Unit 8

Estimating Probabilities Using Simulation

Probability and Sampling

Lesson 6

Expressions and Equations

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Let’s simulate real-world situations.

Unit 8 ● Lesson 6

Learning

Goal

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Spinners

Unit 8 ● Lesson 6 ● Activity 1

Which spinner doesn't belong?

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Warm-up: Which One Doesn’t Belong?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Diego’s Walk

Unit 8 ● Lesson 6 ● Activity 2

Diego must cross a busy intersection at a crosswalk on his way to school. Some days he is able to cross immediately or wait only a short while. Other days, he must wait for more than 1 minute for the signal to indicate he may cross the street.

We will simulate his luck at this intersection using different methods and estimate his probability of waiting more than 1 minute.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Diego’s Walk

Unit 8 ● Lesson 6 ● Activity 2

Your teacher will give your group the supplies for one of the three different simulations. Follow these instructions to simulate 15 days of Diego’s walk. The first 3 days have been done for you.

• Simulate one day:
• If your group gets a bag of papers, reach into the bag, and select one paper without looking inside.
• If your group gets a spinner, spin the spinner, and see where it stops.
• If your group gets two number cubes, roll both cubes, and add the numbers that land face up. A sum of 2–8 means Diego has to wait.
• Record in the table whether or not Diego had to wait more than 1 minute.
• Calculate the total number of days and the cumulative fraction of days that Diego has had to wait so far.
• On the graph, plot the number of days and the fraction that Diego has had to wait. Connect each point by a line.
• If your group has the bag of papers, put the paper back into the bag, and shake the bag to mix up the papers.
• Pass the supplies to the next person in the group.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Diego’s Walk

Unit 8 ● Lesson 6 ● Activity 2

1. Based on the data you have collected, do you think the fraction of days Diego has to wait after the 16th day will be closer to 0.9 or 0.7? Explain or show your reasoning.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Diego’s Walk

Unit 8 ● Lesson 6 ● Activity 2

• Continue the simulation for 10 more days. Record your results in this table and on the graph from earlier.
• What do you notice about the graph?
• Based on the graph, estimate the probability that Diego will have to wait more than 1 minute to cross the crosswalk.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Designing Experiments

Unit 8 ● Lesson 6 ● Activity 3

For each situation, describe a chance experiment that would fairly represent it.

1. Six people are going out to lunch together. One of them will be selected at random to choose which restaurant to go to. Who gets to choose?�
2. After a robot stands up, it is equally likely to step forward with its left foot or its right foot. Which foot will it use for its first step?�
3. In a computer game, there are three tunnels. Each time the level loads, the computer randomly selects one of the tunnels to lead to the castle. Which tunnel is it?�
4. Your school is taking 4 buses of students on a field trip. Will you be assigned to the same bus that your math teacher is riding on?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Designing Experiments

Unit 8 ● Lesson 6 ● Activity 3

• How could a standard number cube be used to simulate the situation with the buses?
• If one of the buses was numbered with your math teacher's favorite number and you wanted to increase the probability of that bus being selected, how could you change the simulation to do this?
• Two of the tunnels in a video game lead to a swamp that ends the game. How could you use your simulation to estimate the probability of choosing one of those two tunnels?
• You and a friend are among the people going to lunch. How could you use the simulation you designed to estimate the probability that you or your friend will be the one to choose the restaurant?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Estimating Probabilities Using Simulation

Unit 8 ● Lesson 6

• What is a simulation?
• Why might you want to run a simulation rather than the actual event?
• If you conduct a few trial simulations of a situation and record the the fraction of outcomes for which a particular event occurs, how might you know that you have done enough simulations to have a good estimate of the probability of that event happening?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 8 ● Lesson 5

I can simulate a real-world situation using a simple experiment that reflects the probability of the actual event.

Learning

Targets

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Video Game Weather

Unit 8 ● Lesson 6 ● Activity 4

In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Word:

Simulation

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Definition:

A simulation is an experiment that is used to estimate the probability of a real-world event.

Example:

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For example, suppose the weather forecast says there is a 25% chance of rain. We can simulate this situation with a spinner with four equal sections.

rain

sun

snow

wind

Lesson Video

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