Decanomial Bead Bars

Decanomial Bead Bars

A detailed guide to understanding the Decanomial Bead Bars material and how it is used within the Lower Elementary and Upper Elementary curriculum.

How does it work?

The Decanomial Bead Bars are a versatile material! Your child will use these to explore a range of math concepts from whole number operations, properties of addition and multiplication, arithmetic relationships such as multiples and squaring, concepts of equality, to polynomial expansions.

As the name indicates, the “decanomial,” — the amazing physical representation of multiplication facts from 1 to 10 — can be built with this collection of beads. In Lower Elementary, your child will first work with the Decanomial Bead Bars to explore the concept of multiples. In Upper Elementary, they can explore commutative and distributive laws, squaring work, or decimal multiplication. Because the Decanomial Bead Bars can be used so flexibly, we recommend that you keep them accessible on your child’s shelf of learning materials. 

Our Bead Decanomial includes 55 of each of the colored bead bars from 1-10 and a wooden box for storage. This bead set is so versatile, you’ll wonder how you ever did math without it. Each bead bar represents a different quantity:

  • 1 = 1 red bead
  • 2 = 2 green beads
  • 3 = 3 pink beads
  • 4 = 4 yellow bead
  • 5 = 5 light blue beads
  • 6 = 6 lavender beads
  • 7 = 7 white beads
  • 8 = 8 brown beads
  • 9 = 9 dark blue beads
  • 10 =10 gold beads

Prerequisite Skills - The Decanomial Bead Bars are used across many topics from as young as first year Lower Elementary through Upper Elementary. Still, the child is best prepared for the Decanomial Bead Bars if they have good familiarity with:

  • Skip counting
  • Understanding place value
  • Operations with the Stamp Game
Decanomial Bead Bars Part 1

Sample lesson

Start by watching this sample lesson from our Guidepost Homeschool platform that will familiarize you to the Decanomial Bead Bars and their use.

If you are already subscribed to Guidepost Homeschool, scroll down to see all the corresponding lessons where the Decanomial Bead Bars are used in our curriculum. To unlock more than 2,000+ lessons subscribe to Guidepost Homeschool today.

How to set up

Setup - The Decanomial bead bars are best used at a child-height table (with a felt mat or placemat), or on a work rug on the floor.

  • You can eventually use these bead bars with The Checkerboard
  • Keep the golden 10-bars that are included in the Decanomial Bead Bars separate from your Golden Bead Set, if you have one
  • Be sure that there are always 55 of each color so that you’re equipped to explore far and wide with the beads

Additional materials - The following materials are typically used when working with the Decanomial Bead Bars. Have these materials available for your child to access independently when setting up their work:

  • Pencil
  • Colored pencils in the colors of the bead bars
  • Felt mat (18” x 24”) or 2 woven placemat (each 13” x 19”); this keeps the beads from rolling across the work surface
  • Cut square pieces of paper, called "tickets" (approximately 1” in size)

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 Decanomial Bead Bars 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 Decanomial Bead Bars are used

    Commutative And Distributive Law (Ages 7-12)

    • Commutative Law
    • Identity Law: Addition
    • Associative Law: Addition
    • Associative Law: Multiplication
    • Distributive Law Part 1
    • Distributive Law Part 2
    • Steps to Abstraction
    • Application to the Decimal System
    • Noticing the Hierarchies

    Multiples (Ages 6-12)

    • Introduction to Multiples
    • Common Multiples with Bead Bars

    Squaring (Ages 9-12)

    • Analysis of a Square: Binomial
    • Analysis of a Square: Trinomial
    • Analysis of the Square: Advanced Notation – Binomial
    • Passing from One Square to Another
    • Passing to a Non - Successive Square
    • Squaring a Sum: Binomial
    • Squaring a Sum: Binomial Advanced Notation
    • Squaring a Sum: Binomial - Product of Unlike Terms
    • Squaring a Sum: Trinomial
    • Squaring a Sum: Trinomial Advanced Notation
    • Squaring a Sum - Tens and Units


    Checkerboard (Ages 7-12)

    • Orientation to the Checkerboard
    • Introduction to the Checkerboard
    • Making Numbers
    • Multiplication with a One-Digit Multiplier
    • Carrying Over
    • Multi-Digit Multiplier
    • Multi-Digit Multiplier with Facts
    • Multi-Digit Multiplier with Facts and Partial Products
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