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Algebra 1 9-12 / Week 05 / Wednesday
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Week 05 · Linear Models and Sequences

Wednesday

Loft Lab: tower and drip
// The cup tower and the filling jug
⏱ about 20 min

Wednesday: Loft Lab, Tower and Drip

Comet sets a tray on the bench with the jug, the tube and a measuring pitcher. "Two labs, one afternoon."

"Tower first," Wren says. "Stack, count, record. Then the drip, reading every minute."

Comet stacks fast and the tower sways. She stops, steadies it, and starts again more slowly.

"What do you notice about the counts?" Wren asks after four rows.

"Four, seven, ten, thirteen. Same as Monday. The rule held." She opens the drip clip and starts the timer.

Nova projects a two-column table: minutes and milliliters. "Would you like a hint? Read at the same spot each time."

At 1 minute: 240. At 2: 280. At 3: 320. "Forty a minute," Wren says. "Our engineer, your turn."

What you need

  • About 30 paper cups and a floor space to stack them.
  • A clear jug or jar, a measuring pitcher or cup with milliliter marks, and a tray to catch spills.
  • A way to drip water slowly: a tube with a clip, a squeeze bottle, or a cup with a tiny hole.
  • A timer, your Loft Log and graph paper.
Safety first
Water stays over the tray or the sink, and spills are wiped up right away so no one slips.
Stack cups on the floor, never on a chair or table edge. Keep the tower below shoulder height.
Nothing from the lab goes in anyone's mouth, and a grown-up handles any cutting of tubing.

Run the lab

  1. Tower: stack 3 cups a row with 1 cup on top. After each row, write the total cups as the next term.
  2. Write the recursive rule and the explicit rule for your tower. Predict the cups for 8 rows, then stack and check.
  3. Jug: pour a starting amount into the jug and write it as the value at t = 0.
  4. Start the drip and the timer together. Read the milliliters every minute for 5 minutes.
  5. Plot minutes across and milliliters up with labels and a scale. Find the rate from two readings.
  6. Write your jug rule V = rate × t + start and check it against a reading you did not use.

The crew's lab log

The crew's own counts and readings from the Loft. Every number is theirs, made up for this lesson.

RowsCups (tower)MinutesMilliliters (jug)
141240
272280
3103320
4134360
5165400
READ THE CREW'S LAB
  • Read the question.
  • Tap your answer.
The crew's tower sequence is 4, 7, 10, 13, ... How many cups for 12 rows?
The crew's jug read 240 at 1 minute and 320 at 3 minutes. Which rule fits?
The crew has exactly 31 cups. Using 4, 7, 10, 13, ... how many rows can they stack?
The crew's jug followed V = 40t + 200. What did it read at 5 minutes, in milliliters? Type the number.
WHY THIS EXERCISEA rule built from early readings predicts later ones, as long as the drip stays steady.
StatementTrue or false?
Reading the jug at the same spot each time keeps the readings fair.?
A tower stacked on a chair is safer than one on the floor.?
In the sequence starting 4 and adding 3, term 8 is 25.?
The crew's jug rate was 40 milliliters a minute.?
320 - 240 = 40 × 2?
WHY THIS EXERCISEClean readings make clean rules. Wobbly setups make wobbly dots.
Try it
Change the tower to 2 cups a row with 1 on top. Predict the sequence, then stack and check.
Keep the tower low and on the floor.
Draw your jug graph with labeled axes and a scale, and the line through your readings.

Fine lab work, engineer. Tomorrow the crew reads a flag string, a second pitcher and more of their Loft data.

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