In my last post I spoke about the reasons for following the C.R.A model as math teachers when introducing new concepts/skills. I appreciate all the responses that I got through twitter: @darcmathcoach and I found that so many of you have the same philosophy.

I feel so strongly about this, that have dedicated this week and the next few weeks to model for my teachers here at Chattahoochee * HOW* to do this. This is only year 3 for me and as Marilyn Burns put it in a tweet “

*Math coaching is often a job without a clear job description.*“…BOY was she ever correct! I assumed that all the teachers in my building believed in the same mathematical practices as I did, but I have come to find out that they don’t. Therefore, a big part of my job is to teach them to be effective math teachers through discussion, planning, observations, modeling, etc…

I wanted to share some of these results from this week in the math lab:

This first video is from a 5th grade class that is about to delve into adding and subtracting fractions with unlike denominators. When I met with the teacher we discussed how she wanted to start this unit. She is new to 5th grade after teaching 3rd for a few years, and she wanted to start her students off with the idea of commons denominators, but she wasn’t sure how to do it. My suggestion was that we would let the students “play” with fraction towers before getting into the nuts and bolts of adding/subtracting fractions. She gave me a quizzical look, but agreed. Later on she came back and said,”I have a problem with the word play” I just asked her to trust me….

After our estimation warm up, I let the students know that they were going to be playing with some cool new math toys. They all lit up with excitement! **BUT**, I said, as you play, you must record at least 3 observations…..

If anyone had come in and observed, also what you see from the video, it looks as though they are playing without a purpose. By giving them directions to make observations, they became focused on what the fraction towers could do.

This young man wrote about the fact that the yellow and blue towers were equal, because they weighed the same! Understanding of equivalent fractions through play!

Can you believe it? This young lady came to the conclusion that 5/10 + 6/12 = 1 Wait a second, she didn’t make any common denominators using multiplication. Where is the “standard algorithm”? This is exactly what the teacher wanted to teach, and yet we didn’t do anything but let the students play!

I met with a 3rd grade teacher who was about to work on adding and subtracting within 1,000 and was concerned about how to teach borrowing without using the standard algorithm. My advice? Bring them in and we are going to let them play…

After making all these observations, I gave them a challenge: “Using only the blocks, no pencils or paper, solve the following 62 – 27” It was wonderful, the students discussed how they could take 7 away from the two single cubes. I heard things like: “let’s make a trade”, “we need to exchange a ten rod for 10 cubes”, “let’s take the two rods away first”, and “I know, get rid of the two cubes and cover up 5 on the rod to make 7″…awesome!!!!

I kept poking away at them asking very simple questions: “how did you do that?”, “why did that work?”, “can you show me what you did?” Their responses told me so much about where the lesson needed to go, as well as what lesson should come next. They did a few more and then I asked them if they wanted a “challenge”…YES!!! They all yelled…this is easy! I gave them 103 – 58, almost all of them did the same strategy. They started with 10 rods instead of 1 flat, and 3 cubes. They removed the 5 rods, then traded 1 rod for 10 cubes to get 13 cubes, lastly removing 8 cubes to get the answer of 45. But there was one young man who did the following…

Are you kidding me? He realized that if he removed 3 cubes from each number to get 100 – 55, he could see it better….wow. Conservation of numbers….understanding that the difference of two number is the distance they are apart on a number line and by shifting that distance, it’s easier to compute!

I met with both teachers later on to debrief about what they saw and noticed, and both were brimming with excitement. My advice was to continue this in small groups and to follow this simple recipe:

How can we…

- Model it?
- Record it? (with drawings and numbers)
- Use a number line?

One responded by saying that she had no idea that they could learn so much from just “playing” with manipulatives…

I just wish all math teachers knew this…