Summary:

Armed with rulers, calculators, and pricing information sheets, students must estimate and measure surface areas of their unassembled rectangular and circular wooden pencil box pieces. Since some of their measurements are fractional units, students decide to round off measurements or convert common fractions into their decimal equivalents so that their calculators can be used. The context of this problem is making a decision about how much stain will be needed to cover the surface area of twenty-six completed boxes. This activity is full of rich mathematical experiences for the students.

Standard Connection:

(Practice Standard)—The first Common Core Practice Standard—Make sense of problems and persevere in solving them—is exemplified in this lesson. Notice how the students demonstrate their problem sense-making ability as they discuss their measurement proposals and carry them out. In particular, three girls, confused at first, struggled to make sense of the measurement units to use and calculations required to solve the problem. Despite a few miscalculations, they persevered and arrived at a quantity of stain to request. With context-rich problems, given without prescribed solution methods, students can develop the "habit of mind" to stick with problems when solutions are not easily obtained.

(Content Standard)—Measurement and Data 4.MD—is the domain that best encompasses the content of this lesson. Students "solve problems involving measurement and conversion of measurement from a larger unit to a smaller unit." Students demonstrated that they could apply area formulas for rectangles in real world settings.

Questions to Consider:

If you were the teacher in this context, what would you do to get these girls closer to solving the problem? How do you help your students persevere in problems, particularly when students seem lost or frustrated? How can you avoid temptation to simply give the answer, and instead build students' repertoire of problem solving approaches and habits of mind?

1. Make sense of problems and persevere in solving them

4.MD Measurement and Data