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Teaching Math: A Video Library, K-4

Pencil Box Staining

Video Overview
Students in this lesson are working on a project to build and stain wooden pencil boxes. Students are faced with the task of finding out how much stain to buy from the hardware store and encounter several problems as they work with many mathematical ideas in the context of a real-world application. Each student receives an instruction sheet and each group receives a ruler, a calculator, and the wooden pieces needed to complete a pencil box. Students make and use estimates and actual measurements to find the surface area of some pieces of wood. As students use rulers to measure rectangular and circular objects, they have to decide on the degree of accuracy each situation needs. Calculators are used as needed to determine sums, products, and quotients. Some measurements result in fractional units, and students must decide whether to change the fractions to decimals or to approximate, because the calculators do not directly handle numbers involving fractions. Communication is emphasized as students clarify their thinking about mathematical ideas and situations. Students' answers are recorded on the chalkboard and the class finds that the recommendations differ. The lesson ends with students suggesting strategies for reaching consensus on how much stain to purchase.

Topics for Discussion

The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.

Designing Projects in Mathematics

  1. Projects allow for integrating many mathematical ideas and create opportunities for learning new mathematics. What mathematics was in this lesson?

  2. What connections were students making among the various mathematical topics?

  3. Identify the problems that students encountered as they tried to determine how much stain should be purchased. How did they deal with these problems?

  4. What other activities related to the pencil boxes could be planned for students? What mathematical connections could be emphasized in these related activities? What mathematics might emerge?

  5. What are some advantages and disadvantages of using projects in mathematics?

Organizing for Small-Group Work

  1. To what extent were students cooperating and communicating as they worked in small groups? What did you observe that makes you think this way?

  2. How did Mr. Levy develop and nurture the students' abilities to learn with and from others in this lesson? What were the characteristics of his interactions with the small groups? What questions did he ask? What statements did he make?

  3. Why do you think Mr. Levy assigned roles to each group member? Did the assigned roles work?

  4. In the lesson, one student said, "inFour 12s, that1s one side. . .then turn it over, same thing. . . .That's 96." Here the child is confusing perimeter and area. How did the other students in his group react to this explanation? What are some ways to approach this situation?

  5. Sometimes when students work in small groups, one person tends to dominate. Did this situation occur in this lesson? How would you ensure that this problem does not occur?

Extensions
Making Connections across the Curriculum

Think of and list additional connections that could be made from the pencil box project to other curricular areas. For example, purchasing the wood stain can be connected to economic issues of why it might be cheaper to buy more stain than is needed - buying something in a larger quantity is sometimes, but not always, cheaper. Students could research this economic issue for wood stain and for other consumer products. Developing Projects
Formulate "inauthentic" projects for elementary students that call for students to build or create or plan something real with tangible results. Then select one project to develop further, identifying the mathematical ideas that might emerge and the mathematical connections that could be emphasized. Investigate the use of computers for organizing and displaying data. Consider the advantages and disadvantages of different pieces of software. Discuss how to choose software to supplement mathematics lessons. For example, you can work with a spreadsheet program and specific graphing packages to investigate displaying data as was done in the video. Once you become comfortable using some of the programs, think of and list ways to integrate them into mathematics teaching.


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