The Arizona STEM Acceleration Project

Counting in Statistics

Counting in Statistics

A 9-12 grade STEM lesson

Michael Matteson

6/19/2024

Notes for teachers

This lesson investigates the fundamental counting principle, permutations, and combinations.

This can be used in a math lesson exploring statistics, or (as in my case) in an introduction to statistics course. Anywhere where fundamental counting theorem, permutations, or combinations are being used (typically with probability).

List of Materials

• Course materials for fundamental counting, permutations, and combinations.
• Escape Room templates, I used https://genial.ly/
• You could also just use the one I made: https://view.genially.com/6661dd78d9dba500155b9775/interactive-content-intro-to-stats-probability-review

Standards

P.S-CP.B Use the rules of probability to compute probabilities of compound events in uniform probability models.

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QR.P.S-CP.B.9 Use permutations and combinations to compute probabilities of compound events and solve problems.

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Standards

QR.MP.1 Make sense of problems and persevere in solving them.

QR.MP.2 Reason abstractly and quantitatively.

QR.MP.4 Model with mathematics.

QR.MP.5 Use appropriate tools strategically.

QR.MP.6 Attend to precision.

Objective(s):

Students will investigate different counting methods to find out total number of outcomes to be applied in probabilities. They will learn about fundamental counting principle, permutations, and combinations. They will then be assessed on their knowledge by participating in a digital escape room.

Intro/Driving Question/Opening

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How do I count the total number of events?

How do I find out how many choices are possible given options from different categories?

How do I find out how many options there are when order matters? How do I find out how many different ways to arrange or rank something?

How do I find out how many options there are when order does not matter?

Hands-on Activity Instructions

• This should be done individually, but with room for students to discuss with each other how to do each method.
• Explain why we need to find the total number of outcomes to help us calculate things in probability.
• Explain the fundamental counting principle, and how it applies to finding the total number of choices while choosing from different categories.
• Explain how permutations are when you are finding the total number of outcomes when order matters.
• Explain how combinations are when you are finding the total number of outcomes when order does not matter.

Assessment

Students must “escape” from the digital escape room. You can create one using a template (I used https://genial.ly/) or you can use the one I created: https://view.genially.com/6661dd78d9dba500155b9775/interactive-content-intro-to-stats-probability-review

By students “escaping” they are showing understanding of the concept.

Students must also turn in a paragraph reflection that demonstrates their understanding of fundamental counting principle, permutations, and combinations.

Differentiation

Some students may need more guidance on which choice would be best, or how to do an analysis. Some students could just do the escape room and not the reflection, while others could just turn in the reflection.

Remediation

Extension/Enrichment

You can have students create their own escape room on the topic.