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Lesson plan · Grade 11 · 50 minutes

Undo Machine

I can compose functions, write and verify an inverse by undoing steps in reverse order, read inverses as a reflection across y = x, and restrict a domain to make a function one-to-one.

▶ Open the tool Download the tool
Standard
F-BF.A CCSS-Math
F-BF.B CCSS-Math
Shape
Explore first
Grouping
Pairs on devices, with whole-class pauses.
You need
The tool on the projector and on student devices. Graph paper.
Tool
curioclass.org/tools/undo-machine/
  1. Hook5 min
  2. Explore17 min
  3. Make sense10 min
  4. Apply13 min
  5. Exit check5 min

Before class

  • Open Workshop with an empty floor.
  • The 8 test tokens are −6, −2.5, −1, 0, 0.5, 2, 3 and 9.
  • Keyboard: select a card and press [ or ] to move it.

Hook 5 min

  1. "You put on socks, then shoes. How do you undo that?" (Shoes off first.)
  2. "Functions work the same way. Today you build machines and the machines that undo them."

Explore 17 min

  1. On the projector, tap Multiply by a, then Add a, and set them to 3 and 4. The strip reads f(x) = 3x + 4.
  2. Build the undo line in the "obvious" order: Divide by 3, then Subtract 4. Press Run. "2 came back as −0.6667. Why?"
  3. Pairs swap the two undo cards and run again. All 8 tokens come home, and the strip shows g(x) = f⁻¹(x).
  4. Pairs build three of their own top lines, then the undo lines, and check with Run and Send my number.
  5. Pairs build Add 3, Square and look at the verdict: Can't be undone as built. "−2 and −4 both come out as 1."

Make sense 10 min

  1. "Why must the undo line run in reverse order?"
  2. Open Graph: f solid, g dashed, y = x dotted. Press Mirror. "Why is the inverse the mirror image across y = x?"
  3. For Add 3, Square, turn on Gate with x ≥ −3 and build the undo line. "Why does the gate fix it? What does the vertical line on the graph show?"

Apply 13 min

  1. Pairs open Puzzles and work through levels 1 to 8. Hint gives up to three hints.
  2. On level 9, ask: "Rounding forgets more than a sign. Why can no gate fix it?"
  3. Pairs who finish try level 11: "Which 2-machine chains undo themselves?"

Exit check 5 min

On a card: "f(x) = (x − 5)/2. Write f⁻¹(x) and check it with x = 9." Then: "Why does g(x) = x² need a restricted domain to have an inverse? Name one domain that works." Cards that subtract before multiplying in the inverse show who needs the swap again.

Support and stretch

  • Support: stay with two-machine top lines and say each step out loud before undoing it.
  • Support: use Send my number to trace one value through both lines.
  • Stretch: "What is the smallest gate that works for Add 3, Square?"
  • Stretch: build a 4-machine top line with a gate and verify its inverse on the graph.

Short on time

  • The 3x + 4 swap in Workshop (8 min).
  • Mirror on the Graph (5 min), then the exit card (5 min).

How each button works is in the teacher notes. From Curio Class, free under CC BY 4.0: change it, print it, share it.