Wow! As the first quarter of teaching wraps up for me at school, I have finally had some time to sit and reflect further on number talks.

I have been consistently doing them anywhere from one time to three times a week depending on our schedule. I have had several challenges and several successes during the past 5 weeks and I want to share some of these now.

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Number Talks with Addition

I have taken my number talks in two different directions depending on my classes. As I have discussed before, I began with addition problems, mainly focused on problems that could employ strategies such as rounding, moving numbers flexibly (for example 19+ 34 is the same as 20 + 33), and breaking down numbers into tens and ones.

Here are some highlights of the boards from some of the number talks with addition. I spent 6 weeks doing addition with my students. By the end, students were getting much more comfortable using strategies besides the traditional algorithm and were bringing up the same methods during each number talk. On the other hand, I would say only about 60% of my students have shared their strategies. I have been pushing new students to try and explain their methods, but it seems like the same students are constantly wanting to share. This is still a challenge that I am facing and I hope that I can work towards pushing these quieter students to eventually share their ideas.

9th grade class:

10th grade, Period 2

10th grade class, Period 1

10th grade class, Period 4

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10th grade classes--Multiplication Number Talks

In my 10th grade classes, I decided to take my number talks in the direction of multiplication. I decided to do this for a few reasons. First, in these classes we are doing a unit on area and volume and I thought that doing problems with multiplication could fit nicely into making number talks fit a little more closely with the curriculum. This coming week I plan on introducing the area model for multiplication as I think that it can connect some of the things we have learned about area with the number talks.

Secondly, I decided that multiplication would be a nice transition from addition--it can be a little more challenging, but I was hoping that students would be able to use some of the strategies that they had for addition with multiplication--primarily seeing numbers as tens and ones and being able to break up numbers to make the problems more simple.

So far, I have seen students using strategies such as those mentioned above and have been impressed with students' thinking about the multiplication problems. In my first set of number talks on multiplication, not one student mentioned the traditional algorithm, although I'm sure some students still used this method and it has come up several times since then. I presented the problems such as

Below are some of the boards with the number talks with multiplication.

10th grade class, period 1

10th grade class, period 2

So far I have not used multiplication problems with two double digits and that is my plan for this coming week. I think that this will lend itself to introducing the area model for multiplication as well.

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9th grade class: Percentages

For my freshman class, I decided to do percentage problems with number talks. The reason I chose this is because they are currently in a unit on probability. I thought this would be a good way to strengthen their idea of percentages and flexibility in working with percentages. Additionally, when we did percentages last year at Fremont, my students seemed to be scared of percentages initially, but I think that my students definitely had a breakthrough in thinking about percentages during these number talks. I am excited to see how my current students are thinking about percentages and if they have a similar experience.

My freshman were pretty nervous when they first saw me put up a percentage problem and there were many groans around the room. However, I think that some students have really started to catch on to some of the strategies of their classmates. I had one number talk where 5 different students shared their ideas (see below). Again, a challenge is still getting all students to participate in sharing their thinking. I have not yet done a pair share with my students and I think this is something I want to try this week. Or, another idea would be to have them record their own strategies and collect them so that I can see how individual students are thinking about these problems as well.

Below is one of the number talks done with percentages: