I am a little bit late–sorry! I forgot a few important pictures that I needed in order to properly share. Hopefully you’ll still read (and learn with us!). 🙂
There’s not a lot to explain behind this one except that I wanted to continue to focus on the idea of a fraction being EQUAL pieces, not just the number of pieces in the denominator. As you can see in many of the post-its, most kiddos understand this when they partition the cookie cake for 4 people.
As I mentioned with a problem or two last week, kiddos are to have a basic foundation of groups and arrays to help them with further multiplication concepts in 3rd grade. We played a game called Circles and Stars last week, which is basically where they roll a dice twice, once drawing circles and then filling each with the 2nd number’s worth of stars. Then they figure out an equation to go with the model as well as how many stars there are altogether. I wanted to build on this idea and see what they’d do with a new problem. As is seen on their answers, they almost all drew circles with stars (or dots). I wanted to help them see the same idea as an array, as well, so I connected the equation to brownies (so they pan/array would make more sense).
Somewhere I had saved a picture of my original problem which looked like this (the purple writing on the chart): If I had a pan of brownies that had 7 brownies on one side and 5 brownies on the other, how many would I have? When I looked at the answers, I was completely baffled as to why so many had answered 6X2=12. We had a great decision about how they used 7+5=12 and then made a multiplication equation that matched. There were also some pretty interesting models/pictures of the equation, too, so I drew an array to show what I meant. Once they saw it, they could see what I meant, but we agreed that the problem I had written didn’t lead them to that understanding. I asked them to help me figure out how I could have better written the problem so that they could have seen what I meant. We worked to revise the question so it made more sense. This was a GREAT conversation both about math and revision, which is something Rm. 202 friends know happens ALL THE TIME, not just in writing. They did a super job of helping me redesign the warm-up so that it better matched what I wanted to know.
Now it reads: If I had a rectangular pan of brownies that had 7 columns of brownies on the long side of the pan, and 5 rows of brownies on the other, how many would I have in the whole pan? Draw a picture. Great work on the writing and the math, Rm. 202 friends!
We’re still working on many concepts all at once, and solidifying our understanding of them. Love my little speech bubble? We always talk about how the numbers in the problem scream at us to tell us which strategy is most efficient for them, so it just seemed fitting. 😀