Thursday
Thursday: The Folding Log
Raven opens the Puzzle Post log. "Card folding race. Rocket, you folded 3 cards every minute, starting from none."
"And you started with 6 cards already folded," Rocket says, "then folded 3 a minute too."
"So after 4 minutes you had 12," Raven reads, "and I had 18. What do you notice about the gap?"
"Always 6," Rocket says. "You never lose your head start, and I never catch up."
Nova hovers over the log, her light moving down the minutes column. "Write each rule," she says. "Then graph both."
Rocket writes c = 3m for himself. Raven writes c = 3m + 6. On the graph, two lines climb side by side.
Nova hums. "Same steepness. Different start."
Two rules from one log
The minutes m are the independent variable: the crew chose how long to fold. The cards c are dependent.
Rocket: c = 3m. Three cards for every minute, and zero cards at zero minutes.
Raven: c = 3m + 6. Three cards for every minute, plus the 6 she had ready at the start.
These are the crew's own counts from the folding race, written in Raven's log. They are made-up Puzzle Post numbers.
| Minutes m | Rocket's cards (3m) | Raven's cards (3m + 6) |
|---|---|---|
| 0 | 0 | 6 |
| 2 | 6 | 12 |
| 4 | 12 | 18 |
| 6 | 18 | 24 |
| 8 | 24 | 30 |
Both lines climb 3 cards for every minute, so they are parallel. Raven's line starts 6 higher and stays 6 higher.
At 8 minutes Rocket has 24 cards and Raven has 30. The gap is still 6.
- Read the question.
- Tap your answer.
- Read the question.
- Tap your answer.
| Statement | True or false? |
|---|---|
| In the folding race, the minutes are the independent variable. | ? |
| Raven's line and Rocket's line cross after 6 minutes. | ? |
| Both lines climb 3 cards for every minute. | ? |
| At 0 minutes, Raven already has 6 cards. | ? |
Write your own folding rule, and say whether it has a head start.
Two rules, read and graphed. Tomorrow you find rules like these all over everyday life and review the week.