Raven pins the week's puzzle to the board: "Each kid on the street gets c cards. There are 5 kids."
"So the crew needs 5c cards," Rocket says. "But c is not hiding in an envelope. We have not decided it."
"That is the point," says Raven. "What do you notice if c is 2? If c is 6?"
"Ten cards. Thirty cards. The expression works for every c we might pick."
Nova hovers beside the board, her light flicking across the numbers. "Sometimes a letter is one hidden number," she says. "Sometimes it is any number in a set."
"Like a slot," Rocket says. "5c is a machine waiting for c."
Raven writes it on a card. "Next week two expressions will match for every number. That is a different kind of puzzle."
A letter can stand for one unknown number, like the beans in the envelope. You find it by opening the envelope or by reasoning.
A letter can also stand for any number in a set, like the cards each kid might get. Then the expression is a rule that works for every choice.
In 5c, try c = 2, 4 and 6: you get 10, 20 and 30 cards. One expression, many answers.
| Situation | Letter | Expression |
|---|---|---|
| Each of 5 kids gets c cards | c = cards per kid | 5c |
| A puzzle takes m minutes, plus 10 minutes to set up | m = minutes | m + 10 |
| Rocket is 3 steps ahead of Raven, who has walked s steps | s = steps | s + 3 |
| A board has 20 cards and k are taken | k = cards taken | 20 - k |
| Half the beans in a jar of b beans | b = beans | b ÷ 2 |
| Week review | True or false? |
|---|---|
| A variable can stand for an unknown number or for any number in a set. | ? |
| In 4n + 7, the coefficient of n is 7. | ? |
| 2(8 + 7) is a product of two factors. | ? |
| If s = 3, then s³ = 27. | ? |
| "Subtract y from 5" is 5 - y. | ? |
A letter can hide a number or stand for all of them. Tomorrow is Puzzle Day: the envelope game with your family.