# Pascal's Triangle Activities & Games

Instructor: Heather Jenkins

Heather has a bachelor's degree in elementary education and a master's degree in special education. She was a public school teacher and administrator for 11 years.

Pascal's Triangle is a unique number pattern that has many different applications in mathematics. Use these multi-sensory games and activities to help students learn about Pascal's Triangle.

## Special Shape

Most triangles are just three-sided shapes, but Pascal's Triangle is truly special. When students study Pascal's Triangle, it can help reinforce their understanding of number theory and numeric patterns. Additionally, students can learn how to apply Pascal's Triangle to more complex mathematical problems. Let's look at games and activities to help students learn about Pascal's Triangle.

## Sticky Note Triangle

Have students recreate a large version of Pascal's Triangle using sticky notes.

### Materials

• Poster of Pascal's Triangle
• Poster board
• Markers
• Sticky notes
• Classroom wall (optional)
• Tape (optional)

### Teacher Directions

1. Show students a poster of Pascal's Triangle. Describe how the triangle is made.
2. Divide the class into pairs, and provide each pair with poster board, sticky notes, and markers.
3. Have students recreate Pascal's Triangle on their poster board. Students will write the number 1 on a sticky note and place it at the very top of the poster board. Then, students will write the number 1 on two other sticky notes and place them directly under the first sticky note.
4. Students will continue creating the triangle until they run out of space on the poster board. Consider using smaller sticky notes so that students can be engaged in creating more rows of the triangle.
5. An extension/option for this activity would be to recreate Pascal's Triangle with sticky notes on a classroom wall. You could assign students different rows to create the numbers, and students could work together to place sticky notes from floor to ceiling. Add tape to the back of each sticky note so it sticks more firmly to the wall.

### Discussion Questions

• What was difficult about recreating Pascal's Triangle?
• What do you think would happen if you recreated Pascal's Triangle beginning with another number, such as 2 or 3?

## Crack the Combination

Engage students in a timed game to find the combinations for probability problems using Pascal's Triangle.

### Materials

• Copies of Pascal's Triangle
• Sets of probability word problems
• Markers

### Teacher Directions

#### Preparation

1. Prior to the game, create probability word problems that ask students to find the number of possible combinations for an event. For example, a problem might be: ''If there are 16 types of cupcakes, how many different combinations of three cupcakes could you make?''
2. Ensure there are no repeated answers to the word problems.
3. Make copies of the word problems for groups of students to use.

#### Game

1. Show the class Pascal's Triangle. Discuss how it can be used to determine the number of possible combinations for an event.
2. Model an example for the students, such as the example provided in the Preparation section. If there were 16 types of cupcakes, students would look at row 18 in Pascal's Triangle. If they were looking for the number of combinations when selecting three cupcakes, they would look at the third number, which is 560. That means there are 560 possible combinations for that event.
3. Divide the class into small groups. Provide each group with a copy of Pascal's Triangle, markers, and a copy of the word problems.
4. When you say 'go,' have each team use Pascal's Triangle to solve the word problems about combinations.
5. Once students have solved a problem, they must color in the space on Pascal's Triangle that shows the correct number of combinations.
6. When students are finished, they should bring their triangle to you. The first team to fill in the correct spaces in Pascal's Triangle wins.
7. Review the correct answers to the word problems.

### Discussion Questions

• Why would someone need to use Pascal's Triangle to find out the number of combinations for an event?
• How is it possible for Pascal's Triangle to accurately predict the number of combinations?

## Patterns in Art

Engage students in an art project to identify patterns in Pascal's Triangle.

### Materials

• Copies of Pascal's Triangle (at least up to 20 rows)
• Poster board
• Colored pencils
• Glue
• Scissors

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