The release of the new IM curriculum for middle school is huge. Most of us have been salivating over the release for months, and it’s finally here.
In my 8th grade math class, I realized that several of my students were still struggling on solving multi-step equations with rational numbers. I went into Unit 4 looking for something that might help, and I found it in Section 6: Which Would You Rather Solve?
Students had to choose 3 equations (without solving) that they would classify to be the “least difficult” and then 3 that they would classify to be the “most difficult”. Once they did this task on their own, they had conversations in their group about which equations they chose for each category and why. I did a quick “no tech” poll under the document camera to help me figure out what types of problems to focus on that day in our VNPS groups:
If you’ll notice, I didn’t use the words “least challenging” and “most challenging”. That’s not a knock against the IM task, but I overheard the word “easy” A LOT in their group conversations.
Aha moment – What a great opportunity to help my students reframe the word “easy” after this excerpt from Chapter 2 of “Becoming the Math Teacher You Wish You’d Had” by Tracy Zager :
Reframing “easy” (“I know how to do this”) to “familiar” was incredibly powerful for me last year. I realized this task was a great opportunity to push that discussion and involve my students. So, back to the poll. I’m going to try to recreate this conversation – it went a little something like this:
Me: “Talk to your group and discuss what you notice about the equations we predominantly felt were most ‘familiar’ – equations “d”, “i”, and “j”. What made them seem familiar?”
~~multiple group discussions involved the word “easy” – I picked the table that seemed to use it the most often.~~
Me: “Table 3, talk to me about what you noticed about those 3 equations.”
Table 3: “They were all the easiest equations to solve.”
Me: “Say more about what made them seem ‘easy’ to your group.”
Table 3: “Uhhh. We just knew how to do them. You just do distributive property and solve them.”
Me: “Ah – so you noticed they all had distributive property in them. When did you learn to do equations with distributive property?”
Table 1: “Last year – we did A TON of equations with distributive property.”
Me: “So would you say those are more familiar because you learned and used distributive property last year?”
Table 3: “Yeah! That’s why we picked them.”
Me: “…..what about equation ‘a’? That’s got distributive property in it. Why didn’t you choose that one?”
Table 3: **silence and stares at each other.**
–> I gave some serious wait time here
Me: “Everyone talk in your groups about why you think Table 3 didn’t choose equation ‘a’ – pick someone to share out. ”
**waiting… waiting… waiting… I’m noticing that Table 3 students are still looking at each other mouthing “I don’t know” while other groups are pointing and nodding. Most of the other groups see the connection. I find it interesting that Table 3 can’t quite see it yet. This reminds me of when I’m looking for my phone and I can’t see it, but my son can point right to it and it’s right under my nose.
Me: “Table 7 – what do you think?”
Table 7: “Equation ‘a’ has fractions in it, but the 3 that we all picked didn’t. Fractions might have made it seem harder.”
Me: “Table 3 – was that it?” **Table 3 talks for a second – lots of nodding.”
Table 3: “Yeah – the 3 we picked for ‘familiar’ had easier numbers to deal with than that one.”
Me: “So let me ask the room – is that why you didn’t choose ‘a’ for the familiar category?”
** A lotta nods. **
Me: “So what if we took a field trip t-”
Random Student yells: “YES! Field trip!”
Me: *grin and playful eye roll*
“…so what if we took a hypothetical field trip down the road to the elementary school and walked in on a 2nd grade class. They’re learning to add things like 3 + 6 and 10 + 5 and 2 + 9. Would you consider that to be ‘easy’ math?”
**a bunch of nods and “DUH, Hedge” glances at me**
Student in the back: “Adding is easy.”
Me: “…how long have you been adding numbers like that if you started in 2nd grade? Do the math in your groups and let me know.”
***I hear students counting up and having conversations like: “so starting 2nd grade, then 3rd, 4th, 5th, 6th, 7th, 8th… so six years?” “Yeah, six years.” “Is it six or seven?” “Is that what she wants to know?” “I don’t know – say it and see what she says.” “Why don’t YOU say it?” “…because you’re taller.” –I love middle school kids.–
Random student: “Six years.”
Me: “Does that sound about right? That you’ve been adding numbers like that for about six years?” **I get nods.** “Do you think it’s easy for the 2nd graders who only learned how to count up to ten in 1st grade? And NOW they’re just now learning to count past ten? Do you think it’s easy for them? ”
Student in the front: “…probably not.”
Me: “Then why is it easy for you?”
Student in the back: “We’ve been doing that kind of stuff for a long time.”
Me: “… so you’re more familiar with it?” *nods*
Me: “How long have you been doing equations like the equation ‘a’?”
Student from Table 3: “We started that with you this year.”
Me: “So you’re less familiar with it than the other equations you chose for this category?” *nods*
After that, we had a conversation about making a purposeful shift away from what Tracy calls “thorny words” because of the impression it gives us when when we aren’t fast/easy at a particular topic. I reminded them about my own issues on my pathway to learning to love calculus (big conversation with them on Day 1 that I bring back up every time they’re feeling uneasy with a topic in class). But I also talked about how much I lean into that discomfort with calculus and how I have to remind myself about my journey with more familiar areas of math (like stats). I think it’s really important for me to always remind students about my own struggles, failures, and discomforts with math. I’ve done that for years because I don’t want them to think I only teach math because “I’m good at it.” If you know my story, you know that’s NOT how I found myself on this whole “teaching” pathway.
NOT. AT. ALL.
After we talked about the “familiar” section, we talked about the “challenging” section and those became our VNPS equations. Before we jumped into them, however, we did a little more work going back to how the “familiar” equations and “challenging” equations had similar characteristics and structure. This whole “notice/wonder” discussion allowed me to create some connecting equations to bridge the familiar equations to the challenging equations. Every time I overheard “easy”, I would obnoxiously sing, “Familiar!!!”
That day’s exit tickets confirmed that this 30-minute on the fly discussion and equation work was well worth the time. In the remaining days, I heard students self-correct each other when they heard/said “easy” or “difficult”.
Student A: “This is easy!”
Student B: **intense stare** “… it’s familiar…”
Student C: “This is too hard…”
Student D: “It’s not hard, it’s just less familiar right NOW….”