How to teach algebra

Early algebra uses a letter to stand for an unknown number, then finds its value. An equation like x plus 5 equals 12 is a balance: whatever you do to one side you must do to the other. Solving means undoing the operations around the letter until it stands alone.

Early algebra is usually introduced from Grade 4 to Grade 6. Students begin with a missing number in a box, move to a letter for the unknown, and learn to solve one-step and then two-step equations using inverse operations.

It means the two sides balance, that they have the same value, not 'here comes the answer'. Treating equals as a signal to write a result is a major stumbling block. Using scales or a bar model shows that an equation keeps both sides equal.

Use the inverse operation on both sides. Since 5 is added to x, subtract 5 from both sides, giving x equals 7. Keeping the equation balanced, doing the same to each side, is the core method. Always check by substituting 7 back into the original equation.

Inverse operations undo each other: addition undoes subtraction, and multiplication undoes division. To free the unknown you apply the inverse of whatever is done to it. So to solve 3 times x equals 12, divide both sides by 3, which undoes the multiplication and gives x equals 4.

The usual causes are reading the equals sign as 'work out the answer' rather than 'the sides balance', changing one side without doing the same to the other, and using the same operation instead of its inverse. Starting with a missing number in a box before letters helps build the balance idea.

3x means 3 multiplied by x, not the digit 3 followed by x. When a number sits directly before a letter, it multiplies it, so 3x is three lots of the unknown. Misreading 3x as two separate things is a common early error.