^{th}grade students. “Who cares?” they asked. “Why is that so important?” It didn’t matter to them that the answers were different!

While reflecting on the day’s lesson that had not been as
convincing to my students as I had hoped, I started playing with snap cubes and
realized that I could show them each step. Maybe this would help them clarify
their thinking about why multiplication and division had to be done before
addition and subtraction.

I wrote problems on a sheet of paper and projected them on
the screen. “How can I build 4?” I asked. “Show me on your desk.” The students
responded and each connected 4 snap cubes on his or her table. “Now show me

*3 times 3*,” I continued. “And what does*2 times 2*mean? Then what if I divide the*2 times 2*in half? Now what does it look like?” The class followed along with me, constructing each step on their desks.
“Alright,” I paused. “Now what if we combine each of our
steps? What do we get when we add the

*4*plus*3 times 3*plus*2 times 2 divided by 2*?” The children carefully combined each step by adding 4 + 9 + 2 to get 15. Then I went back to the order of operations rule. “If we wanted to force the addition of 4 + 3 before multiplying by three, then we could use the parentheses,” I said and built it on the overhead for them to see. Suddenly, the students burst forth with an understanding, “Ohhhh!” I chuckled. “Okay, now you try one on your own."
I gave them 16 ÷ 2 + 3
x 2—the parentheses were added later when we debriefed the problem.

Here Rigoberto is finding 2 x 4 + 2 + 3 x 3. "That's 8 plus 2 plus 9," he stated triumphantly. "That's 19."

Several were starting to get it! I know I will need to review these concepts to keep them alive for the children, but at least we have a starting place from which to build.

Several were starting to get it! I know I will need to review these concepts to keep them alive for the children, but at least we have a starting place from which to build.