We've been doing a lot of division lately and I began to notice that the preferred method is the traditional algorithm, mainly because that’s what parents are more comfortable with at home when helping with homework. Because of this, I was noticing that if students made a mistake in following the steps, they really didn't notice they were making a mistake, let alone that their answer was not reasonable. So, I decided to encourage more mental math. We did this through some number talks and the use of slates. In previous Number Talks, I didn't allow my students to write anything down to force them to do work mentally, however, for the division number talks (at least at first) I allowed them to write down their thinking on slates so they wouldn't confuse themselves. The only stipulation was that they weren't allowed to divide the “normal way.” No “houses!”
We started with smaller, simpler numbers: 25 ÷ 4. Here is a picture of their thinking:
|Molly began by saying, "I know that 4 x 5 = 20 , and that was too small, so I added another group of 4 to get to 24. Then, I knew I just had to add one more to get to 25. So I had 6 groups of 4 with one left over."|
Once some students saw how others were using basic facts to help them, they began to catch on. More and more students began volunteering their thinking. This is something we will continue to build a knowledge base of. My hope is that this will lead my students to a greater understanding of division and answers that are reasonable.
|Blake is one of my students that has an amazing sense of numbers: he does almost all of his calculations mentally. I always try to see what he is thinking to guide the other students.|
|This was a great example of two students building from something they already knew: multiples of ten. I love how one counted up from ten and the other counted down from 20!|
|We are really improving and they are finally telling me how much they love math!|