One-Step Addition and Subtraction Equations
Balance Workshop
Solve six mystery parcels on a workshop balance. Choose an inverse operation, apply the same move to both pans, and watch the scale settle as the unknown weight is revealed. Check each solution by substitution, with fresh addition and subtraction equations on every run.
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How to Play Balance Workshop
- 1
Read the equation
Look at the mystery parcel marked x and its signed extra weight. The other pan shows the known total. Both sides begin equal.
- 2
Choose the inverse
For x + 7 = 15, select Remove 7. For x − 7 = 15, select Add 7. A wrong choice explains which term needs its opposite and leaves the equation unchanged.
- 3
Move both pans
Tap Left pan and Right pan in either order. After the first tap the scale tips and asks for the same move on the other side. After both taps the scale balances and shows x by itself.
- 4
Read the check
The game reveals the answer and substitutes it into the original equation. For x + 7 = 15, the result is x = 8 and the check is 8 + 7 = 15.
- 5
Finish the run
Select Next parcel until six parcels are balanced. Select Play again for six new equations. Reset starts a new run at any time. Use Tab and Enter or Space to activate the same controls with a keyboard.
Key Features
A balance you operate
Select Add or Remove with the displayed amount, then tap Left pan and Right pan in either order. The first move tips the scale; the matching move restores balance and isolates the mystery parcel.
Addition and subtraction
Rounds alternate between x + a = b and x − a = b, with the unknown appearing on either side in later rounds. A signed weight represents subtraction rather than pretending that a negative quantity is ordinary physical mass.
Visible substitution
Once both moves are applied, the parcel reveals its value automatically. The original equation is shown again with that value substituted for x, so the solution can be checked without typing an answer.
Six fresh parcels
Each run contains six distinct equations using positive whole-number solutions. Play again draws a new set. There is no countdown or loss of lives, and incorrect choices can be retried.
Score, Best, and sound
Each balanced parcel earns 100 points, up to 600 per run. Best and the sound preference are saved in this browser when storage is available. Mute controls the quiet workshop music.
What is Balance Workshop?
Balance Workshop is an illustrated sixth-grade algebra game about one-step addition and subtraction equations. A mystery parcel stands for x, a signed weight shows the extra term, and the two pans represent the two sides of an equation. Players choose an inverse operation and apply it to each side themselves. For x + 7 = 15, remove 7 from both sides. The unknown pan becomes x, the known pan becomes 8, and the scale returns to level. The revealed parcel has value 8; substituting gives 8 + 7 = 15. In x − 7 = 15, add 7 to both sides instead, giving x = 22 and the check 22 − 7 = 15.
Why Play Balance Workshop?
- 1
Connect actions and symbols
The displayed equation changes with the pan actions, connecting an operation on a balance model to an equivalent algebraic equation.
- 2
Practice inverse operations
Addition and subtraction alternate so players must read the signed term and choose its opposite instead of repeating one button.
- 3
Preserve equality
Applying the operation to only one side visibly tips the scale. The second matching action shows why the same operation is needed on both sides.
- 4
Check the solution
Each result includes substitution into the original equation, including later rounds with the unknown on the right. There is time to read the check before moving on.
Frequently Asked Questions
What equations are included?
The game uses x + a = b and x − a = b with positive whole-number solutions, and later reverses the sides. The added or subtracted amount is from 2 to 12; addition solutions are from 2 to 20, and subtraction solutions are larger than the subtracted amount. Each six-round run contains distinct problems.
What does a negative weight mean?
It is a signed algebra model for subtraction, not a claim that a physical object has negative mass. Adding the matching positive amount cancels the negative term and leaves x alone.
What if I choose the wrong operation?
The equation does not change. Feedback identifies the term to cancel and asks for its opposite. You can try again without losing points or lives.
Why does the scale tip after one tap?
You have changed just one side of the equation. Apply the same selected operation to the other pan. The scale then levels and reveals the solution automatically.
How does scoring work?
Each completed parcel adds 100 to Score. Six parcels give 600. Best is saved locally when browser storage is available; Reset and Play again clear the current Score but keep Best.
Do I need to type answers or race a timer?
No. All moves use selectable buttons and pans, with touch, mouse, or keyboard. The value of x is calculated from your balance moves. There is no timer, and the substitution check stays visible until Next parcel.
Can I turn off the music?
Yes. Mute stops the music, and Sound on enables it again. The preference is saved in this browser when storage is available. Music pauses when the page is hidden.
