It’s been far too long since I last blogged…so now I have an epically long one to write. Sorry! Feel free to skim 🙂

I have been looking forward to teaching the 4th grade multiplication and division unit all year. Finally, over February break I was able to analyze pre assessment data and make some plans for the unit. I was stoked to begin the unit by working with factors. When I taught this unit last year (for the first time) I hadn’t realized how important the factor standard was. I taught them the vocabulary and we used it, but it wasn’t until we began working with multi digit multiplication and division problems that I realized the importance and benefits of being able to manipulate numbers by using their factors.

So off to the blogosphere and Twitterverse I went. I got a ton of great ideas from Simon Gregg. If you don’t follow him or know his blog, you should check it out (http://followinglearning.blogspot.fr). I was going to start with cuisenare rods. I had never thought to use them to explore equal groups that make a larger number. We definitely didn’t use them last year to find the factors of a number. So we started by exploring. It was super fun! Kids love using the cuisenare rods to explore. They are pretty and fit together in satisfying ways. My students immediately assigned values to the rods, which was fine and actually necessary for our investigation of factors. I asked them to start with the 10 rod and see how many different single color walls they could make that would equal 10. Then we tried 9 and then 7. We discussed what was different about the walls of those three numbers and students were starting to recognize that some numbers have lots of combinations and other numbers don’t really have any at all. I told them they were finding factors and asked them to think about how they might define a factor. We continued our investigation for another day and they’re definitions changed gradually and eventually they were able to explain what a factor was in their own words. Cool! I thought we were in a great place, and ready to move on!

Next up, we were going to explore the Sieve of Eratosthenes. This was an activity I did on paper last year, but this year I was inspired to try a life size version thanks again to Simon. It was fun, and we made a great design on the floor, but it took forever! And it wasn’t permanent. So while we had some good discussion during the activity, not everyone was involved and then we had to pick it up and couldn’t go back to look at the patterns again another day. The goal of doing the Sieve is to find the prime numbers. We had been able to do that, so overall I thought it was a success.

Now it was time for the activity that I had looked forward to the most! I wanted to create a factor forest with my class. And we would be able to put it up on the bulletin board and parents would be so impressed at parent teacher conference time, go me! If you have not seen the factor forests created by Simon’s students you need to check them out (http://followinglearning.blogspot.fr/2016/02/art-for-maths-sake.html) they are gorgeous!

I started by showing them these inspirational pieces of artwork. We talked about the math that they represented. My kids thought they were the coolest, I totally had them hooked! We made a plan for our forest. They wanted it to be nighttime, so we would use black paper. They wanted the primes to be stars and the number one would be an owl. They were itching to get started, so I passed out the paper, students picked numbers and away they went. There was about 1 minute of excitement and then groans of annoyance and then the whole class seemed to revolt and give up. It was crazy! I was running around helping students, and they were creating these tiny little trees that could barely be seen and they were mad and didn’t want to do anymore. We stopped and went to lunch. I looked through their artwork, bewildered by the lack of effort in a project that they were so excited about 30 minutes ago. I ~~complained~~ processed with some of my coworkers and that’s when it hit me. It wasn’t the art that was frustrating them, it was the math. So I took a moment to reflect on my whole carefully planned week.

I quickly realized that I had planned a week of activities, NOT a week of learning. I had carefully thought out and taught what students would need to know in order to DO each activity. I hadn’t thought about a progression of *understanding*. And I certainly hadn’t left anytime to be responsive to what the kids needed. Wow, not the teacher I strive to be.

I spoke to the students about their frustration with the factor forest and told them that it was my fault. I hadn’t spent enough time on the math, and so the representation was confusing. We needed to back up. There was a great convo happening on Twitter about the Sieve and I decided to go back to that. I wanted to stay with the 100s chart representation for awhile. It’s familiar and the students enjoyed looking for patterns. I showed them several different representations of the 100s chart and we did some great noticing and wondering. First we looked at this piece of artwork by Paul Ashwell (paulashwell.co.uk/prime.html )

It was a great notice and wonder. Students found patterns and then connected the patterns to numbers. They saw the representations of different numbers and began talking about figuring out the number by multiplying the symbols. This is some of their thinking.

At this point I talked to my lovely math coach Sarah Caban (https://mathontheedge.wordpress.com) and she suggested that I try some number talks using Jo Boaler’s circle number representations from Week 1 of Inspirational Math (https://www.youcubed.org/week-of-inspirational-math/).

I showed a few “numbers” at a time, not the whole chart. These image talks were a hit!

Students could “see” the multiplication of factors within the image. This is when they started to make some real connections. One student even exclaimed, “Hey! These are like those trees!” Yay! They were finally getting it.

We are finally in place where students are seeing that they can manipulate their numerical representations based on what they “see” for groups. I think this will be immensely helpful when we get to multi digit multiplication and division. Next week I’m going to attempt some number strings and I am curious to see if they will use primes and factors as strategies for solving. Wouldn’t that be cool!?

I love your reflection on planning Chrissy. It is so easy to get caught up in the shiny things, to provide opportunities for our students to have fun “doing” math, that we can easily loose sight of the progression of learning. Thanks for sharing your process as you work through the planning cycle. Your kids are doing amazing things!!

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Thanks for reading Abby!

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It’s lovely to see you using all these approaches, Chrissy. You’re right, it’s the learning that counts. Factors so useful to understand, like you say, but it’s a new step at this age. I don’t know what the best path through is. Certainly the Cuisenaire rod “walls” gives a really hands-on understanding of how certain numbers “fit in” to other numbers.

For the forest, we’d got to grips with the idea of prime numbers first, mainly through that Cuisenaire activity. (When Prime Climb came out we had that up on the wall as a frieze and referred to it lots). Practically I then had the students with whiteboards first. After some trees together, I got them to write their chosen number at the bottom, and then said ‘what 2 numbers multiply together to make that bottom number? – then draw the 2 branches. If one ends in a prime it got a flower, if not, again, what 2 numbers multiplied together to make that one? Etc.

Only once they’d got it on the whiteboard did they go to the “artistic” stage.

It happens so often that I have to say, oops, I’ve gone too fast, or too far. But then I guess it’s part of adventurous and ambitious teaching that that should happen!

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Thank you so much for the thoughtful comment, Simon! I am looking forward to doing the artistic representations again, with a bit more scaffolding and now that we are in a better place of understanding. It has been an insightful journey. Factors are so fascinating!

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