Welcome to my 6th grade math classroom! Today we are learning the algorithm for fraction division with one of my favorite math manipulatives, play-doh!
I’m using the fantastic Illustrative Mathematics curriculum through Open Up Resources. We’ve been doing some work on conceptual understanding of fraction division using diagrams, but today we are building upon the previous lessons and working toward the algorithm. The warm up from Illustrative Mathematics, Unit 4, lesson 10 asks students to work with partners on these questions:
Students then compare answers for each question to see that dividing a number by a is the same as multiplying by 1/a. This worked great with groups that had answers, but several of my students are coming in with gaps from 5th grade, so we had to review that 12 groups of 1/3 meant that you had 1/3 twelve times. So I had to scaffold here a little bit but most groups were able to see the connection. But what about dividing by 1/a?
From the warm up, I asked students to think about the work that they had done and write on their whiteboards, “What does 12 divided by 3 really mean?” (without using the word division.) I listed their explanations on the board using their names:
We talked about how these were great ways to explain division, but we were going to focus on the last one as we worked on division today: How many groups of a number are in another number?
Illustrative Mathematics then goes into a nice sequence of dividing by unit fractions. What is 6 divided by 1/2? 1/3? 1/4? any unit fraction? We’ve done quite a bit of work with tape diagrams, and I decided to mix things up by using play-doh! I needed a manipulative that could easily be divided up into different units. After some ground rules (don’t eat the dough, people), I gave a little context also: We have 6 balls of dough (yes, I said “balls” in a 6th grade class, which is always a risk.) We need 1/3 a ball of dough to make a pie. How many pies can we make?
I will post some more pictures throughout the day, but I saw some fantastic representations. We did this with 1/2 and 1/3. As we worked on 1/4’s, most students no longer needed the dough, and were intuitively able to see that dividing by 1/4 was the same as multiplying by the reciprocal. Yeah for SMP!
But what about non-unit fractions? Come back tomorrow to see part 2 of this lesson!