SWBAT explain the connections between equivalent equations and between the equations and the structure they represent.

The structure of the figure is what determines the formulas for area and perimeter.

This lesson is meant to show students the relationship between different strategies for calculating the perimeter of a rectangle. In addition to strengthening their understanding of perimeter it also helps them develop greater flexibility in mathematical modeling (mp4). Students also use the structure to help them recognize the distributive property and strengthen their operational sense. My students often don't refine their methods to make them more efficient. This activity not only helps them see the connections between the operations, but also helps them recognize more efficient methods for calculating the perimeter.

20 minutes

In the warm up students are given a diagram of a rectangle labeled with it's dimensions (15 ft. and 10 ft.). They are also given four equations showing strategies for calculating it's perimeter.

P=15+15+10+10 P=2(15+10) P=2(15)+2(10) 50=15+15+10+10

Students are asked to describe what each number and variable represents in the figure. They are also given some "useful vocabulary" terms they might use.

If your students are anything like mine they will try to write one word answers, thinking they are supposed to "match" the correct term to the equation. We spend a moment discussing the difference between matching and describing. I may also clarify that I'm asking them to explain what the number or variable represents about the diagram.

The second expression may be harder for them, because they don't see a 2 in the diagram. I remind them that they might not see the actual number. I tell them if they can figure out why the two is there (and not in the first one) then they can explain what it represents.

Answers may vary. I have students share their possible answers.

30 minutes

For this activity I only use some of the sorting cards. I only give them the 18 cards that show the three strategies for calculating perimeter of the form:

P=l+l+w+w P=2(l)+2(w) P=2(l+w)

Students are asked to sort the equations into three different categories showing each of the strategies. As I circulate I make sure groups have read the directions. They may be sorting the equations that show different strategies for the same rectangle. If so, I direct them back into the directions.

Students are then asked to copy the strategies onto their paper and describe the math being done in the strategy and then explain why it works to find the perimeter.

Their homework is to then write 3 equations to show each strategy for calculating the perimeter of the given rectangles.

4 minutes

I draw a rectangle with dimensions 2x and 5 and ask students to write three equations to show each of the strategies for calculating perimeter (warm up matching expressions to model extension)