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K–12 teaching and learning · from the UNC School of Education

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 grade 4 Mathematics

By Bonnie Boaz

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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

Either a computer lab with Internet access or a One Computer classroom with an Internet connection
Web site for activities:
http://www.shodor.org/interactivate/lessons/PascalTriangle/

Pre-activities

None

Activities

  1. 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:http://www.shodor.org/interactivate/media/worksheets/78.pdf 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.
  2. 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.
  3. 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.) Completed copies of Pascal’s Triangle can be found at:http://www.shodor.org/interactivate/media/worksheets/186.pdf For additional activities see Lesson Outline at-http://www.shodor.org/interactivate/lessons/PascalTriangle/
  4. Now go to your computer(s) and either alone or whole class and do the computer activity-”Coloring Multiples in Pascal’s Triangle”. See Shodor activity- http://www.shodor.org/interactivate/activities/ColoringMultiples/

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

None

Related websites

Shodor Educational Foundation,Inc.-Coloring Multiples in Pascal’s Triangle
http://www.shodor.org/interactivate/media/worksheets/186.pdf
http://www.shodor.org/interactivate/activities/ColoringMultiples/

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
Lesson on Geometric Fractals
Lesson on Patterns in Pascal’s Triangle
Lesson on Pascal’s Triangle

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.