Tomorrow, the Grade 6’s are participating in a Duct Tape Challenge. As part of our Science Unit on flight, the students have been challenged to design and build a flying device completely out of duct tape. My teaching partner and I decided to add a math component to this activity, and we’ve also asked the students to create a landing pad made out of chart paper with an area of 500 cm2. The students can now also apply what they’ve learned about area in math. This is an exciting activity, and the students and teachers are both looking forward to tomorrow.
This morning though, my teaching partner came into my class as soon as she arrived, and she was very concerned. She said to me, “When we spoke on the weekend, we said that we wanted the landing pad to be 5m2, but we only asked students to create one that’s 500 cm2?” My response was, “Isn’t that the same thing?” Well no, it actually isn’t. Then she sat down and explained how squared units change things.
I was getting so confused though. Yes, if I picked the dimensions of 10 cm times 10 cm (for 100 cm2) and 1 m times 1 m (for 1 m2) could see the difference, but what if I picked 50 cm and 2 cm for both options. If 1 metre equals 100 cm then why wouldn’t 1 m2 equal 100 cm2? I knew that my teaching partner had to be correct, but I wasn’t seeing the difference. It was then that my teaching partner approached the Learning Resource Teacher and one of the Grade 8 teachers to help explain the rationale for why 100 cm2 does not equal 1 m2. To get 1 m2, you need to multiply 1 m times 1 m, which is like multiplying 100 cm times 100 cm. I guess that the 5 m2 that we wanted as the area for our landing pad would actually be 50 000 cm2.
To help illustrate this abstract concept to me, these two teachers tried to make the comparison more concrete. The Grade 8 teacher drew a diagram on the board of a rectangle, and told me that this was a square of carpet. It was 1 m by 1 m. She said though, that she wanted to find out the area, but as cm2. The Learning Resource Teacher then jumped in and explained that it’s easier to make the conversion of units first instead of later. He then got me involved: converting 1 m by 1 m to 100 cm by 100 cm. The use of the visual, the real world application, personal involvement in the solution, and the conversion initially instead of afterwards, helped me understand something that was first so confusing for me.
While I certainly learned something new in math today, I think that even more importantly, I learned something new about teaching math. We need to take the time to simplify complex operations. We need to make abstract concepts concrete for students. We sometimes need to work with numbers as well as visuals. We need to take the time to ensure that all students understand what’s being taught, and not just say that they know. I may have known that my teaching partner was correct, but if it wasn’t for a number of teachers that took the time to show me what this really meant, I still wouldn’t understand this concept any more than I did before the day began.
How have you “re-framed” concepts in math to be sure all learners experience that aha moment? How do these strategies transfer to other subjects you teach?
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