Algebra
Algebra is maths that uses letters, like x or n, to stand for numbers we don't know yet or numbers that can change. For example, if n + 3 = 10, then n = 7.
Maths · Ages 11–12 · 55 minutes
Solving simple equations
Pupils solve one- and two-step linear equations by doing the same inverse operation to both sides, and check solutions by substituting back.
Success criteria
- I can use inverse operations to solve a one-step equation
- I can solve a two-step equation in the right order
- I can check my answer by substituting
Key vocabulary
- equation
- unknown
- solve
- inverse operation
- balance
- substitute
- solution
- both sides
You will need
- a balance scale or a drawn balance
- cups and cubes (cups hide the unknown)
- mini whiteboards
Curriculum links
- Year 7· England
- Grade 6· United States
- JSS 1· Nigeria
- Class 7· India
- Common Core 6.EE.B.5: Understand solving an equation as finding which values make it true.
- Common Core 6.EE.B.7: Solve problems by writing and solving one-step equations of the form x + p = q and px = q.
- Common Core 7.EE.B.4.A: Solve word problems leading to equations of the form px + q = r and p(x + q) = r.
- England NC Y6.MA.AL.3: Express missing number problems algebraically.
- England NC KS3.MA.ALG.7: Solve linear equations in one variable, including all forms that need rearranging.
Practice sheets
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Solving equations: one step
Solving equations: two steps
Solving equations: x on both sides
1.Starter
7 minutes"I'm thinking of a number. I multiply it by 3 and add 4. I get 19. What's my number?" Take answers and, more importantly, methods. Most pupils will work backwards: 19 − 4 = 15, 15 ÷ 3 = 5. "You just solved an equation. Today we write that thinking down so it works for any number, not just easy ones."
2.Teach
15 minutesDraw a balance. On the left, a cup (hiding x cubes) and 5 loose cubes. On the right, 12 cubes. "This is x + 5 = 12. The scale balances, so both sides are equal."
"To find what's in the cup, I need the cup alone on one side. If I take 5 cubes off the left, the scale tips, unless I also take 5 off the right." Do it. "x = 7."
"That's the one rule of equations: whatever you do to one side, do to the other. And choose the inverse of what's been done to x."
Now a two-step equation: 3x + 4 = 19.
"Two things have happened to x: it was multiplied by 3, then 4 was added. To undo them, I go in reverse order. Socks go on before shoes, but shoes come off first. Undo the last thing first."
- "Subtract 4 from both sides: 3x = 15."
- "Divide both sides by 3: x = 5."
- "Check: 3 × 5 + 4 = 19. ✓"
Step by step
- Spot what's been done to xAnd in which order.
- Undo the last operation firstDo the inverse to both sides.
- Keep going until x is aloneWrite each step on a new line.
- Substitute to checkPut your answer back into the original equation.
