What we had in mind
Goals of this activity
Students will be able to...
This lesson helps students count large numbers of things by using the mathematical structures of area and proportionality. Students use a ratio table to keep track of their work as they count the number of tiles required to cover a floor, and the time required to put those tiles in place.
Set the stage for this lesson by talking with them about the context. Ask, If you were going to tile a floor, what are some things you would want to know before getting started?
Students begin by tiling a 4-square-foot section of floor. They are free to use the given tiles in any combination that will fill the section. Students estimate, then they calculate, the number of tiles required to for a 72-square-foot floor.
The tool students use for these calculations is a ratio table. There are many ways of working with this ratio table—all of them exploit the proportional relationship between area and number of tiles. For example, if a student knows that there are 16 tiles in 4 square feet, and that there are 48 tiles in 12 square feet, she may find the number in 20 square feet in any of these ways:
Look for different strategies that your students use—by examining their tables, talking with them, and by reading their written responses.
Observe student work both from the dashboard and by students’ sides as they work. Use the dashboard to keep track of student progress and to identify students to give individual attention.
Wrap up the lesson by drawing student attention back to the relationships in the ratio table. There are two sets of relationships that are important:
The constant of proportionality expresses this first relationship. Use the tables students produce at the end of the lesson to draw out conversation about the constant of proportionality.