Algebra students have been solving multi-step equations. Quite a great, semi-sneaky way to review all sorts of topics students should already be “fluent” in – operations with rational numbers, the concept of “isolating the variable”, properties of equality, and so on.
I presented students with this simple equation:
Rather than rush to strategies to solve for a, I asked students to tell me the story behind this equation. “Once upon a time…”
Students’ first inkling was to describe half of something:
EX) “I have half of an apple… no… half of an… armadillo!”
They had “half of” all sorts of appropriate and inappropriate things. I asked, “Do you have half of just one of those things…? How many halves do you have?” Hmmm…
Next, students seemed to notice the other decimal values and opted to talk about money:
EX) “So, something costs five cents each…” Whoops. Why does that ALWAYS happen?
We got our place value straightened out pretty quickly:
EX) “No wait, that’s FIFTY cents each…”
I heard a story about Hawaii:
EX) “So I’m going to Hawaii by bike and it costs eight dollars and seventy-five cents…” Wait… waaah? Gotta love 8th graders!
I heard a story about underpaid restaurant staff:
EX) “A waitress makes fifty cents an hour and gets $8.75 in tips. If she gets $13.25 at the end of the day, how many hours did she work in this awful restaurant?”
I heard a story about gum:
EX) “I buy some packs of gum for fifty cents each, and a container for $8.75. If I pay $13.25, how many packs of gum did I buy?”
I heard a story about lemonade:
EX) “Some little kids have a lemonade stand. They charge fifty cents for a glass of lemonade. A lady feels bad and gives them $8.75 for no lemonade. How many glasses of lemonade did the kids actually sell if they made $13.25?”
What I can’t capture in a blog post is the energy in the room. Even for goofy problems, or problems with wrong thinking, students OWNED these stories. Turning a strategy on its head and ASKING FOR the word problem rather than GIVING the word problem and asking kids to write and solve an equation was a simple, novel, and apparently unexpected strategy. When we solved the equation (using several different, valid methods), the solution had meanings that students had assigned to it, whether it be gum, lemonade, or hours.
I’d recommend the 5-minute (story) time investment. 🙂