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Expressions and Equations 6-8 / Week 01 / Puzzle Day
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Week 01 · Powers and the Order of Operations

Puzzle Day

Puzzle Day: The folding race
// Fold a sheet again and again, then agree on which step comes first
⏱ about 20 min

Puzzle Day: The Folding Race

Saturday morning the Puzzle Post has a crowd of two: Rocket's cousin and Raven's uncle. Rocket holds up a sheet. "Folding race."

"The rule," says Raven, "is that you say the layers as a power before you fold. What do you notice if you guess wrong?"

"You fold anyway," Rocket says, "and count to check. Then the beans."

Nova hovers above the bean tray, her light steady. "Build a square with 6 on a side," she says. "Say the power before you count."

"Thirty-six," says the uncle. Rocket counts. Thirty-six. "Nova, did you give the answer away?"

"I gave the side," Nova says. "The power was all yours."

  1. A power is repeated multiplication: 2 × 2 × 2 = 2³. The base is the number multiplied, the exponent counts the factors.
  2. Squares and cubes are powers: 4² = 16 beans in a square, 3³ = 27 blocks in a cube.
  3. The order of operations: parentheses, powers, multiply and divide, add and subtract, left to right inside each step.
  4. Parentheses say "this first": (3 + 4) × 2 = 14, but 3 + 4 × 2 = 11.
  5. The exponent is never a multiplier: 2⁵ = 32, not 10.
◇ THE FOLDING RACE WITH A GROWN-UP
Each player takes a sheet. Before every fold, say the layers you will have as a power of 2.
Fold, then count the layers to check. A right call scores a point.
Switch to beans: one player names a side, the other says the square as a power and then builds it to check.
Finish with an expression challenge: write 2 + 3 × 4 and (2 + 3) × 4 and work both out together.
For a grown-up
This week your student wrote repeated multiplication as powers and learned the order of operations.
Ask them to explain why 2⁵ is 32 and not 10. The answer should mention counting factors.
Beans and buttons are counters, never food. They stay away from children under three and pets.
Safety first
Fold with hands only. No scissors or blades.
Beans stay on the tray. Nothing goes in a mouth.
PUZZLE DAY CHECK
  • Read the question.
  • Tap your answer.
After 4 folds, how many layers does the sheet have?
How many beans fill a square with 6 beans on each side?
What is (2 + 3) × 4?
What is 2 + 3 × 4?
Draw the bean square with 6 on a side and write its count as a power beside it.

Great puzzling, crew. Next week: a number hides in an envelope, and a letter stands in for it.

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