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An interactive math experience · Grade 8

What IS a
function,
really?

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.

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The Two Pillars

Built on two radical ideas

Students learn math best when they struggle productively with meaningful problems — not when they're handed formulas to memorize.

01

Building Thinking Classrooms — Peter Liljedahl

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.

02

A growth mindset in math — inspired by Jo Boaler's research

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

Seven tasks. One big idea.

Each task is a low-floor, high-ceiling problem. Everyone can start. No one finishes easily. Every one opens up deeper.

TASK 01

A shape is growing

Discover linear functions through a visual growing pattern. Build a recipe that predicts any step — even step 1,000.

TASK 02

Is it actually a function?

Sort relations into functions and non-functions. Discover the vertical line test. Master domain and range — by arguing, not memorizing.

TASK 03

Maya's mystery rental

Three clues. Two unknowns. Three different student methods. Which do you find most elegant — and why?

TASK 04

A function in four outfits

Match stories, tables, graphs, and equations. Discover that a function is one idea wearing many faces.

TASK 05

The slope playground

Predict before you play. Then drag sliders and tell stories that match negative slopes, zero slopes, steep slopes.

TASK 06

Linear, or something else?

Three scenarios. Reason first, calculate second. Discover why "growing" doesn't always mean "linear."

TASK 07

Your turn: create

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.
Thinking is the point — and so is defending what you think.
— our classroom motto

For teachers

How to run this

The app is one HTML file. No account, no login, no installation. Works on any browser, any device.

  1. Form visibly random groups of 3 Use playing cards, a random name generator, anything visibly random. Do this every lesson.
  2. Give each group a vertical whiteboard Or chart paper on the wall. Vertical. Non-permanent. One marker per group. Students stand.
  3. Project one task at a time Don't race ahead. Each task is rich enough for 15–30 minutes of real thinking.
  4. Don't answer. Nudge. The hint buttons are your model. "What do you notice?" "Will that work for step 500?" "How do you know?"
  5. Consolidate at the end Compare group boards. Ask: "How are these the same underneath?" This is where the big idea lands.

A note on pacing

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.

Ready to think?

No account. No login. No installation. Just open the app and start wondering.

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