The calendar worked out such that I was scheduled to introduce lesson 1.3 on a Wednesday, which meant only 45 minutes of instruction.

**Here are my thoughts before the lesson: **

**This is my debrief from that first day:**

**After lesson 1.3, day 2:**

**Period 2:**Super chatty and unfocused during the WU (also I spent some extra time teaching/practicing English words and pronunciation for exponents), so we only had about 10 min in groups. Most groups had good discussions, but not a lot of crystallization and clarity on the big questions of the day.

**Period 3:**Pretty stuck on the explicit equation. One group wrote the recursive as previous*2, and when I said there should be an equals sign in front, someone else suggested Current=previous*2. Another group said current*2 but we didn’t get a chance to discuss what should go in front.

**Period 5:**Two groups got 3*2^t. Or rather, two kids got that; I’m not really sure how well they were able to explain it to their group members. No one had a recursive equation.

**Period 6:**Everyone was super confused by the explicit equation. However, a lot of groups had decent recursive equations, and we had a pretty good discussion at the end of class comparing the various recursive equations and collectively deciding that both Current=previous*2 and Next=current*2 are correct, and that you have to specify Initial=3.

**After lesson 1.3, day 3, which you will see was a rather eventful day for me:**

**Period 2:**….had quite a bit of disruption at the beginning of class. However, once we moved to another room they were actually quite lovely and had some great discussions in their groups. This is the class that was already behind, so our end-of-class discussion was just about how we can represent the doubling of the dots using either addition or multiplication. I honestly need to think over the weekend about how I want to proceed with this group.

**Period 3:**This class is always a bit of a struggle, and the lack of structure from being relocated to another room definitely did not help. Some of the groups made tables where they drew arrows to show the multiplication by 2 between rows. I asked them how we might represent this repeated multiplication and a few thought of exponents, but they’re still not super clear on how and why their equations might be correct.

**Period 5:**A couple of kids got 3*2^t, and we sort of talked about it at the end of class, but the discussion was rushed and I know a lot of kids aren’t comfortable with it. Not a lot of recursive equations, and I’m wondering if I need to do more to review/teach the English vocab words “next”, “current”, and “previous”. With this class, I’m sort of debating between doing Guided Notes vs. some sort of card sort similar to what I’m doing with period 3.

**Period 6:**This is the class that had a good discussion on recursive equations yesterday. Today I really pushed them to focus on the explicit.

**That last email was after a long Friday! The next email was sent two days later, on Sunday night:**

Here are my finalized plans for tomorrow, and an overview for the coming week.

Tomorrow:

**Period 2**

My WU for the sheltered classes reviews the vocab “current” “next” and “previous”. These English words have been barriers to students’ ability to create recursive equations.

Period 2 honestly still needs independent work time in groups, so that’s what I’m giving them.

**Period 3**

I’m doing a card sort with students’ equations from last week. I’m going to ask them the following three questions in their groups:

1.Sort the cards into two piles:

**recursive equations** and **explicit equations**

- Decide which equations accurately describe the pattern of growing dots.

3.**Make your thinking visible:**

__Draw pictures__ and __write words__ to explain ** why** your chosen equations accurately represent the pattern of dots.

I’m hoping that after this sorting activity we’ll be able to have a productive class discussion with STUDENT ideas and reasoning taking center stage.

**Period 5**

I’m going to have them make posters showing their thinking and multiple representations. I’m hoping that the conversations students have making these posters will diffuse more of the understanding around the explicit equation, and that the WU might help support the recursive equation.

**Period 6**

A card sort focused on the explicit equation, possibly followed by making posters.

On Wednesday I’m going to use an Illustrative Mathematics lesson to discuss representing addition of signed numbers on the number line. https://im.openupresources.org/7/teachers/5/2.html

I’ve mostly formatted the lesson for myself, but still need to finish the HW. This lesson starts with a “Which One Doesn’t Belong?” as the Warm Up. Tuesday’s lesson will be entirely dependent on what happens tomorrow (probably some combo of discussion/notes/posters), but I’m going to introduce the WODB structure in Tuesday’s WU. This is a great structure to promote discourse with a low entry-point. See here http://wodb.ca/ for tons of examples, and check out the hashtag #WODB.

I don’t know how helpful my card sorts will be for other people since they’re very specific to the equations that my students came up with.

## 2 thoughts on “MVP Lesson 1.3”