Mathematics · Year 7

Active learning ideas

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.

• National Curriculum Attainment Targets
• KS3: Mathematics - Algebra

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Present students with four number lines, each showing a different inequality representation (e.g., open circle at 3 shaded right, closed circle at -2 shaded left). Ask students to write the corresponding inequality for each number line and identify if it is strict or inclusive.

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

Activity 02

• 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.

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.

What to look for

Give each student a scenario, such as 'A bus has a maximum capacity of 40 passengers.' Ask them to write an inequality representing the number of passengers (p) and then draw the correct representation on a number line.

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

Activity 03

• 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.

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.

What to look for

Pose the question: 'What is the difference between x = 5 and x > 5?' Facilitate a class discussion where students explain the meaning of each statement and how they would be represented on a number line, focusing on the concept of a single solution versus a range of solutions.

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

Activity 04

• 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.

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.

What to look for

Present students with four number lines, each showing a different inequality representation (e.g., open circle at 3 shaded right, closed circle at -2 shaded left). Ask students to write the corresponding inequality for each number line and identify if it is strict or inclusive.

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

A few notes on teaching this unit

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.

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

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

  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?'

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

  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'.

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

  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.

---

Methods used in this brief

• Concept Mapping