Equality & Balance

What is an equation?

An equation is a statement that two things are equal. The equals sign is a promise: whatever is on the left weighs exactly the same as whatever is on the right.

Equality & Balance draws it that way. One side is a pan of weights, the other side is a pan of weights, and the bar in the middle only stays level when the two sides match.

What is this module?

The module opens with an equation like x + 3 = 7. The left pan holds an x block and three unit weights. The right pan holds seven unit weights. The x block hides a number you are trying to find.

You can add a weight or remove a weight from either pan with the plus and minus buttons, or by tapping a weight to remove it. The scale tips whenever the two pans are not equal. Your job is to get x alone on one side while keeping the scale level.

There is also an Inequality mode, where the two sides are not equal and you test values of x.

What they're learning

The whole unit is one rule: whatever you do to one side, you must do to the other.

• Keep it balanced. An equation stays true only when you make the same change to both sides.
• Subtract to undo adding. If x + 3 = 7, remove three weights from each pan and x is left alone. Then x = 4.
• Add to undo subtracting. The same idea in reverse.
• Divide to undo multiplying. If 2x = 8, splitting both sides into two equal groups leaves x = 4.
• Inequalities have many solutions. In x + 3 > 7, any x greater than 4 works. That is a whole ray of numbers, not one answer.

The rule "do the same to both sides" is the single idea that carries a student through years of algebra. If they get this, they are set.

Aliases

• Solving equations
• One-step equations
• Balance scale model
• "Do the same to both sides"
• Inverse operations

Refresher

An equation says two amounts are equal. Picture a balance that stays level only when both pans weigh the same. To solve it, do the same thing to both sides until the variable sits alone on one side.

Try this together

Keep it short. The scale does the explaining.

1. Look at x + 3 = 7 together. Ask which number is hiding behind x.
2. Remove three weights from each pan and watch x sit alone next to four weights.
3. Add a weight to just one pan on purpose and watch it tip. That tip is the lesson.
4. In Inequality mode, drag x back and forth across 4 and read the true or false line underneath.

If your kid guesses x = 4 right away, that is good, but ask how the scale proves it. Proof is the point, not the guess.

Words you might hear

• Equation: a statement that two amounts are equal, joined by an equals sign.
• Variable: a letter, usually x, standing in for a number you do not know yet.
• Solve: find the value of the variable that makes the equation true.
• Inverse operation: the undo move. Addition undoes subtraction, and division undoes multiplication.
• Inequality: a statement that one side is greater or less than the other, using > or <.
• Solution set: all the values of x that make a statement true. An inequality usually has many.

Deeper dive

Look at x + 3 = 7. The left pan holds an x and three weights, the right pan holds seven. Take three weights off each pan. The left pan keeps x, the right pan keeps 4, and the pans still balance, so x = 4.

For 2x = 8, split both pans into two equal groups. One group is x on the left and 4 on the right, so x = 4. The scale in the module tips the moment you change one pan without the other.