Introduction to Equations with Balancing Scales
How Are Equations Related to Balancing Scales?
An equation is a statement of equality where one or more numbers are replaced with a variable that needs to be found. This school topic can be tricky to grasp. Fortunately, equations have a real-world counterpart — balancing scales, which stay level when both sides carry weights of the same mass. In this case, the variable can be represented by any object of unknown weight, like a suitcase.
Why Does It Matter for Kids?
When kids play with scales, try to balance objects, and compare what’s heavier — a suitcase or three seagulls — they begin to understand what “equal” really means. One key discovery in these games is that if you remove the same mass from both sides, the balance stays. This forms the basis for understanding equations later on.
Psychologist Jean Piaget showed back in the mid-20th century that the idea of conservation doesn’t develop right away — kids build it through hands-on experiences like balancing objects or one-to-one matching.
Modern studies confirm this: kids who work with balancing and equality tasks tend to develop a stronger understanding of number relationships and algebraic thinking. Playing with scales in early childhood helps build a better sense of equality, numbers, and operations — and this effect continues into primary school. Kids who use hands-on tools like scales are better at grasping symbolic equality, and later use that understanding when transforming expressions and solving written math problems.
So balancing scales aren’t just fun — they’re an important step toward feeling confident with equations and understanding algebra not only through abstract logic, but through physical, hands-on experience. This kind of knowledge helps kids feel more secure and prevents the kinds of mistakes that often happen when learning math in a purely formal way.
How Do We Teach?
We introduce the idea of equality through play with seesaws or balancing scales. When the same objects are placed on both sides, the scale stays level. If you add a 1-pound weight to each side, it still stays balanced. If you take away 5 pounds from both sides, the balance remains. This helps kids physically feel how equality works in number sentences.
Step by step, numbered weights begin to appear — showing how much each object “weighs.” Kids start comparing the values of the parts on each side, learning how to keep things equal while also simplifying the problem. To figure out the unknown weight, kids try out different strategies: removing equal weights from both sides or shifting weight from one side of the equation to the other. In doing so, they’re actually solving real equations — just in a hands-on, visual way.
Later, kids face new situations where they need to think about two different things at once.
First Steps
Playing with Balance and Finding the Missing Part
By age 5, most kids have already encountered the idea of equal amounts. Even if they’ve never seen real balancing scales, they usually have experience playing on a seesaw. The key concept is simple: if the scale is balanced, you can remove two identical objects — one from each side — and the balance will stay.
Addition
Addition equations with scales
At first, kids solve simple problems like “How many blocks do I need to add to make both sides equal?” They start with familiar objects — blocks, apples, seagulls. But gradually, those objects are replaced with weights labeled with numbers, and kids begin to understand that numbers can represent weight.
Sometimes, the weight of an object is known, and the task is to find which combinations of weights match it. In other games, kids have to balance ice floes holding unit-weight objects (like seagulls), along with mysterious suitcases and chests whose weight they have to figure out.
Addition
Add up (up to 10)
Addition
Addition equations with scales
Addition
Crossing ten
Division by 2 and 3
Equations with unknown addend within 10 (objects and numbers)
Deep Understanding
Learning to Keep Things Equal and Shift Weight Around
By age 6, kids begin solving problems with weights labeled by their mass. The method stays the same: remove the same weight from both sides and see what’s left.
Addition
Addition equations with scales
They also encounter problems where two sums must be equal, and one of the numbers is missing. At first, these are solved using objects like blocks. Later, the same types of problems appear with numbers. The ability to shift a few unit blocks from one part of the sum to the other helps kids build different addition strategies.
Kids begin to notice what happens when you move a single unit from one number to another. To their surprise, they discover that the difference between the numbers doesn’t change by 1, but by 2!
In the monkey game, they now have to keep track of two things at once — the number of berries and the number of leaves. Later on, this experience helps them tackle not just one equation, but a system of two equations with two unknowns.
Addition
Compensation strategy (up to 20)
Addition
Compensation strategy (up to 20)
Addition
Compensation strategy
Quantities & addition
Addition with two variables within 10 (numbers only)
Confident Mastery
Getting to Know Two Variables
By age 7, kids learn how to find a missing number in addition problems with two-digit numbers.
Addition strategies
Fluent addition (up to 100)
They begin solving trickier problems with missing parts in both addition and subtraction.
The idea of working with two parameters also grows stronger. Kids face challenges where they need to find one unknown value first, and then use it to figure out another. This leads to classic “heads and legs” puzzles — for example, if you know the number of hats and the number of shoes, how many giraffes with four legs and ostriches with two legs are there?
Subtraction
Subtraction as a difference
Addition & subtraction
Еquations
Hats, legs and other problems
Heads and legs
Addition & subtraction
Systems of equations
Big Ideas
Balancing scales turn out to be a powerful and productive metaphor for understanding equations. They give kids a strong push toward developing early algebraic thinking.
Games with objects of unknown weight build a solid foundation for grasping one of the most challenging algebra concepts — the idea of a variable.
The rule that you can change both sides of the scale in the same way shows kids that you can apply the same operation to both parts of an equation. This helps explain something that often feels mysterious at first: why you’re allowed to “move a number to the other side and change its sign.”
Finally, solving problems with two parameters — in a clear, visual, and accessible way — lays the groundwork for understanding systems of equations later on.
