Primary 6 maths · Algebra · About 12 minutes
Substitute values into expressions
Say what one letter means before grouping terms or substituting a value.
Start the interactive lesson →Practise: Expression codebreakers
What you will learn
- Substitute values into expressions
Models used: number sentences, stories, tables.
Before you start
Open every bag
The expression 3x + 2 means three equal bags and two loose counters.
Matching bags hold the same amount. A level balance means both sides have equal value.
The expression 3x + 2 means three equal bags and two loose counters.
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
There are 3 groups, with 4 objects in each group. Count a group before counting them all.
We learn that each bag contains 4. Replace every x with 4.
3 × 4 + 2
4 + 4 + 4 = 3 × 4 = 12
The complete bar is the whole. Each labelled section is one part of it.
The three bags give 12 counters. Add the 2 loose ones.
3 × 4 + 2 = 14
What did the picture help us see?
The three bags give 12 counters. Add the 2 loose ones.
Worked example: A new example, together
Find 2x + 6 when x = 5.
| Expression | Given value |
|---|---|
| 2x + 6 | x = 5 |
Replace x by the given number before calculating. Read each value with the heading above its column.
Say what one letter means before grouping terms or substituting a value.
Substitution replaces every occurrence of a letter by the same given number.
Replace x by the given number before calculating. Expression Given value 2x + 6 x = 5 Replace x by the given number before calculating. Read each value with the heading above its column.
Replace x by 5.
Replace x by the given number before calculating. Expression Given value 2x + 6 x = 5 Find 2x + 6 when x = 5.
16
Replace x by the given number before calculating. Read each value with the heading above its column.
Multiply first: 2 × 5 = 10.
Replace x by the given number before calculating. Expression Given value 2x + 6 x = 5 Replace x by the given number before calculating. Read each value with the heading above its column.
Add 6: 16.
Replace x by the given number before calculating. Expression Given value 2x + 6 x = 5 Replace x by the given number before calculating. Read each value with the heading above its column.
Check the result against the question we started with.
16 − 6 = 2 × 5.
We found 16. Substitution replaces every occurrence of a letter by the same given number.
Replace x by the given number before calculating. Expression Given value 2x + 6 x = 5
Common mistakes to discuss
- Writing the digits side by side. A number before a letter means multiply. When x = 5, 2x is 10, so 2x + 6 is 16, not 256.
Check your understanding
- Substitute values into expressions
- interpret and use an expression through the meaning of its unknown
- check the answer against the original quantities and units
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.
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