Raven fans five index cards across the workbench. "This week's puzzles for the street. Each one is a balance in words."
Rocket reads the first card aloud. "An envelope plus 7 beans balances 15 beans. That is x + 7 = 15."
"What do you notice about the second card?" Raven asks. "Four equal envelopes balance 28 beans."
"No plus," Rocket says. "Four of the same thing. 4x = 28." He grabs a pencil. "Share 28 among 4."
Nova hovers over the cards, her light flicking from one to the next. "Write the equation before you solve," she says.
"Then the card does the thinking," Raven says, "and we just undo."
Nova hums. "Card five has a fraction. Do not let it scare you."
A puzzle in words becomes an equation in three moves. Name the unknown with a letter. Write what the puzzle says. Solve.
"An envelope plus 7 beans balances 15" says x + 7 = 15. "Four equal envelopes balance 28" says 4x = 28.
Plus means something was added to the envelope. Equal envelopes means the hidden number was multiplied.
| Card | Written by | The puzzle | Equation |
|---|---|---|---|
| 1 | Rocket | An envelope plus 7 beans balances 15 beans. | x + 7 = 15 |
| 2 | Raven | Four equal envelopes balance 28 beans. | 4x = 28 |
| 3 | Rocket | An envelope plus 2.5 beans-worth balances 9 beans-worth. | x + 2.5 = 9 |
| 4 | Raven | Six equal envelopes balance 27 beans. | 6x = 27 |
| 5 | Nova | An envelope plus 1/2 balances 3. | x + 0.5 = 3 |
These five puzzles are the crew's own cards for this week. Card 3 and card 5 use a decimal and a fraction, which the balance cannot show.
Those puzzles live on paper. Card 5 says x + 1/2 = 3, so x = 2.5: subtract 1/2 from both sides.
| Statement | True or false? |
|---|---|
| "An envelope plus 7 beans balances 15" is written x + 7 = 15. | ? |
| "Four equal envelopes balance 28" is written x + 4 = 28. | ? |
| x = 7 is a solution of 4x = 28. | ? |
| x = 22 is a solution of x + 7 = 15. | ? |
Five cards, five equations. Tomorrow you find one-step equations in everyday life and review the week.