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Expressions and Equations 6-8 / Week 12 / Puzzle Day
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Week 12 · Big Numbers, Small Numbers and Puzzle Night

Puzzle Day

Puzzle Night
// Powers, roots and Puzzle Night
⏱ about 20 min

Puzzle Night

The string lights come on and the garage glows. The balance hangs level, the rule machine waits, the strings are taped.

"Welcome to the Puzzle Post," Rocket says. "Three stations and a jar. Hint cards only."

At the balance, a cousin writes 3x + 2 = x + 10 and takes one envelope off each side. "x is 4!"

"What do you notice before you open it?" Raven asks. "Check both sides." Fourteen and fourteen. The envelope holds four.

At the machine, cards go in and come out. "Times 3, minus 1," someone guesses, and the next card proves it.

Nova hovers above the crossing strings, her light pooling where they meet. "Who can check this point in both?"

"(3, 6). Three plus three is six, and two times three is six."

"The jar holds about 2 × 10³ beans," Rocket announces. "Count a spoon if you doubt me."

  1. Powers of the same base: multiply adds the exponents, divide subtracts, a negative exponent means one divided by the power.
  2. Square roots undo squares and cube roots undo cubes. √2 is irrational.
  3. Scientific notation is a number from 1 to 10 times a power of ten. Compare by dividing fronts and subtracting exponents.
  4. Multiply in scientific notation by multiplying fronts and adding exponents. Add only when the powers match.
  5. The whole course: letters, balances, rules, lines, systems and powers, every answer checked.
◇ RUN YOUR PUZZLE NIGHT
Station 1, the balance: load envelopes on both sides. The family writes the equation and solves it before opening an envelope.
Station 2, the rule machine: feed three cards through your secret rule. The family guesses the rule and tests a fourth card.
Station 3, the strings: lay two lines on the floor grid. The family predicts the crossing, then checks it in both equations.
The jar: one spoon counted, spoons counted, answer in scientific notation. Give hints, never answers.
For a grown-up
Check the hook before the balance hangs, and keep it at chest height. Tape the floor grid flat and keep shoes on.
Beans and buttons stay away from children under three and pets. Nothing goes in a mouth.
Scissors for string and the box slot stay with a grown-up. Celebrate a wrong guess as a chance to check.
PUZZLE NIGHT CHECK
  • Read the question.
  • Tap your answer.
The balance station shows 3x + 2 = x + 10. How many beans hide in each envelope?
The machine rule is × 3 - 1. What comes out when 7 goes in?
The strings are y = x + 3 and y = 2x. Which point is on both?
The jar holds about 2,000 beans. Which is that in scientific notation?
A square-root bag holds 81 beans. How long is the side of the square they make? Type the number.
WHY THIS EXERCISEEvery Puzzle Night answer is checked by multiplying or substituting back. That habit is the course.
Draw your Puzzle Night: the three stations, the jar and the family around them.
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