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Unit 8

Designing Simulations

Probability and Sampling

Lesson 10

Expressions and Equations

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Let’s simulate some real-life scenarios.

Unit 8 ● Lesson 10

Learning

Goal

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Division

Unit 8 ● Lesson 10 ● Activity 1

Find the value of each expression mentally.

(4.2 + 3) ÷ 2

(4.2 + 2.6 + 4) ÷ 3

(4.2 + + 2.6 + 4 + 3.6) ÷ 4

(4.2 + + 2.6 + 4 + 3.6 + 3.6) ÷ 5

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Warm-up: Number Talk

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

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Breeding Mice

Unit 8 ● Lesson 10 ● Activity 2

When flipping two coins, what is the probability of both landing heads up?

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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.

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Breeding Mice

Unit 8 ● Lesson 10 ● Activity 2

A scientist is studying the genes that determine the color of a mouse’s fur. When two mice with brown fur breed, there is a 25% chance that each baby will have white fur. For the experiment to continue, the scientist needs at least 2 out of 5 baby mice to have white fur.

To simulate this situation, you can flip a coin twice for each baby mouse.

  • If the coin lands heads up both times, it represents a mouse with white fur.
  • Any other result represents a mouse with brown fur.

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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.

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Breeding Mice

Unit 8 ● Lesson 10 ● Activity 2

  1. Simulate 3 litters of 5 baby mice and record your results in the table.

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  • Based on the results from everyone in your group, estimate the probability that the scientist’s experiment will be able to continue.
  • How could you improve your estimate?

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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.

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Breeding Mice

Unit 8 ● Lesson 10 ● Activity 2

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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.

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Breeding Mice

Unit 8 ● Lesson 10 ● Activity 2

  • How could we get a better estimate than what you got in your group?
  • Collect data from the class to find a better estimate.
  • Notice that we used a two-part experiment (flipping two coins) to represent a single thing (one offspring). Why was this ok to do?
  • Can you think of another method that would work to simulate a single offspring?

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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.

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Designing Simulations

Unit 8 ● Lesson 10 ● Activity 3

Your teacher will give your group a paper describing a situation.

  1. Design a simulation that you could use to estimate a probability. Show your thinking. Organize it so it can be followed by others.
  2. Explain how you used the simulation to answer the questions posed in the situation.

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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.

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Designing Simulations

Unit 8 ● Lesson 10

  • What are some things you had to consider when designing your simulation?
  • What did you learn from the simulations the other groups did?
  • Were the results of any of the simulations surprising?
  • Why would it make sense to design and run a simulation rather than repeat the actual experiment multiple times?

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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.

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Unit 8 ● Lesson 10

I can design a simulation to estimate the probability of a multi-step real-world situation.

Learning

Targets

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The Best Power-Up

Unit 8 ● Lesson 10 ● Activity 4

Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time.

Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times.

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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.

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This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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