Theoretical and Experimental Probability

Introduction

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As a hook, ask students why understanding probability is important in everyday life. For example, you can ask them why it's important to know the probability of winning a lottery or the probability of getting a certain outcome in a game. Refer to the last page of the guided notes as well as the FAQs below for more ideas on how to engage students in the discussion.

Use the first page of the guided notes to introduce the concept of theoretical probability vs. experimental probability. Walk through the key points of the topic, including how to calculate the theoretical probability of an event. Emphasize that theoretical probability is based on what we expect to happen in an ideal situation. Explain that experimental probability is based on collecting data from actual trials or experiments. Walk through the key points of the topic, including how to calculate the experimental probability of an event. Emphasize that experimental probability can vary from the theoretical probability because it is based on actual data. Refer to the FAQ below for a walk-through on this, as well as ideas on how to respond to common student questions.

Based on student responses, reteach any concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

Practice

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Have students practice theoretical and experimental probability using the practice worksheet activity (pg. 2 of guided notes). Walk around to answer student questions.

Fast finishers can dive into the maze (pg. 3 of guided notes) and color by number activities (pg. 4 of guided notes) on the practice worksheet for extra practice. You can assign it as homework for the remainder of the class.

Real-Life Application

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Use the last page of the guided notes (pg. 5) to bring the class back together, and introduce the concept of real-life applications of probability. Explain to students that probability is used in many different fields and industries to help make informed decisions and predictions. Some examples of real-life applications include:

1. Weather Forecasting: Meteorologists use probability to predict the likelihood of rain, snow, or severe weather. By analyzing historical weather data and current atmospheric conditions, they can calculate the probability of certain weather events occurring in a specific area.
2. Sports Statistics: Probability is used in sports to analyze player performance, predict game outcomes, and determine the chances of a team making it to the playoffs. Statistics such as shooting percentage in basketball, batting average in baseball, or completion percentage in football are all based on probability.
3. Insurance: Insurance companies use probability to determine the likelihood of certain events, such as accidents or natural disasters, occurring to their policyholders. This helps them calculate insurance premiums that accurately reflect the level of risk involved.

Refer to the FAQ section in the teaching resource for more ideas on how to incorporate real-life applications of probability into your lessons.

Additional Print Practice

A fun, no-prep way to practice theoretical and experimental probability is Doodle Math. It's a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Here are some activities to try:

• Theoretical and Experimental Probability | Doodle Math: Twist on Color by Number Worksheets

Additional Self-Checking Digital Practice

If you’re looking for digital practice for theoretical and experimental probability, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

Here are some activities to explore:

• Theoretical & Experimental Probability Digital Pixel Art Activities