Primary 6 maths · Algebra · About 14 minutes
Letters and balanced equations
Use a letter for an unknown number
Start the interactive lesson →Open practice activity
What you will learn
- Use a letter for an unknown number
- Substitute a value into a simple expression
- Solve equations by keeping both sides equal
Models used: balance scales, bar models, number sentences, stories.
Before you start
Do the same to both sides
Each bag has the same hidden number of counters. Call that number x.
Matching bags hold the same amount. A level balance means both sides have equal value.
Each bag has the same hidden number of counters. Call that number x.
Equality is a relationship between both sides. Adding or removing the same amount on both sides keeps that relationship true.
xxx = x · balanced
Matching bags hold the same amount. A level balance means both sides have equal value.
Three bags contain x + x + x counters. We write that more briefly as 3x.
x + x + x = 3x
Equality is a relationship between both sides. Adding or removing the same amount on both sides keeps that relationship true.
xxxxxx3x = 3x · balanced
Matching bags hold the same amount. A level balance means both sides have equal value.
Add two loose counters. The total is 3x + 2, whatever number is hidden in each bag.
3x + 2
Equality is a relationship between both sides. Adding or removing the same amount on both sides keeps that relationship true.
xxxxxx3x + 2 = 3x + 2 · balanced
Isn’t there a shortcut where the sign changes?
Some people write “+ 3 moves across and becomes − 3”. That shortcut is only a description of what happens when you take 3 from both sides. If you learn it as a rule on its own, it is easy to misuse; the balance always tells you what is really allowed.
x + 3 = 8 · balanced
Worked example
2x + 3 = 11
What does 2x mean?
2x means…
2 lots of x
Take 3 off both sides.
2x = 11 − 3
xx2x = 8 · balanced
What is 11 − 3?
8
Two boxes balance 8, so split both sides into 2 equal groups.
x = 8 ÷ 2
What is x?
4
So x = 4.
2 × 4 + 3 = 11 ✓
Common mistakes to discuss
- Reading 3x as 3 + x. 3x means 3 lots of x. When x = 5, 3x is 15, not 8.
- Moving a term across without doing the same to both sides. The equals sign means both sides weigh the same. Taking 3 from one side only tips the balance; take it from both.
Check your understanding
- read 3x as three lots of x
- work out 3x + 4 when x = 5
- solve x + 3 = 8 and 2x + 3 = 11
- explain why the same must be done to both sides
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
Try this lesson →Related Primary 6 lessons
- Use a letter for an unknown numberUse a letter for an unknown number · About 12 minutes
- Form simple expressions involving an unknownForm simple expressions involving an unknown · About 12 minutes
- Simplify linear expressions without bracketsSimplify linear expressions without brackets · About 12 minutes
- Substitute values into expressionsSubstitute values into expressions · About 12 minutes
- Solve linear equations with whole-number coefficientsSolve linear equations with whole-number coefficients · About 12 minutes