Contents
Y14 · Linear Equations
KO

Middle school maths, year 1 · unit 4

Linear Equations

The equals sign is not an order to "write the answer". It says "both sides are the same". So an equality is a level scale. We start by putting the pouches and marbles from the last unit on a balance.

Two students looking at a balance scale holding a pouch and marbles

The equals sign is a level scale

A board to arrange

The number of marbles in the pouch is x. Drag marbles from the pile into the pouch and watch for when the scale goes level.

Take the same from both sides

A board to arrange

Take from one side only and the scale tips. Drag marbles and pouches off the pans until just one pouch is left on the left.

Cross over, change sign

A board to arrange

Now do on the equation what you did on the scale. Drag the gold-edged card across the equals sign.

Turn sentences into equations

Joining board

Call the unknown x, turn "is" into an equals sign, and a sentence becomes an equation. Drag the dot of each sentence on the left to the dot of its equation.

Try it yourself

Use what you found on the boards. The numbers change every time and the easy questions come first. Get three right and the lamp lights.

What to take away from this unit

  1. A statement that two sides are equal, written with an equals sign, is an equality. One that is true or false depending on x is an equation, and the value of x that makes it true is its solution. An equality true for every x is an identity.
  2. Add the same number to both sides, subtract it, multiply by it, or divide by the same non-zero number, and an equality stays true. These are the properties of equality, just as a scale stays level when you take the same off both pans.
  3. Moving a term across the equals sign with its sign changed is transposing. In x + 3 = 7, move +3 across and x = 7 − 3.
  4. The order of work: move letter terms to the left and numbers to the right → tidy both sides into the form ax = b → divide both sides by a. 2x + 3 = x + 8 → 2x − x = 8 − 3 → x = 5.
  5. For a problem in words, call what you want x and turn "is" into an equals sign to set up the equation. Once you have the answer, put it back into the sentence to check.

See where this unit sits on the maths family tree