Where We've Been: Students have just had a refresher on the concepts of area and perimeter. They have also practiced applying the formulas for perimeter, area, and circumference to non-scale drawings with dimensions given.
Where We're Going: In the near future, we'll be using coordinate geometry to find perimeters and areas in the coordinate plane. But first we'll do some good old fashioned hands-on measuring with a ruler to find real areas.
So for this lesson I start by having students complete the APK_Measure Area and Perimeter student resource. I give students five minutes to complete the handout, and then I spend 5 minutes going over the correct answers.
For this section of the exercise, students receive a copy of the Measuring Area and Perimeter student resource.
Several things are intentionally left to student discretion. For example, students will need to decide how precise to be with their measurements and how best to organize and notate their work.
My job during this activity is to circulate the room looking for misconceivers and directionphobics. As usual, my approach is to ask open ended questions that force these students to confront their errors and move past them. The biggest issues tend to be lack of precision with measurement, incorrect or missing units, not using the correct height for triangles, and quitting on the hexagon figure (not seeing it as a composition of triangles and rectangles).
Now that students know how to measure a figure that already exist to determine its area and perimeter, the next level of cognition is for students to create their own figures that have specified areas and perimeters.
So giving them that chance is the Creating Figures to Specifications student resource.
I run this activity as a guided practice.
Starting with the first figure, I tell the class that they'll have x number of minutes to complete their drawings. At the end of the time, I ask for volunteers (or later on non-volunteers) to come to the document camera and argue for their figure meeting the specifications. Then I ask if anyone would like to challenge the validity of the student's claims. If applicable, I would also ask if anyone wants to show how they did it another way that is also correct.