# Practicing multiples using Pascal's Triangle

This lesson will introduce students to Pascal's Triangle. Students will be introduced to the patterns in Pascal's Triangle and complete a 9 level triangle. Then they will color the multiples of specified numbers. This lesson uses resources of Shodor Education Foundation, Inc. Permission has been granted for the use of the materials as part of the workshop "Interactivate Your Bored Math Students".

**A lesson plan for grades 3–4 Mathematics**

## Learning outcomes

Students will:

- be introduced to Pascal’s Triangle.
- be introduced to the patterns in Pascal’s Triangle and complete a 9 level triangle.
- color the multiples of specified numbers.

## Teacher planning

### Time required for lesson

2 days

### Materials/resources

- An empty Pascal’s Triangle template for 9 levels (See attachment)
- Crayons, colored pencils, or crayons

### Technology resources

Color monitor with access to the internet for each student

## Activities

- Use the activity “Coloring Multiples in Pascal’s Triangle” activity online to introduce Pascal’s triangle. Start with one in the top space. The one or two numbers above each space are added together to form the numeral below. This pattern is continued. See: Coloring Multiples Exploration Questions or use the overhead projector with an overhead copy of Pascal’s Triangle. Talk about the relationship between numbers on Pascal’s Triangle and start to fill in the triangle together. Teacher will be in front of the room and the students will be working on their copies at their seats.
- Have students complete their triangle for at least 9 levels, and more if they are able, either in class or as homework once they understand the patterns.
- The next day with your completed Pascal’s Triangles students will need coloring materials. Ask students to choose a color to color all the multiples of 3. Then choose another color for the multiples of 5, another for 7. You may want to have multiple copies of a completed Pascal’s triangle and color different multiples (ex: 2, 9, etc.). See Pascal’s Triangle Handout for a completed copy of Pascal’s Triangle. (For additional activities see Pascal’s Triangle).
- Now go to your computer(s) and either alone or whole class and do the computer activity Coloring Multiples in Pascal’s Triangle.

## Assessment

Students will be able to complete a 7 level Pascal’s Triangle.(Completing the triangle is not the main objective of this lesson therefore the whole triangle should be completed by all students.)

Rubric for evaluation:

- No errors-5pts
- 1-2 errors-3pts
- 3-4 errors-1pt
- More than 4 errors-0 pts

Students will then color the specific multiples on their Pascal Triangle.

Rubric for evaluation:

- Complete 5 different specific multiples without error-5 pts
- Complete 4 different specific multiples without error-3 pts
- Complete 3 different specific multiples without error-1 pt
- Complete 2 or less-0 pts

## Supplemental information

### Comments

Much of this lesson is drawn, with permission, from Shodor.org. You may want to extend this lesson by using lessons found at Shodor.org.

- Common Core State Standards
- Mathematics (2010)
#### Grade 3

- Operations & Algebraic Thinking
- 3.OAT.7Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products...

#### Grade 4

- 4.OAT.1Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
- 4.OAT.4Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether...

- Operations & Algebraic Thinking

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 4

**Goal 1**: Number and Operations - The learner will read, write, model, and compute with non-negative rational numbers.**Objective 1.02**: Develop fluency with multiplication and division:- Two-digit by two-digit multiplication (larger numbers with calculator).
- Up to three-digit by two-digit division (larger numbers with calculator).
- Strategies for multiplying and dividing numbers.
- Estimation of products and quotients in appropriate situations.
- Relationships between operations.

**Objective 1.05**: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.