of Question 12 by varying the location of the border. Write each location on an index card with notes to yourself about the complexity on an attached sticky note. Distribute the locations based on students' needs. Do not reveal the differences in complexity to students.

Identify locations that measure as multiples of 3 or 5.
Identify locations that do not measure as multiples of 3 or 5.
Change the location slightly: length of board to perimeter of board.

Talking about Problem Solutions. All students need to talk about their solutions before putting them in writing or some other published form. Talking about their solutions helps them organize their ideas. Provide opportunities for students to talk through problems, especially those involving multiple steps.

There are several strategies you can use to get students to talk through their solutions before writing them down. One way to meet individual needs is to vary the way students report their solutions. Some students are prepared to record their solutions in writing. For others, the writing is an obstacle, but their solutions should still be shared in some way. Below are some strategies for varying the product or supporting students before they record their solutions in writing.

Ask students to report to another group how they solved the problem. Then have them record what they reported in writing or using other media, such as a video recorder.
Ask students to record explanations on a video recording device. Students can then record their work in writing as they play these back. The video-recorded explanations can be made available for others to review and evaluate.
Have students display their solutions on large pieces of chart paper for others to see. Students discuss the problem during the creation of the poster and their work becomes easily accessible for others to review and evaluate.
Have each student group explain their solution to you or a classroom helper before they start to write their explanation. Ask clarifying questions and encourage students to describe what the numbers mean in the context of the problem.