Here’s my first attempt. I'm starting with something very easy! This example uses some affordable materials that can be repurposed for many different math concepts. In this example, the goal is to help the child understand how to find a square root of a number with two periods.
FINDING THE SQUARE ROOT OF 625 ON THE ALGEBRAIC PEGBOARD
Preparing the board to find the square root of 625... Note that Montessori kids already understand that each color represents a value. Green = units, blue = 10s and red = hundreds
We put 6 red beads (6 hundreds), 2 blue beads (tens) and 5 green beads (units) in their respective dishes. Starting with the red beads we make a square.
Below: Building the largest possible square with 100s pegs, 4 X H square. The student will not be able to add another row to the bottom and right sides with the 100s pegs. So they will need to exchange the remaining 100s pegs for 10s, giving 20 more 10s, for a total of 22.
If you're thinking, "Well, that was a lot of work when there are many shortcuts that could have been taken." I'd say - you're right. But the purpose behind all Montessori materials is to first be sure the child has a deep understanding of what is happening in an operation, before he is shown any shortcuts. This develops a deeper understanding that will last a lifetime, rather than a memorization of steps that last only until the test on Friday.
The saying is really true... "To teach is to learn twice." Although, I'm not sure I ever learned the first time, so I'm thrilled to be able to learn it now! Particularly since these materials make it fascinating and fun. I can't count how many times I've said, "OH, so THAT'S why they taught me to do the steps that way in school!"