Their Work vs. My Work

“Always start by celebrating their work!” I love that bit of advice that my math teacher gave us and hope to remember to focus on their work when I am a full-time teacher. I am learning how important it is to let it be their work instead of mine. I need to let my students give me their strategies to do a problem, rather than only offering them an “official” solution. We learn by doing, and that applies to thinking as well. If I do not give them a chance to figure things out for themselves, they won’t learn how to think critically. My job is to teach children to think for themselves, not mimic me.

One of the fun things we have been doing in my math class is to see how many different ways a math problem can be done. For instance, we were given the problem 12 x 15. Because we had been practicing mental math, simplifying calculations so we could do the problems in our heads, I approached this problem using this same concept. I remembered that when you multiply a number by 10, you just need to add a 0 to that number to come up with the answer. Thus, 12 x 10 = 120. That left 12 x 5 to be solved. I knew that 5 is half of 10, so I just divided the 120 in half and added the 60 to the 120 and got 180. It was that simple!

Others in my class did it differently but used similar mental math methods. Some multiplied 15 x 10 to get 150. Then they multiplied 15 x 2 to get 30 and added it to the 150 to get 180. Another started out the same way with 15 x 10, but then added 2 x 10 and 2 x 5 to get 30. Again, it ended up the same, but the process was longer. Even longer was the FOIL method, but it worked as well: (10 x 10 + 10 x 5 = 150) plus (2 x 10 + 2 x 5 = 30). One in our class even did the traditional place value multiplication method and multiplied 12 x 15 in her head. She began multiplying 2 x 5 to get 10 and then carried the ten and did mentally what most write on paper.

We even made arrays in a lattice model, also called a four-square model. We multiplied the numbers similar to a FOIL method, but in a four square place value format.

To make a long story short, I know this sounds complex, but it was actually quite enlightening to see how many different ways a small class can solve the same problem. The key is to let the students think about it first, and then have them share their different solutions. Students learn from students, and again we celebrate their work!