**(45–60 minutes)**

### Overview:

The LiC: Population Statistics Tool is ideal for exploring the connection between statistical and experimental probability. This lesson uses colored counters; please modify the materials to fit the learning needs of your students.

### Objectives:

In this lesson, students will:

- Collect experimental data to predict statistical probability
- Explore the connection between sample size and accuracy of results

### Materials/Technology:

- Colored counters
- Paper bags
- LiC: Population Statistics Tool

### Instructional Plan:

- Prepare multiple bags of 100 counters. Using two colors of counters, vary the number of counters of each color in each of the sample bags.
- Discuss and define statistical and experimental probability. You may want to use flipping a coin to provide a concrete example. The statistical probability of landing on heads is 50%. However, in an experiment, depending on the sample size, it may not turn out to appear this way.
- Tell students that they will be predicting the statistical probability of an event by conducting an experiment. Ask them to think about how the sample size connects to the accuracy of their prediction.
- Explain that each group will get a bag containing counters in two different colors totaling 100 in all. By repeatedly pulling out groups of 10 and using the LiC: Population Statistics Tool to record and analyze their results, students will make a prediction about how many counters of each color are in their bag.
- Model how to set up and use the LiC: Population Statistics Tool to record the data as it is collected.
- Give groups time to work. Tell students that you want their results to be as accurate as possible, but the number of samples they collect is up to them.
- Ask students to analyze their results and share their predictions about the contents of their bags with the class.
- Have students empty the contents of their bag and calculate the statistical probability. Then they should compare the statistical probability to the experimental probability they predicted.
- Discuss any student observations. Ask students how increasing the sample size affected the accuracy of their predictions.

### Assessment Strategies:

- Observe students conducting the experiment and making predictions.
- Ask students to complete an exit ticket delineating the difference between statistical and experimental probability.

### Standards:

This lesson is designed to address the following Common Core State Standards:

- CCSS.MATH.CONTENT.7.SP.A.1
- CCSS.MATH.CONTENT.7.SP.A.2
- CCSS.MATH.CONTENT.7.SP.B.3
- CCSS.MATH.CONTENT.7.SP.B.4

### Next Steps:

This would be an effective lead-in to a more in-depth project focused on exploring sample size outlined on the LiC: Population Statistics Ideas page.

In this lesson, students use the LiC: Population Statistics tool to collect data to predict statistical probability and explore the connection between sample size and accuracy in results.

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