4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
Ideas presented here for Robbie's Dilemma are based on Antoinette Villarin's
Area and Perimeter Lesson.
We worked on this activity for 3 math periods, as I had to address a lot of misconceptions.
I explained to my bilingual students that perimeter means the part of the crust "around the edge."
Next, I presented Robbie's thoughts about the area of his pizza, and asked the children to independently write their responses in their writing journals.
After sharing out ideas, thoughts, and uncertainties, I had the children work with their table groups to solve Robbie's Dilemma.
Each member of the team had a job.
1. The Construction Engineer
2. The Artist
3. The Recorder
4. The Lead Presenter
The children used snap cubes to determine how much "crust" was on each pizza.
The tricky question was, "Do we just count the cubes? Or do we count the sides of each cube as we turn the corners?"
At this point, the Artist and Recorder had to decide how to display information on their presentation poster and write how they solved the problem.
This Artist decided to cut the pizza area out of graph paper and glue it on their poster.
Other Artists decorated their pizzas with various toppings and Recorders wrote the group's solution about which pizza Robbie should buy to get the most cheesy stuffed crust around the edge.
Since it was almost lunchtime, we had to stop and continue our pizza projects another day.
One group realized that the pizza with less crust around the edge was actually a larger pizza and had more toppings. I told them they should try to persuade Robbie to buy the larger pizza, because he could sell some of it to friends and come out ahead. They decided to think about that one some more.
One difficulty my students had in proving their solutions was that they referred to one pizza as the "square" pizza and the other as the "rectangle" pizza. I still need to work on this vocabulary to help them see that squares are also rectangles.
Everyone had a lot of fun with the problem--and even the principal joined a group and interacted with us!
I created followup review lessons to keep these ideas about area and perimeter fresh in everyone's mind. The children always love to see their names in the math Problem of the Day, and it keeps them engaged.