Summary:

At the Bowman School in Lexington, Massachusetts, Mr. Levy's fourth graders are faced with the task of determining how much stain they need to purchase to stain their handmade pencil boxes. Several measurements are fractional units, so some students decide to round off measurements or convert common fractions into decimal equivalents so as to use calculators. Since pricing information is given in cost per square feet, students also need to convert their square inch measurements into square feet equivalents. One group of boys ingeniously decides to take four rulers, tape them together to form a square, place their disassembled pieces on this structure, and compute their estimates. Mr. Levy expresses his hope that this activity reinforces procedural skills while demonstrating understandings of concepts like the area model of multiplication, surface areas formulas, and conversions of measurement units.

Standard Connection:

(Practice Standard)—Common Core Practice Standard #5—Use appropriate tools strategically—is possible in this class because Mr. Levy did not prescribe how to solve the problem, but rather left choices for tools and strategies to the students. Most students make the expected tool selections, and strategically use rulers, calculators, and surface area formulas to solve the problem. But, one group of boys cleverly decides to create a "square-foot" tool to aid them in estimations. They use an appropriate tool—their rulers—but in a strategically innovative fashion. Realizing that the answer only needs to be an estimate, the boys place all major pieces on their square-foot structure. They calculate the area of one side, and then double that calculation. They multiply the result by twenty-six (the total number of class pencil boxes). Now, all that is left is to determine how many quarts and pints of stain this estimate requires.

(Content Standard)—Measurement and Data 4.MD—is the domain that best encompasses the content of this lesson. The boys solve the problem involving measurement even though they did not convert their measurements from a larger unit to a smaller unit. They clearly demonstrate that they can apply area formulas for rectangles in a real world setting.

Questions to Consider:

What do you think the main objective of Mr. Levy's lesson was? Do you think it was reached? What kind of assessment would you design given what you believe to be his primary objective?

5. Use appropriate tools strategically

4.MD Measurement and Data