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Algebra 2 9-12 / Week 12 / Wednesday
3/6
Week 12 · Seedling Heights and the Open House

Wednesday

Glass House Lab: is nine surprising?
// From a sample to the whole bench
⏱ about 20 min

Wednesday: Glass House Lab, Is Nine Surprising?

"Our model from the spring trays says a seed sprouts half the time," Comet says. "This tray of 10 gave 9 sprouts."

"Lucky, or is the model wrong for this tray?" Wren asks. "What do you notice? We can ask chance itself."

"Flip 10 coins. Count heads. That is one tray under the model," Comet says. "Do it 20 times."

Coins rattle on the bench. Nova tallies. "3, 4, 4, 5, 5..." The counts pile up around five.

"20 runs," Nova says at last. "The most heads in any run was 8. Would you like a hint? Look for 9."

"Never," Wren says. "Not once in 20 tries. Under the half model, 9 of 10 is rare."

"So the model probably does not fit this tray," Comet says. "Something about it is different. A simulation told us that."

What you need

  • 10 coins, or one coin flipped 10 times per run. A cup to shake them in.
  • Your Glass House Log with a tally column for 0 to 10 heads.
  • A flat bench or table, and a tray or box lid to keep the coins from rolling.
Safety first
Coins are for counting only. Nothing goes in the mouth. Keep them away from younger children.
Shake the cup over the tray so coins do not roll to the floor. Pick up any that do, so no one slips.
A grown-up handles any hot water or ladder in the Glass House. Nothing heavy is lifted alone.

Run the lab

  1. Decide the model: each seed sprouts with chance 1/2, like a coin landing heads. One run is 10 flips.
  2. Shake and tip out the coins. Count the heads. Make a tally mark in that row of your Log.
  3. Repeat for 20 runs. More is better if you have time.
  4. Draw a dot plot of your counts: heads across, one dot per run.
  5. Mark the crew's tray result, 9, on the plot. Count how many runs reached 9 or more.
  6. Decide: is the result surprising under the model? Write your reason.

The crew's runs

The crew's 20 head counts are made up for the Glass House. Yours will differ, and that is fine; the shape should look similar.

Run1234567891011121314151617181920
Heads34455556647563564758
A dot plot of the crew's 20 simulated head counts, from 3 to 8, with the tray result 9 marked in red.

The runs average 5.2 heads, close to 5. Runs of 3 reached 7 or more; none reached 9.

A result that chance almost never produces under the model is surprising. The crew decides the half model does not fit this tray.

A result like 6 of 10 would not be surprising. Chance gave 6 or more in 7 of 20 runs.

READ THE SIMULATION
  • Read the question.
  • Tap your answer.
In how many of the 20 runs did the crew count exactly 5 heads?
In how many of the 20 runs were there 7 or more heads?
In how many of the 20 runs were there 9 or more heads?
SURPRISING OR NOT?
  • Read the question.
  • Tap your answer.
Under the half model, chance never gave 9 of 10 in 20 runs. What should the crew conclude?
A tray gave 6 sprouts of 10. Chance gave 6 or more in 7 of 20 runs. Surprising?
What is the largest number of heads in any of the crew's 20 runs? Type the number.
WHY THIS EXERCISEThe biggest chance result was still below 9. That gap is the whole argument.
StatementTrue or false?
A simulation shows what chance alone produces under a model.?
3 + 17 = 20?
A result that the simulation produces often is surprising.?
The crew's runs averaged close to 5 heads out of 10.?
WHY THIS EXERCISEDeciding whether a model fits is a comparison: the real result against what chance produces.
Draw your own dot plot of head counts, 0 to 10 across. Mark 9 in red and shade the runs at or above it.

Good lab work. Tomorrow a simulation builds a margin of error and compares two trays of misted seedlings.

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