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A Grade 8 functions unit redesigned from the ground up — where students don't mimic procedures, they notice, wonder, argue, and revise. Because thinking is the point.
The Two Pillars
Students learn math best when they struggle productively with meaningful problems — not when they're handed formulas to memorize.
Students work in randomly-assigned visible groups on thinking tasks — not mimicking tasks. They use vertical whiteboards so their process is public. Teachers don't rescue or give answers; they give nudges.
This app replicates those conditions digitally: progressive hints that never reveal, multi-path solutions that defront the classroom, and tasks designed to spark argument.
Struggle isn't a sign you're bad at math — it's how the brain builds new connections. Speed and correctness aren't the goal; depth and reasoning are. Drawings, diagrams, and spatial thinking count as real mathematics, not just a crutch for the "textbook version."
Students here are explicitly invited to notice, wonder, predict, revise, and defend — the moves of actual mathematicians. For deeper reading on this philosophy, see Jo Boaler's Mathematical Mindsets (2016) and the free resources at Youcubed.
What's inside
Each task is a low-floor, high-ceiling problem. Everyone can start. No one finishes easily. Every one opens up deeper.
Discover linear functions through a visual growing pattern. Build a recipe that predicts any step — even step 1,000.
Sort relations into functions and non-functions. Discover the vertical line test. Master domain and range — by arguing, not memorizing.
Three clues. Two unknowns. Three different student methods. Which do you find most elegant — and why?
Match stories, tables, graphs, and equations. Discover that a function is one idea wearing many faces.
Predict before you play. Then drag sliders and tell stories that match negative slopes, zero slopes, steep slopes.
Three scenarios. Reason first, calculate second. Discover why "growing" doesn't always mean "linear."
Invent a story for a function. Design a deceptive graph. Predict the future — and question your own prediction.
Here, the right answer isn't the point.— our classroom motto
Thinking is the point — and so is defending what you think.
For teachers
The app is one HTML file. No account, no login, no installation. Works on any browser, any device.
This isn't a 45-minute lesson. It's a 5–7 day unit. Each task can expand to fill a full period of rich discussion, or contract into a 20-minute warm-up.
Resist the urge to race through. The whole point of a Thinking Classroom is that depth matters more than coverage.
If a group finishes early, their next task is to find someone else's method and explain it back — not to move ahead.
No account. No login. No installation. Just open the app and start wondering.
Enter the classroom →