What students learn
Most students can follow the steps for solving an equation long before they understand why those steps are allowed. Tip the Scales makes the why visible. Each side of the equation sits on one pan of a balance: blue x-blocks for the variable, orange circles for ones, and balloons pulling up for negative amounts. If a student subtracts 3 from only one side, the scale tips. If they subtract 3 from both sides, it stays level.
That picture carries the whole unit: an equation is a statement that two amounts are equal, and any operation done to both sides keeps it true. Students choose inverse operations to isolate x, then type the value of x to finish the level.
The four levels
- 1-Step Equations (grade 6), like x + 3 = 8 or 4x = 12.
- 2-Step Equations (grade 7), like 2x + 1 = 7.
- Variables Both Sides (grade 8), like 3x + 2 = x + 8. Students first collect the x-blocks on one side.
- Complex Equations (grade 8), like 2(x + 1) = 4, with grouped blocks and some fractional coefficients.
Each level has 15 equations. The Expand button appears in the last two levels: it multiplies out a group so 2(x + 3) becomes 2x + 6, and when every term shares a factor it turns into a Factor button that does the reverse. The first time a student reaches those levels, a pop-up points to the button and explains it.
Sandbox mode has no answer to find. Students build any equation they like and test values of x, which works well for a whole-class demonstration on the projector.
Worked examples
Two-step: 2x + 1 = 7
Remove one orange 1 from each side: 2x = 6 Divide both sides by 2: x = 3
On the scale, the two x-blocks balance six ones, so each x-block balances three.
Variables on both sides: 3x + 2 = x + 8
Remove one x from each side: 2x + 2 = 8 Remove 2 from each side: 2x = 6 Divide both sides by 2: x = 3
Taking away an x-block from both pans is the step students most often skip on paper. On the scale it looks just like removing a one.
Distributive property: 2(x + 1) = 4
Path A, expand first: 2x + 2 = 4 → 2x = 2 → x = 1 Path B, divide first: x + 1 = 2 → x = 1
Both paths work. Ask students which one they chose and why. Dividing first is shorter here, but expanding is the safer habit when the numbers don't divide evenly.
Common mistakes and how the game handles them
Doing an operation to one side only. The scale tips immediately, so students see the equation stop being true.
Dividing too early and creating fractions. If a division would split blocks into fractions, the game warns "Fractions Ahead!" and lets students undo. When they do go ahead, fractional pieces are drawn as a whole block with only part of it filled in, so ¼x really looks like a quarter of an x-block.
Distributing to only the first term (writing 2(x + 1) as 2x + 1). The Expand button animates every term in the group being multiplied, which is a good moment to pause the class and ask what happened to the 1.
Sign errors with negatives. Negative amounts appear as balloons lifting the pan rather than blocks pushing it down, which gives students a physical meaning for "subtracting a negative."
Ways to use it in class
- Printables. A free worksheet with an answer key and a two-to-a-page exit ticket match this game, ready to print or save as a PDF.
- Launch a new lesson. Project Sandbox mode, build x + 3 = 8, and ask the class what you could take off both pans. Record their moves as algebra on the board next to the scale.
- Warm-up. Five minutes of 1-Step or 2-Step Equations at the start of class. Students call out the level number they reached.
- Station rotation. One station plays the level that matches that group's current skill while you pull a small group.
- Connect to paper. Have students write each move they make on a whiteboard as an equation. Every click is one line of a written solution.
- Exit ticket. "Solve 3x + 2 = x + 8. Draw the scale after your first step."
Discussion questions
- Why does the scale stay level when you divide both sides by the same number?
- In 3x + 2 = x + 8, does it matter which side you collect the x's on? Try both.
- What would it mean if the scale balanced for every value of x? For no value?
Real-world connections
Variables on both sides model comparing two plans: a gym that charges $10 a month plus a $30 fee against one that charges $15 a month with no fee. Setting the costs equal (10m + 30 = 15m) finds the month when the two plans cost the same. One-variable equations show up in budgets, recipes, and any time you know a total and need a missing part.
Standards
CCSS.MATH.CONTENT.6.EE.B.7Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q. (1-Step Equations)
CCSS.MATH.CONTENT.7.EE.B.4aSolve equations of the form px + q = r and p(x + q) = r fluently. (2-Step and Complex Equations)
CCSS.MATH.CONTENT.8.EE.C.7bSolve linear equations with rational number coefficients, including equations that require expanding expressions using the distributive property and collecting like terms. (Variables Both Sides and Complex Equations)
Access and privacy
The game runs in the browser with no accounts, no logins, and no student data collected. It works with a mouse, a touchscreen, or the keyboard alone (arrow keys to move between buttons, Enter to press). On a phone, turn it sideways.