Mathematics · Grade 6

Active learning ideas

Graphing Inequalities on a Number Line

Active learning works especially well for graphing inequalities because students need to physically plot points, discuss circle types, and interpret symbols in real time. Moving from abstract symbols to concrete number line representations builds lasting understanding that static worksheets cannot provide.

• Ontario Curriculum Expectations
• 6.EE.B.8

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Gallery Walk
• 30 min · Pairs

Pairs Relay: Inequality Graphing

Pairs take turns drawing a given inequality on mini number lines, such as x < 4, while their partner checks for correct circle type and arrow. Switch roles after five inequalities. Debrief as a class to share common patterns.

Explain how to graphically represent the solution set of an inequality.

Facilitation Tip

During Pairs Relay, place a timer visible to all students to keep energy high and ensure every pair completes each round before rotating.

What to look for

Present students with three inequalities: x < 5, y ≥ -2, and z > 0. Ask them to draw a number line for each, correctly placing the boundary point, using the appropriate circle type, and shading in the correct direction. Review their number lines for accuracy.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Gallery Walk
• 45 min · Small Groups

Small Groups: Real-World Inequality Hunt

Provide scenarios like 'ages greater than 12 for a movie.' Groups write inequalities, graph them on shared number lines, and justify choices. Rotate graphs for peer review and revisions.

Differentiate between an open circle and a closed circle on an inequality graph.

Facilitation Tip

In the Real-World Inequality Hunt, provide measuring tools like rulers or measuring tapes so students collect precise data for their inequalities.

What to look for

Give students a pre-drawn number line with a boundary point, circle, and shading. Ask them to write the inequality that this graph represents and explain in one sentence why they chose an open or closed circle.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 20 min · Whole Class

Whole Class: Interactive Number Line Demo

Project a large number line. Call out inequalities; students use sticky notes to mark boundaries and arrows as a group. Discuss adjustments based on class input.

Analyze how the direction of the inequality symbol affects the graph.

Facilitation Tip

For the Interactive Number Line Demo, use masking tape on the floor to create a large number line that students can stand on while demonstrating solutions.

What to look for

Pose the question: 'Imagine you are explaining how to graph inequalities to a younger student. What are the two most important things they need to remember about the circle and the arrow on the number line, and why?' Facilitate a brief class discussion to consolidate understanding.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 25 min · Individual

Individual: Inequality Graph Journal

Students solve and graph 10 varied inequalities in journals, coloring solution regions. Pair share to verify before submitting.

Explain how to graphically represent the solution set of an inequality.

Facilitation Tip

In the Inequality Graph Journal, require students to write both the inequality and a brief justification for each graph to reinforce metacognition.

What to look for

Present students with three inequalities: x < 5, y ≥ -2, and z > 0. Ask them to draw a number line for each, correctly placing the boundary point, using the appropriate circle type, and shading in the correct direction. Review their number lines for accuracy.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Teachers should start with strict inequalities before introducing inclusive ones, as the distinction between open and closed circles is foundational. Avoid teaching shading on number lines, since arrows alone represent infinite solutions clearly. Research shows that students benefit most when they explain their reasoning aloud while graphing, so prioritize verbalization over silent work.

Successful learning looks like students confidently choosing between open and closed circles, orienting arrows correctly, and explaining their choices to peers without hesitation. Mastery is evident when they can translate between inequality notation and number line graphs fluently.

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Watch Out for These Misconceptions

• During Pairs Relay, watch for students who automatically use closed circles for all inequalities.

  Remind relay pairs to read each inequality aloud and discuss whether the boundary point is included before plotting. If a pair makes this error, have them exchange papers with another pair for verification.

• During Real-World Inequality Hunt, watch for students who assume the arrow always points right.

  Prompt students to compare their inequality symbols with the direction of their arrows. Ask, 'Why does your arrow point left for x < 5?' to push them to connect symbols to graphical representation.

• During Interactive Number Line Demo, watch for students who instinctively shade the number line.

  Pause the demo and ask, 'Does shading help us show all solutions here?' Have students experiment by drawing arrows without shading to test which method clearly communicates the solution set.

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Methods used in this brief

• Gallery Walk