I believe in a problem-based approach to learning math (I brought IM to my school, damnit!), but for some reason whenever Unit 4: Linear Equations and Systems of Equations rolled around, I felt the need to deviate from IM’s curriculum.
I couldn’t quite envision how it would work: the equations seemed to get too complicated too quickly. It didn’t seem like kids would get enough practice. My students were still struggling with integers, fractions, and two-step equations—how would they be able to make sense of these equations? I realize now, as I type, that ultimately I didn’t think kids would be capable of grappling with/reasoning about equations. I trust kids to reason with problems in context, but the abstractness of solving equations made me doubt their capability.
For several years, instead of doing the IM lessons on linear equations, I would use just use IM’s hanger diagrams to get my students started but then quickly resort to showing my students how to solve equations procedurally.
This year, I chose to “stay true” to the curriculum.
Here’s how it went:
- My students really benefited from all of the problems asking them to analyze and compare solutions. They seemed to enjoy digging into the fake students’ work: They reasoned, made connections, and learned from these examples. I will never skip problems like these again. It’s a highly effective way to push kids to make sense of more advanced algebraic reasoning.
An example from Lesson 3:
- Lesson 5: Small group for kids who needed more time to make sense of how apply their reasoning about hanger diagrams to reasoning about equations. (This set them up well for Lesson 6 because which offers them the choice to continue working on simpler equations.)
- Lesson 8: Created a second version of the card sort that includes some balance diagrams and simpler equations with friendlier numbers
3. Kids did seem to need more practice to build fluency than IM offers, but maybe that’s because we’re still in a pandemic and absences were wild during the omicron surge. In any case, we added in a day of “Building Thinking Classroom” thin-slicing practice and a day of “Sage and Scribe” practice where partners could choose equations with different levels of difficulty.
4. At the end of lesson 6, I asked students to share their tips for solving equations. This led to a fantastic anchor chart that supported everyone throughout the rest of the unit. This was SO much better than the direct instruction I used to do, but still made the main skills explicit.
By the end of the unit, most kids still couldn’t consistently solve many of the equations with fractions. They have so much unfinished learning around fractions and I just haven’t been successful at weaving it into 8th grade math in a way that sticks or builds proficiency. What should I try next?