Week 4 Lesson Preparation--'What Happens to the Area?'

The lesson I focused on this week for Color Tiles can be found under the Grade 6 component and is entitled “What Happens to the Area?” The objective is to introduce or expand a student’s knowledge of area. The NJ Core Content area is 4.2.6D 1. “Select and use appropriate units to measure angles, area, surface area, and volume.”
Students at the outset are instructed to create a 3 X 4 rectangle using any color combination of square pieces. The discussion focuses on the length and width of the creation to introduce how length multiplied by width equals the area.
Students can then be paired or be allowed to work individually to create their own geometric constructions using the introductory exercise as a guide. Students are asked to begin with their own design and then double, triple, and quadruple the length and width of their initial design. For example, if someone began with a design of two squares next to each other (length of two and a width of one), they would have to extend this to a length of four across and width of two. This activity is extended to both tripling and quadrupling the initial construction to see if doing so affects the total area in the same ratio.
As students perform this activity, they are asked if doubling the length and width doubles the total area. The same is asked of tripling and quadrupling. As the activity is extended out to the several constructions, they will hopefully realize a pattern develop and discussion can ensue to generalize the findings.