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Ever wondered how to teach theoretical and experimental probability in an engaging way to your 7th grade students?

In this lesson plan, students will learn about probability concepts and their real-life applications. Through artistic and interactive guided notes, check for understanding activities, a doodle and color by number worksheet, and a maze worksheet, students will gain a comprehensive understanding of theoretical and experimental probability.

The lesson concludes with a real-life example that explores how probability can be applied in everyday situations.

- Standards: CCSS 7.SP.A.1, CCSS 7.SP.A.2, CCSS 7.SP.C.5, CCSS 7.SP.C.6, CCSS 7.SP.C.7, CCSS 7.SP.C.7.a, CCSS 7.SP.C.7.b
- Topic: Statistics & Probability
- Grade: 7th Grade
- Type: Lesson Plans

$4.25

After this lesson, students will be able to:

Define theoretical probability and experimental probability

Calculate theoretical probability of a simple event

Collect data to approximate experimental probability

Compare and contrast theoretical probability and experimental probability

Apply theoretical and experimental probability to real-life scenarios

Solve problems involving theoretical and experimental probability

Before this lesson, students should be familiar with:

Basic understanding of probability vocabulary such as outcome, event, sample space, and probability.

Basic understanding of fractions and decimals.

Basic knowledge of data representation such as tables, charts, and graphs.

Pencils

Colored pencils or markers

Theoretical probability

Experimental probability

Chance event

Data collection

Probability

Probability model

Outcome

Sample space

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.

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.

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:

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.

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.

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.

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:

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 probability is the probability based on mathematical calculations and reasoning, without any actual experimentation or data collection.

Theoretical probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes.

**Steps to calculate theoretical probability:**

Identify the desired outcomes.

Determine the total number of possible outcomes.

Divide the number of desired outcomes by the total number of possible outcomes.

Experimental probability is the probability based on actual data collected from experiments or observations.

Experimental probability is calculated by dividing the number of times an event occurs by the total number of trials or observations.

**Steps to calculate experimental probability:**

Conduct trials or observations.

Count the number of times the event of interest occurs.

Divide the number of occurrences by the total number of trials or observations.

The main difference between theoretical and experimental probability is that theoretical probability is based on mathematical calculations and reasoning, while experimental probability is based on actual data collected from experiments or observations.

Theoretical probability can be used in real-life situations to make predictions or informed decisions based on mathematical calculations and reasoning. For example:

Predicting the chances of winning a game or lottery.

Determining the likelihood of certain weather conditions.

Estimating the probability of a certain event occurring in a scientific experiment.

Experimental probability can be used in real-life situations to make predictions or draw conclusions based on actual data collected from experiments or observations. For example:

Estimating the success rate of a new medical treatment based on clinical trials.

Evaluating the effectiveness of a marketing campaign based on customer responses.

Assessing the probability of a certain outcome in sports based on past performance data.

To teach theoretical and experimental probability effectively, consider the following strategies:

Use visual aids and manipulatives to illustrate the concept.

Provide real-life examples and applications to make the topic relatable.

Engage students in hands-on activities or experiments to collect data and calculate probabilities.

Incorporate interactive discussions and problem-solving tasks to encourage critical thinking.

Offer opportunities for students to practice and apply their knowledge through worksheets or interactive games.

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