Mathematics 6-12
The Montessori Algebraic Peg Board is an excellent material to be used in the elementary years. It consists of a square wooden board containing 900 holes. The board is accompanied by hierarchical colored pegs and metal bowls with which learners are familiar. In some exercises, the colors won’t matter, whereas; in other exercises, green will represent units, blue will represent tens, and red will represent hundreds.
The Algebraic Peg Board is introduced in the second year of Lower Elementary, around age 7. It is first used to find multiples of a number, to find the Lowest Common Multiple (LCM), to learn about factors, to identify prime numbers, and to build squares of numbers or extract square roots.
In this post, we would like to demonstrate how the Algebraic Peg Board is used to form the square root of two, three, four, or five figure numbers.
Materials
- Algebraic (Square Root) Peg Board – Complete Set (Value Line)
- Guide Squares for Squaring and Square-Rooting
or our Premium Quality materials:
- Algebraic (Square Root) Peg Board (Premium Quality)
- Algebraic (Square Root) Pegs (Premium Quality)
- Algebraic Square Root Peg Board Exercise Set (Printed
- Guide Squares for Squaring and Square-Rooting (wood version available)
Introduction to the basics
First, we would like to remind you that the sign used for square root is called the radical sign (√). The number whose root is to be found is called the radicand (ex: 16 is the radicand in √16). To initiate children to square rooting, our examples in Algebraic Square Root Peg Board Exercise Set do not require remainders. Children will be able to use them with ease, without the use of Guide Squares for Squaring, but the guide would be used to demonstrate how they are used for larger numbers.
Algebraic Peg Board Activity Set Square Roots
The Algebraic Square Root Peg Board Exercise Set is comprised of 20 exercises separated into two sections (A and B) that lead children to competency. Cards A01-A11 provide practice finding the square root of two and three-figure numbers, while cards B01-08 provide practice finding the square root of four and five-figure numbers.
Using the Algebraic Square Root Peg Board Exercise Set, children will be extracting the square root of a given number. Let’s take for instance the √ 625. Children will first organize the hierarchical bowls by placing them at the top of the board, from left to right: red, blue, green. They will place six red beads in the red bowl, which represents 600; 2 blue beads in the blue bowl, which represents 20; and five green beads in the green bowl, which represents five units.
Children will start building a square with the hundred beads (red) anywhere on the top left side of the board. Once they run out of beads to form a 2X2 perfect square, they will need to exchange the remaining two beads for the next lower category where they already have 2 blue tenths. They should have 2 pre-existing two blue beads and the subsequent 20 blue beads from the exchange. Then, using the side of the square, they will build horizontal and vertical arms of blue beads until there are no more beads to build a rectangle. They will have two 8×2 rectangles (2 arms.) They will have two remainders to exchange for 20 green units, totaling 25 green units to distribute on the board. The number of beads left will build a perfect 5×5 square of 25 unit beads. There is no remainder.
Children can read the square root of 625 at the base of the square, which is 25 (read at the bottom of the work, 2 blue beads and 5 green beads is read 25.)
This post intends to introduce how the Montessori materials are used to make abstract mathematical concepts visible to children. The Algebraic Square Root Peg Board Exercise Set is designed to provide independent work for children, with problems that build confidence through practice. A visual control for errors is at the back of each card. We encourage you to learn more about the Algebraic Peg Board through Montessori teacher’s manuals or training centers.
We hope you enjoyed learning about square rooting using the Algebraic Peg Board. This is one of the numerous mathematical concepts introduced using this material. Please visit our website for more conceptual Montessori math materials.
