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Data and Society 9-12 / Week 10 / Mission Quest
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Week 10 · Models and Simulations

Mission Quest

Mission Quest: The sharpener line
// Can a simple model predict what will happen next?
⏱ about 20 min

Mission Quest: The Sharpener Line

Comet has a problem at home. Her whole family shares one pencil sharpener, and everyone needs it at the same time.

"There is always a line," she groans. "I could build a model of it!"

Wren laughs. "What do you notice about when the line gets long?"

"Right before homework time," Comet says. "Everyone shows up at once."

Nova hovers by the sharpener. "Would you like a hint?" she asks. "A die can stand in for when people show up. Your family can help you run it."

Comet grabs a sheet of paper. "Data analyst, let's model the line together."

  1. A model predicts from chosen data and features. Abstraction keeps only what matters.
  2. A simulation uses changing values to show how a situation changes.
  3. Random numbers, like die rolls, can stand in for real-world variety.
  4. Test a model, then refine it. Watch for bias from what you leave out.
◇ THE SHARPENER LINE
You need a die, paper and a pencil. No die? Number six paper slips from 1 to 6 and draw one from a cup.
Play with a family member who says yes. One person rolls, and one person records.
The question: if one pencil sharpener is shared at home, how long does the line get?
Make a table with three columns: Round, Roll, People in line. Write rounds 1 to 10 down the side.
Each round stands for one minute. The line starts empty, at 0.
Roll once each round. A 1, 2 or 3 means nobody new. A 4 or 5 means one person joins the line. A 6 means two people join.
Then, if anyone is in line, the person at the front sharpens and leaves. Subtract 1.
Write how many people are still in line. The line can never go below 0.
If you use paper slips, put each slip back in the cup and shake it before the next draw.
After 10 rounds, circle the longest line. Then swap jobs and run all 10 rounds again.
Talk about it: what did your model leave out? Which detail would you add first?
Example roundRollPeople who joinedPeople in line after the sharpener
1510
2621
3411
4200
For a grown-up
This week your student learned how models and simulations make predictions, and how they are tested and refined.
The die only stands in for when people show up. No one's details are written down.
Ask: what did our model leave out? Would adding it change the line?
Everything in this course is done on paper. No app, website or account is needed.
QUEST CHECK
  • Read the question.
  • Tap your answer.
The line has 0 people. You roll a 6. How many are in line after the sharpener serves one person?
The line has 2 people. You roll a 5. How many are left after the sharpener serves one person?
The line has 0 people. You roll a 2. How many are in line after this round?
About our modelTrue or false?
In this model, everyone takes the same time to sharpen.?
The model includes how dull each pencil is.?
Running the model twice can give a different longest line.?
WHY THIS EXERCISEKnowing what your model assumes tells you how far to trust its answer.
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