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Checking and securing understanding of substitution

I can substitute particular values into a generalised algebraic statement to find a sense of how the value of the expression changes.

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Lesson 2 of 13

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Year 10

Checking and securing understanding of substitution

I can substitute particular values into a generalised algebraic statement to find a sense of how the value of the expression changes.

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Lesson details

Key learning points

Expressions and formulae in context can be evaluated for particular values.
Changing the value of the variable changes the overall value of the expression.
Exploring what value gives a particular solution can help you to understand the expression.
Expressions may have multiple variables and you can substitute some or all of them for numbers.

Keywords

Substitution - Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values.

Common misconception

Incorrect evaluation of expressions is common when negative values are substituted. Especially where negative values are squared or pupils rely on calculators without being confident of their use.

When substituting, always put brackets around the value which is substituted. This helps avoid mistakes when using a calculator as well.

This lesson explores substitution in a range of other topics and contexts. This is a good opportunity for revision of KS3 topics and to highlight the importance of accurate substitution in every branch of mathematics. Pupils could reflect on other subjects where they use these skills.

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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
Simplify the following: $$3(2x + 1) + 2(2x + 1) = \square(2x + 1)$$

Correct Answer: 5

Q2.
Simplify the following: $$4(x - 3) + 3(x - 3) = \square(x - 3)$$

Correct Answer: 7

Q3.
If $$b = 9$$, what is $$b^2$$?

Correct Answer: 81

Q4.
If $$p = 9$$, what is $$2p^2$$?

Correct Answer: 162

Q5.
If $$c = 4$$, what is $$4c + 3$$?

Correct Answer: 19

Q6.
If $$c = 4b + 2$$, what is $$3c$$? Give your answer in expanded form.

Correct Answer: 12b + 6

Assessment exit quiz

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6 Questions

Q1.
Evaluate the expression $$2x - 3$$ for $$x = 5$$

Correct Answer: 7

Q2.
Evaluate the expression $$\frac{3x}{4}$$ for $$x = 8$$

Correct Answer: 6

Q3.
Evaluate the expression $$4x^2$$ for $$x = 3$$

Correct Answer: 36

Q4.
Evaluate the expression $$5(x - 3)$$ for $$x = 7$$

Correct Answer: 20

Q5.
Evaluate the expression $$\frac{3x + 2}{4}$$ for $$x = 6$$

Correct Answer: 5

Q6.
Evaluate the expression $$\frac{x}{x + 1}$$ for $$x = 4$$ and give your answer as a decimal.

Correct Answer: 0.8

Lesson appears in

UnitMaths / Algebraic manipulation

Maths

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Checking and securing understanding of substitution

Checking and securing understanding of substitution

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Simplify the following: $$3(2x + 1) + 2(2x + 1) = \square(2x + 1)$$

Q2.Simplify the following: $$4(x - 3) + 3(x - 3) = \square(x - 3)$$

Q3.If $$b = 9$$, what is $$b^2$$?

Q4.If $$p = 9$$, what is $$2p^2$$?

Q5.If $$c = 4$$, what is $$4c + 3$$?

Q6.If $$c = 4b + 2$$, what is $$3c$$? Give your answer in expanded form.

Assessment exit quiz

6 Questions

Q1.Evaluate the expression $$2x - 3$$ for $$x = 5$$

Q2.Evaluate the expression $$\frac{3x}{4}$$ for $$x = 8$$

Q3.Evaluate the expression $$4x^2$$ for $$x = 3$$

Q4.Evaluate the expression $$5(x - 3)$$ for $$x = 7$$

Q5.Evaluate the expression $$\frac{3x + 2}{4}$$ for $$x = 6$$

Q6.Evaluate the expression $$\frac{x}{x + 1}$$ for $$x = 4$$ and give your answer as a decimal.

Lesson appears in

UnitMaths / Algebraic manipulation

Maths

Q1.
Simplify the following: $$3(2x + 1) + 2(2x + 1) = \square(2x + 1)$$

Q2.
Simplify the following: $$4(x - 3) + 3(x - 3) = \square(x - 3)$$

Q3.
If $$b = 9$$, what is $$b^2$$?

Q4.
If $$p = 9$$, what is $$2p^2$$?

Q5.
If $$c = 4$$, what is $$4c + 3$$?

Q6.
If $$c = 4b + 2$$, what is $$3c$$? Give your answer in expanded form.

Q1.
Evaluate the expression $$2x - 3$$ for $$x = 5$$

Q2.
Evaluate the expression $$\frac{3x}{4}$$ for $$x = 8$$

Q3.
Evaluate the expression $$4x^2$$ for $$x = 3$$

Q4.
Evaluate the expression $$5(x - 3)$$ for $$x = 7$$

Q5.
Evaluate the expression $$\frac{3x + 2}{4}$$ for $$x = 6$$

Q6.
Evaluate the expression $$\frac{x}{x + 1}$$ for $$x = 4$$ and give your answer as a decimal.