I am a true believer that content coaching is a necessity in the improvement and sustainability of math instruction, however we all know that finding time to even use the restroom during the course of the school day is close to impossible! So how do we find time for these important conversations to happen and more importantly, we need to be fortunate enough to have a position in our school that does just that, coach.
Last week, my class was working on finding fraction/percent equivalents using a 10 x 10 grid. They did great with the fourths and eighths, but then we hit 1/3! As I walked around and talked to the students, I saw a range of strategies: shading one out of every 3 squares, shading one out of every 3 rows, then squares, and some just knew that three 33’s was as close as they could get with whole numbers and had just shaded 33. No matter which strategy they chose, the “leftover box” was leaving many perplexed.
After quite a bit of struggling with what to do with this leftover box and some happy to just settle at 1/3 = 33%, Nancy (our math specialist, former 3rd grade teacher, and partner in crime with all things math) came into the room. She helped me by chatting with a group about their thoughts on what do with this 100th box. Class, unfortunately, had to wrap up to go to lunch, and I wasn’t comfortable that some students had had sufficient time to think about it, so I left the class with that leftover box as food for thought that night.
Over lunch, Nancy and I were talking about what she had heard from the students and she made the statement, “It is amazing how they don’t make connections to all of the sharing brownie work we did in 3rd grade when trying to count off by 3’s in the grid..” For those who use Investigations, you will know the exact lessons to which she is referencing, for those who don’t you can probably infer the context 🙂 We discussed the difference of the contexts for students, the array work they do in 4th grade and then tried to figure how to make that connection for my afternoon class. Tall job for the 15 minutes left of lunch, AKA speed eating.
I typically start my class with some type of number talk, so we sketched out a number talk that focused on the brownie problems of years past. Lunch ended and when the class came in the classroom, they headed to the carpet for a number talk.
I did the following sequence of problems, sharing strategies as we went:
How can four people share one brownie?
How can four people share 6 brownies?
How can four people share a pan of 21 brownies?
They did an amazing job and were very confident in their strategies and I definitely put them into a “fraction state of mind.” We then went into finding our percentages and even the strategies for finding the percents equivalent to fourths and eighths seemed smoother and then when we hit 1/3 and that leftover box was much less mysterious. There were still a few who struggled but I definitely could see more perseverance and entry points at problem solving. They seemed to make a connection to the brownie problems at the beginning of the lesson.
This entire rambling of my thoughts really boils down to one thought….Improving instruction is about finding time to have those meaningful math conversations. Had I not had that conversation with Nancy and changed my number talk for the second group, the lesson was going to have the same fate as the first. That conversation helped me make math connections that I could then make my students. Would I have loved to have more time to think out this lesson and retry it the next day, of course, but did Nancy and I improve it…absolutely!