Algebraic Peg Board and Pegs

A detailed guide to understanding the Algebraic Peg Board material and how it is used within the Upper Elementary curriculum

How does it work?

The Algebraic Peg Board and Pegs are used for exploring common multiples, factors, square root, and understanding ratio and proportion. Without the peg board and pegs, these core math concepts risk being understood as numbers only; whereas with them, your child is given the opportunity to explore, problem-solve, and vividly demonstrate their meaning in concrete terms.

Guidepost’s Algebraic Peg Board material includes color-coded wooden pegs and sturdy plastic cups stored in a wooden box with lid, as well as a board with 900 holes in a 30 x 30 grid formation.

Prerequisite Skills - Work with the Peg Board is best introduced when a child has shown a mastery of concepts such as:

  • The ability to count to 100
  • An introduction to multiples

To start squaring work using the Algebraic Peg Board, students should have a strong grasp of:

  • Multiplication (using Large Bead Frame and the Checkerboard)
  • Strong grasp of the Commutative & Distributive Laws
  • For Guidepost Homeschool Subscribers, we recommend first completing the unit called Squaring and Cubing Prerequisites.
Lowest Common Multiple Lesson Using Algebraic Pegs and Board

Sample lesson

Start by watching this sample lesson from our Guidepost Homeschool platform that will familiarize you to the Algebraic Peg Board and its use.

If you are already subscribed to Guidepost Homeschool, scroll down to see all the corresponding lessons where the Algebraic Pegs are used in our curriculum. To unlock more than 2000+ lessons subscribe to Guidepost Homeschool today.

How to set up

Setup - Check that the box has the contents organized in the correct manner as shown in the photo of the left. Position the cups along the top in order from left to right: green, red, blue, green. If you have multiple cups of each color, consider this a bonus and simply stack them in the space provided. Place the pegs along the bottom with the red pegs at left, blue in the middle, and green at right.

Additional materials - In general, you can count on the following supplies being used with the Peg Board and Pegs, so it’s a good idea to have them on hand:

  • Pencil
  • Ruler
  • Cut strips of black or bold paper 2 inches by 1.5 inches
  • Parentheses cut from stiff black or bold paper (about 3” high)
  • 1 inch square cut pieces of paper called "tickets"
  • Colored pencils or highlighters
  • Rubber bands

For Guidepost Homeschool subscribers

If you are already subscribed to Guidepost Homeschool, start in the order below to navigate to the corresponding lesson plans using the Peg Board in our Altitude learning platform.

Wondering about supplies used in particular lessons? Detailed materials lists can be found at the beginning of each lesson in Guidepost’s Altitude system, as well as on the materials cards at the beginning of each unit.

  • Corresponding Altitude lessons

    Lessons (Altitude Cards) where the Algebraic Peg Board is used

    Multiples and Factors (Ages 6-12)

    • Lowest Common Multiples
    • Lowest Common Multiples with Large Numbers
    • Prime Factors: Pegboard
    • Greatest Common Factors - 2 Numbers: Pegboard
    • Greatest Common Factors - 3 Numbers: Pegboard

    Squaring (Ages 9-12)

    • From a Real Square to a Symbolic Square
    • Squaring on the Pegboard - 2 Digits
    • Squaring on the Pegboard - 3 Digits
    • Squaring on the Pegboard - Advanced Notation
    • Squaring on the Pegboard - Binomial Guide Square
    • Squaring on the Pegboard - Trinomial Guide Square

    Ratio and Proportion (Ages 10-12)

    • Ratios on the Pegboard
    • Expressing Ratios as Fractions
    • Equivalent Ratios
    • Ration in Relation to a Whole
    • A Ratio in Three Terms
    • Introduction to Proportion
    • Using Algebra with Ratios
    • Solving Problems with Cross Multiplication
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