The number balance is a math manipulative that I had never used or even seen for many years that is now one of my and my students’ favorites. It is very versatile in that all ages from preschoolers to middle school can use it at different levels.
The basic idea is to place a ten gram weight on a number or combination of numbers on one side. Then you find an equivalent number or combination of numbers on the other by balancing the weight. However, the number of concepts this can be used to explore is more than you would think. Children of all ages absolutely love playing with this. While they play, they’re discovering important mathematical concepts about equivalency, equivalent equations, comparing numbers and equations, variables and more. It is a concrete and visual tool for exploring number relationships and operations. .
While most teachers primarily use this in the early grades for comparing numbers and building equivalent addition equations, it is equally valuable for multiplication as well as introducing algebraic expressions and variables. You can easily demonstrate a problem like 2x + 4= 10 by using the balance.
As an Amazon reviewer said, “It’s better to look at this as an educational tool rather than purely as a toy. As a toy it has quite a bit of appeal, but I think for most kids it would take an adult’s company to see the full learning potential. If you’re willing to play along with your kids this toy can really open their eyes to why math works.”
To introduce the balance, I usually give a child two weights and ask how they can make them balance. They will pretty much always put them on the two tens (since they are on the ends of the balance.) However, they will quickly see that they can use any two identical numbers. We then talk about why this worked. From there we go to three weights, then once they see how it works I let them explore with any number of weights. Here is a full explanation with pictures from Right Start Math that introduces the balance the same way I do.
From there you can use the number balance as a part of many small group lessons, games, or interventions. One of my favorite beginning lessons is to use it with the game Sleeping Queens to demonstrate your equivalent equations. Use it to find missing addend. Use it for subtraction as difference. Look at the video below for how to use it for beginning algebra.