WorksheetsAbout this worksheet
An equation is a balance: whatever is done to one side must be done to the other. One step sheets give equations like x + 7 = 12 or 3x = 21. Two step sheets give equations like 2x + 3 = 11. Every answer is a whole number.
What this skill is
An equation says that two things are equal, with one number hidden behind a letter. Solving it means finding the number that makes the statement true. The method is to undo, one at a time, whatever has been done to the letter, always doing the same thing to both sides so that the balance is kept.
A worked example
Solve 3x − 4 = 17.
- The letter has been multiplied by 3, and then 4 has been taken away. Undo the last thing first.
- Add 4 to both sides: 3x = 21.
- Divide both sides by 3: x = 7.
Check by putting 7 back: 3 × 7 − 4 = 21 − 4 = 17. Both sides agree, so x = 7 is right.
Tips for parents and teachers
- Write each step on a new line, with the equals signs one under the other.
- Undo in reverse order: in 2x + 3 = 11, first take away the 3, then divide by 2.
- Always check by putting the answer back into the equation.
How to use this sheet at home and in class
- At home: do "One step" until the child can say what was done to the letter and how to undo it. Speed is not the aim here; the sentence is.
- In class: draw a balance on the board for the first few equations and take the same weight off both pans.
- Insist on the check line. It turns the answer page into something the child does not need.
Mistakes to watch for
- Doing the operation on one side only: from 3x − 4 = 17 writing 3x = 17.
- Undoing in the wrong order in a two step equation: dividing 3x − 4 = 17 by 3 first and dividing only part of it.
- Learning "change the side, change the sign" as a trick without the balance idea, and then using it for multiplication, so 3x = 21 becomes x = 21 − 3.
What to try next
- Missing numbers worksheets: the same idea with a blank, if this feels too abstract.
- Integers worksheets: for answers below zero later on.
- BODMAS worksheets: the order that solving undoes.