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Inequalities on number lines

I can represent inequalities on a number line and what values satisfy an inequality based on the notation used.

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Year 11

Inequalities on number lines

I can represent inequalities on a number line and what values satisfy an inequality based on the notation used.

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Lesson details

Key learning points

Inequalities can be represented algebraically
Inequalities can be represented graphically on a number line
The diagram can indicate whether the inequality is a strict inequality
Multiple inequalities can be shown on one number line

Keywords

Inequality - An inequality is used to show that one expression may not be equal to another.

Common misconception

Incorrectly interpreting the inequality diagram.

A filled in circle means the value is valid. An empty circle means the inequality is strict.

Pupils could use MWBs to draw their own inequalities on a number line and have a peer write the inequality represented. Additional challenge can be introduced by allowing multiple inequalities to be drawn on the same number line.

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Licence

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.
Match up the inequalities to the statements.

Correct Answer:$$x<-2$$,values less than -2

Correct Answer:$$x\le-2$$,values less than or equal to -2

Correct Answer:$$x>-2$$,values greater than -2

Correct Answer:$$x\ge-2$$,values greater than or equal to -2

Q2.
Which of these values satisfy the inequality $$x<3$$?

Correct answer: $$x=1$$

Correct answer: $$x=2$$

$$x=3$$

$$x=4$$

$$x=5$$

Q3.
Which of these values satisfy the inequality $$x\ge2$$?

$$x=-3$$

Correct answer: $$x=2$$

$$x=1.47$$

Correct answer: $$x=2.06$$

$$x=\frac{5}{6}$$

Q4.
Which of these values satisfy the inequality $$x>-1$$?

Correct answer: $$x=0$$

$$x=-1$$

$$x=-2$$

$$x=-\frac{4}{3}$$

Correct answer: $$x=-\frac{6}{7}$$

Q5.
Which of these values satisfy the inequality $$1<x\le3$$?

Correct answer: 3

Correct answer: 1.3

3.0004

Q6.
What is the value of $$a$$ on the number line?

Correct Answer: 18

Assessment exit quiz

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6 Questions

Q1.
Match the diagram to the correct inequality.

Correct Answer:A,$$x\le1$$

Correct Answer:B,$$x\ge1$$

Correct Answer:C,$$x>1$$

Correct Answer:D,$$x<1$$

Q2.
What inequality is represented in this diagram?

$$-1<x<1$$

$$-1\le x \le 1$$

Correct answer: $$-1<x \le 1$$

$$-1\le x<1$$

Q3.
What inequality is represented in this diagram?

$$1<x<2$$

$$1\le x<2$$

$$1<x$$ or $$x>2$$

Correct answer: $$x\le 1$$ or $$x>2$$

$$x\le 1$$ or $$x\le 2$$

Q4.
Which diagram shows all values which satisfy both $$x<1$$ and $$x>0$$ ?

Correct Answer: An image in a quiz

Q5.
Which inequality represents all values which satisfy both of the drawn inequalities?

$$1<x<2$$

$$x<1$$ or $$x>2$$

Correct answer: $$x<1$$

$$x<2$$

Q6.
Which inequality represents all values which satisfy both of the drawn inequalities?

$$-1\le x < 2$$

$$-1\le x < 1$$

Correct answer: $$0\le x < 1$$

$$0\le x < 2$$

Lesson appears in

UnitMaths / Inequalities

Maths

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Inequalities on number lines

Inequalities on number lines

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Match up the inequalities to the statements.

Q2.Which of these values satisfy the inequality $$x<3$$?

Q3.Which of these values satisfy the inequality $$x\ge2$$?

Q4.Which of these values satisfy the inequality $$x>-1$$?

Q5.Which of these values satisfy the inequality $$1<x\le3$$?

Q6.What is the value of $$a$$ on the number line?

Assessment exit quiz

6 Questions

Q1.Match the diagram to the correct inequality.

Q2.What inequality is represented in this diagram?

Q3.What inequality is represented in this diagram?

Q4.Which diagram shows all values which satisfy both $$x<1$$ and $$x>0$$ ?

Q5.Which inequality represents all values which satisfy both of the drawn inequalities?

Q6.Which inequality represents all values which satisfy both of the drawn inequalities?

Lesson appears in

UnitMaths / Inequalities

Maths

Q1.
Match up the inequalities to the statements.

Q2.
Which of these values satisfy the inequality $$x<3$$?

Q3.
Which of these values satisfy the inequality $$x\ge2$$?

Q4.
Which of these values satisfy the inequality $$x>-1$$?

Q5.
Which of these values satisfy the inequality $$1<x\le3$$?

Q6.
What is the value of $$a$$ on the number line?

Q1.
Match the diagram to the correct inequality.

Q2.
What inequality is represented in this diagram?

Q3.
What inequality is represented in this diagram?

Q4.
Which diagram shows all values which satisfy both $$x<1$$ and $$x>0$$ ?

Q5.
Which inequality represents all values which satisfy both of the drawn inequalities?

Q6.
Which inequality represents all values which satisfy both of the drawn inequalities?