Fostering Critical Thinking Tip #2: Area Outside the Box


I gave my 4th and 5th grade students the following math problem:

“Draw as many rectangles as you can that have the area of 18 square inches. You may use a calculator.”

15 minutes later all of my kids understood that there were three clear possible answers:

1 in X 18 in

2 in X 9 in

3 in X 6 in

But then something magical happened. I pushed them a bit harder and said that there were unlimited answers to this problem. “Can you find other answers besides these three? Don’t forget, you are allowed to use a calculator.”

Every student sat by her/himself and formulated an answer to the best of her/his ability. The students then met others in the back of the room to share their results and reach consensus (while the others continued to try to solve the problem near the board.) Eventually, all of the students realized that they could get answers like:

1.5 in  X 12 in

or

4 in X 4.5 in

My students developed much better mathematical understanding and reasoning skills through this critical thinking lesson. You see, I didn’t spoon feed them the answers. I gave them a challenge and let them figure it out with the help of their peers. The problem was challenging enough for about half my kids to get some correct answers initially on their own, and the other half to at least take a stab at it. Then, by collaborating, the entire class was able to wrap their brains around the idea. This is the direction education is headed with Common Core.