Two of my classes are working with writing linear equations as part of our expressions and equations unit (6.EE.C.9). I’ve been wondering how far to take this concept since most of the problems I’ve seen are related to proportional relationships, I had students work with equations of the form y = ax+b and write equations of this form based on x-y tables and graphs.

After a couple days of working with tables and writing equations, I changed thing up for students with an activity that was simple, but ultimately really cool to witness as it was happening. Each student picked up an index card and made a flap near the top. After writing their equations under the flaps, students made an x-y table for their equation on the remaining space of the index card.

My example is on the left. As you can see, my students are still getting the hang of writing y = and using coefficients.

After modeling the process for students, I had the kids circulate the room and show each other their tables (the flaps covered the equations). After a couple minutes of questioning/discussion, students guessed the pattern (read: equations) they saw the card across from them.

I planned on the activity being a good 5 minute warm-up activity, but after I heard the math being spoken by students I let them circulate around the room for a good 15 minutes. I heard students debating about different equations that could fit the pattern, correcting errors in the x-y tables they saw, and telling students an “easier” pattern for the table they saw. For instance, one student was trying to throw everyone off and wrote 10x+2x +1. Another student puzzled with the x-y table for this equation for a few moments, then the student said, “Couldn’t the pattern just be you’re multiplying by 12 and adding 1?”

I liked this activity because at first it seemed simple, but the difficulty varied as students worked with various tables. I participated in the activity with students, then I used the activity as a lead in to finding the rate of change (slope) in x-y tables. I told students I was using a rule to figure out what people were multiplying by in any table I encountered.

This activity could easily be scaled up for 8th grade or high school for finding the equation of linear equations/functions. Alternatively, I could see myself using the structure of this activity earlier in the year to have students build skill with describing proportional relationships.

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I’ve always run this lesson as a “guess my rule” activity as a whole class or with the students sitting next to them, but I absolutely love the idea of having students up and moving around the class and the having the sort of discussions you’ve described.

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