Week 04 · The Balance: One-Step Equations
Puzzle Day
Puzzle Day: The envelope challenge
// An equation is a level balance, and a solution keeps it level
⏱ about 20 min
Puzzle Day: The Envelope Challenge
Saturday morning, Raven tapes a sign to the garage door: Puzzle Post, open today. The balance hangs ready behind her.
"Every visitor gets an envelope puzzle," Rocket says. "They write the equation, solve it, then open the envelope."
"And if they are wrong?" Raven asks. "What do you notice happens to the balance when they test it?"
"It tips," Rocket says. "The balance never lies."
Nova hovers by the sign, her light warm. "Let them undo on both sides," she says. "Hints only."
"Hints only," Rocket repeats, and hides the first envelope. Nova hums. "That includes you."
- An equation says two sides name the same number, like a level balance.
- A solution is a value that makes the equation true. Test it by substitution.
- To solve x + p = q, subtract p from both sides. To solve px = q, divide both sides by p.
- Whatever you do to one side, do to the other, and the equation stays true.
- Write a puzzle as an equation first, solve it, then check by putting the answer back in.
◇ RUN THE ENVELOPE CHALLENGE WITH YOUR FAMILY
Hang the balance and set out beans, envelopes and index cards.
Hide beans in an envelope. Put it in one cup with a few loose beans, and level the other cup with beans.
Your family member writes the equation on a card, solves it on both sides, and says the number.
Open the envelope together and count. Then swap roles and try a round with two equal envelopes.
Keep score of how many rounds were solved before the envelope opened.
Hide beans in an envelope. Put it in one cup with a few loose beans, and level the other cup with beans.
Your family member writes the equation on a card, solves it on both sides, and says the number.
Open the envelope together and count. Then swap roles and try a round with two equal envelopes.
Keep score of how many rounds were solved before the envelope opened.
For a grown-up
This week your student learned that an equation is a level balance, and solved one-step equations.
Ask them to explain why they subtract from both sides, not one. The answer should mention keeping the balance level.
Check the hook before the hanger goes up. Beans and buttons stay away from children under three and pets.
Ask them to explain why they subtract from both sides, not one. The answer should mention keeping the balance level.
Check the hook before the hanger goes up. Beans and buttons stay away from children under three and pets.
Safety first
A grown-up checks the hook. The hanger hangs at chest height and nothing heavy goes in a cup.
Small beans and buttons stay away from children under three and pets. Nothing goes in a mouth.
Pick up dropped beans right away so no one slips.
Small beans and buttons stay away from children under three and pets. Nothing goes in a mouth.
Pick up dropped beans right away so no one slips.
PUZZLE DAY CHECK
- Read the question.
- Tap your answer.
The balance is level: one envelope and 2 beans on the left, 9 beans on the right. How many beans are in each envelope?
The balance is level: 3 envelopes on the left, 12 beans on the right. How many beans are in each envelope?Which value of x makes x + 5 = 11 true: 5, 6, 16?
What is x if x + 0.75 = 2?
Draw your Puzzle Post sign and the balance ready for visitors, with one envelope puzzle set up.
Great puzzling, crew. Next week the floor becomes a number line, and the answer is a whole set of numbers.