Inequalities on a Number Line

Active learning helps students move from abstract symbols to concrete understanding. For inequalities on a number line, moving, matching, and discussing shifts focus from memorising rules to visualising solutions. These activities make the invisible visible by turning symbols into physical actions and real-world connections.

• Year 7
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Differentiate between an equation and an inequality by identifying the correct comparison symbol and range of solutions.
2. Explain the conventions for representing strict inequalities (<, >) and inclusive inequalities (≤, ≥) on a number line, including endpoint circles and direction of shading.
3. Construct an inequality on a number line to represent a given real-world scenario with a specific constraint.
4. Calculate the boundary value for a given inequality and determine if it is included in the solution set.

Concept Mapping

⏱ 25 min·Pairs

Pairs: Symbol and Statement Match

Provide cards with inequality symbols, verbal statements, and blank number lines. Pairs match them, draw representations, then swap with another pair to check. Discuss any mismatches as a class.

Prepare & details

Differentiate between an equation and an inequality.

Facilitation Tip: During Symbol and Statement Match, circulate and listen for students to justify their pairing using the inequality symbols, not just guess by shape.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 35 min·Small Groups

Small Groups: Real-Life Inequality Challenges

Groups receive scenarios like 'books costing less than £20' or 'scores at least 70%'. They write inequalities, plot on shared number lines, and justify choices. Present one to the class.

Prepare & details

Explain how to represent 'greater than or equal to' on a number line.

Facilitation Tip: In Real-Life Inequality Challenges, prompt groups with questions like 'Could 42 passengers be on the bus? Why or why not?' to push reasoning beyond the obvious.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 20 min·Whole Class

Whole Class: Human Number Line Drama

Students line up as numbers from -10 to 10. Teacher calls inequalities; they step into shaded regions, using hoops for open/closed endpoints. Rotate roles for repetition.

Prepare & details

Construct an inequality that describes a given real-world constraint.

Facilitation Tip: For Human Number Line Drama, assign roles such as 'circle setter,' 'shade director,' and 'symbol reader' to ensure every student participates actively.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 20 min·Individual

Individual: Inequality Number Line Puzzles

Students solve given inequalities, draw number lines, and create their own from prompts like sports scores. Peer review follows for accuracy.

Prepare & details

Differentiate between an equation and an inequality.

Facilitation Tip: During Inequality Number Line Puzzles, ask students to verbalise their first step aloud to uncover hidden misconceptions before they complete the task.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Teaching This Topic

Teach this topic by starting with the visual and physical before introducing symbols. Research shows students grasp inequalities better when they experience the continuum firsthand through movement and manipulatives. Avoid rushing to formal notation; let students describe what they see in their own words first. Emphasise that inequalities are not solved for a single value but explored as a set, so language like 'all numbers greater than' becomes habitual.

What to Expect

By the end of these activities, students will confidently translate inequalities into number line representations and vice versa. They will explain why open and closed circles matter, and recognise that inequalities describe ranges, not single points. Their language will shift from saying 'the answer is' to 'all numbers that' when describing solutions.

Watch Out for These Misconceptions

Common Misconception

During Symbol and Statement Match, watch for students who treat inequalities as having only one solution point like equations.

What to Teach Instead

After pairs finish matching, ask each pair to test three numbers in their matched inequality statement and list them. Circulate to prompt: 'Does your list include all numbers that work, or just one? How do you know?'

Common Misconception

During Real-Life Inequality Challenges, watch for students who assume open and closed circles mean the same thing.

What to Teach Instead

Hand each group a set of tokens and a mat with a number line. Ask them to place the token on the endpoint and discuss: 'If the token stays, is the endpoint allowed? If not, why remove it?' Let groups physically test scenarios like 'up to 10' versus 'more than 10'.

Common Misconception

During Human Number Line Drama, watch for students who assume shading always extends right for 'greater than' inequalities.

What to Teach Instead

After the human number line is set up, freeze the group and ask: 'If we have x > -1, where should the shading go? What about x < 3?' Have students physically move to the correct side and reflect on why direction changes based on the inequality symbol.

Assessment Ideas

Quick Check

After Symbol and Statement Match, present students with four number lines showing different representations. Ask them to write the corresponding inequality and label each as strict or inclusive. Collect to check for accurate translation of symbols to number lines.

Exit Ticket

After Real-Life Inequality Challenges, give each student a scenario like 'A movie theatre has a minimum age of 12 for admission.' Ask them to write the inequality and draw the number line representation. Use this to assess understanding of inclusive versus strict boundaries.

Discussion Prompt

During Human Number Line Drama, pause after setting up x = 5 and x > 5. Ask students to explain the difference in small groups, then share with the class. Listen for mentions of 'one point' versus 'a range' and correct any lingering confusion about single solutions versus continuous sets.

Extensions & Scaffolding

• Challenge early finishers to create a real-world scenario (e.g., temperature ranges, age limits) and represent it with an inequality and number line for peers to solve.
• Scaffolding: Provide sentence stems like 'The open circle means...' and 'The shading goes left because...' for students to complete as they work through puzzles.
• Deeper exploration: Introduce compound inequalities (e.g., -3 < x ≤ 5) and ask students to design a number line puzzle that includes two conditions, then swap with a partner to solve.

Key Vocabulary

Inequality	A mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥, indicating that one side is not equal to the other.
Number Line	A visual representation of numbers, typically a straight line with markings at regular intervals, used to display solutions to equations and inequalities.
Strict Inequality	An inequality that uses symbols < (less than) or > (greater than), meaning the boundary value is not included in the solution set.
Inclusive Inequality	An inequality that uses symbols ≤ (less than or equal to) or ≥ (greater than or equal to), meaning the boundary value is included in the solution set.
Solution Set	The collection of all values that satisfy an inequality, often represented by shading on a number line.