**Overview:** Free probability lesson plan for 6th grade and 7th grade. Rolling a particular number once is random—but what happens when you roll 108 times? Middle schoolers play dice games to reinforce their knowledge of probability before discussing how they can use probability in real-life situations.

**Subject:** Math: Statistics & Probability

**Related Concepts: **General Math, Fractions, Decimals

**Essential Questions:** How can probability help me predict the results of games and situations that have a set number of possible results?

**Vocabulary:** probability, least likely, most likely, frequency, chance, random, theoretical results, experimental results

## Lesson Procedure

**Context:**

The lesson is designed to reinforce students' prior knowledge of probability.

**Introduction: **

Hold up two 6-sided dice. Tell the students that they they are on one team, and you are on the other. Each team will roll two dice; if the biggest number is 1, 2, 3, or 4 then Team A wins; if the biggest number is 5 or 6, Team B wins. Have the class decide which team they want to be - Team A or Team B. When they have chosen, have a representative from their team roll one die and you roll the other. Note the results on the board.

**Direct Instruction:**Play the video to explain which team actually had the higher probability of winning (Team B). After playing the video, ask the class if they'd like to change their team.

**Guided Practice:**Using an interactive white board or projection system, present Activity: An Experiment with Dice. Proceed through the activity and pause at "The Experiment."

Pass out two dice to small groups or partners. Read through the directions and have students work with a partner to keep track of their rolls. Walk around and observe student interaction, clarifying any misunderstandings. When teams have finished rolling 108 times, have them create a bar graph of their data. Have students describe the shape of the bars and attempt to explain why that is. Chart responses.

Refer to the video, as needed, to remind them of why the graph looks the way it does. Then ask why they had to roll 108 times. Encourage students to think about the number of dots on each die and what happens when the pair of dice are rolled to support their responses. Scroll to '108 Throws' in the activity to find the explanation. Answer any questions the students may have, encouraging them to refer to their data to understand. Continue to 'Probability' to explain the formula for probability. **Independent Practice:**Have students complete Activity 10.3 - Two Dice Experiment, #1-3. When most students have completed the tables, regroup as a whole class to discuss #4.

Compare the results for what was found in the Guided Instruction part of the lesson. Review the meaning of probability and relate to real-life situations. For example, how can probability be used when choosing an outfit when the choices are 4 shirts and 6 shorts. How many combinations of outfits can be made? Chart other real-life examples.

**Closure:**For homework, hand out Rolling Dice to Get a Sum of Seven; be sure to white out the answers before distributing. Tell students that they will need to use what they have learned to complete the assessment (since probability was introduced, use fractions to describe the probability. Show how probability can be expressed as a decimal and/or percent when those concepts are introduced/reviewed with the class).

**Assessment:**

- Note student participation and responses during the dice activity.
- Assess worksheets for accuracy and concept comprehension.

## Differentiation

Learners who don't have the patience or focus for 108 dice rolls can reduce the number they need to roll.

For students who are struggling with this concept, have students work with a partner or in small groups to complete the Rolling the Dice activity.

For English learners, it may help to draw a picture of the dice with the number of dots per die, per roll. Students can also review vocabulary, as needed, by drawing pictures or examples as appropriate.

Allow advanced readers to answer the comprehension questions for the introductory video.

## Extension Ideas

At independent work stations/centers, or when students have completed the assessment, they can complete the following activities to reinforce the concept of probability (one with die and one without): Concept: Dice Probabilities and How Many Buttons? Note: Use pictures with people wearing clothes with buttons to complete this activity.

Have the video Skunk - A Probability Game available for students to watch and play independently in groups.

## Attachments

Additional materials to guide your teaching: