Proportional Relationships in Graphs

Grade Level

6th Grade

Duration

60 minutes

Unit Context

Unit 7 of 16 in "Ratios and Proportions Mastery"

Common Core Standards Addressed

CCSS.MATH.CONTENT.6.RP.A.3
*Use ratio and rate reasoning to solve real-world and mathematical problems, including:

(b) graphing points in the coordinate plane and recognizing proportional relationships represented in graphs.*

Learning Objectives

By the end of this lesson, students will:

I can identify whether a graph represents a proportional relationship.
I can describe characteristics of proportional relationships in graphs.
I can analyze tables and graphs to confirm proportional relationships.

Success Criteria

Students will demonstrate success when they:

Accurately determine if a graph represents a proportional relationship by checking for:
- A straight line through the origin (0,0).
- Constant unit rate (slope).
Explain in their own words why a graph does or does not show a proportional relationship.
Complete a quick formative assessment with 80% accuracy or higher.

Materials Needed

Whiteboard/Smartboard
Graph paper (dyslexia-friendly with larger grid lines and color-coded axes)
Dry-erase markers or colored pencils
Printed graph and table handouts with clear fonts and spacing (dyslexia-friendly font such as Open Dyslexic)
Calculators (optional)
Projector or chart for visual examples
Exit ticket handouts

Lesson Breakdown

1. Engage (10 minutes)

Warm-up Question: Present two graphs side-by-side: one proportional, one not.
Ask students: “Can you tell which graph shows a proportional relationship? How do you know?”
Facilitate brief discussion to activate prior knowledge.
Introduce the “I can” statement: I can recognize proportional relationships in graphs.
Write it clearly on the board and ask students to repeat it aloud.

Dyslexia-friendly tip: Use colored overlays or colored board markers for visual distinction between graphs.

2. Explain (15 minutes)

Define proportional relationships in graphs:
- Straight line through origin (0,0)
- Constant rate of change/slope
Demonstrate with 2-3 examples on the board/projector:
- Graph a table with proportional values (e.g., doubles or triples of x-values).
- Non-proportional example showing curve or line not through origin.
Use simple language and write key phrases in bold.
Highlight the two main characteristics students should check:
1. Does the line pass through the origin?
2. Is the slope / unit rate constant?

Dyslexia-friendly tip: Use a colored highlighter or underline important terms and steps.

3. Guided Practice (15 minutes)

Hand out printed worksheets with 3-4 graph and table pairs.
In pairs, students identify if the relationship shown is proportional or not.
Provide sentence stems to support responses:
- “The graph is proportional because…”
- “The line passes through…”
- “The slope/ratio is constant because…”
Circulate to scaffold for students who need additional support.

4. Independent Practice (12 minutes)

Give a set of 2 new graphs for students to analyze individually.
Students write a short paragraph explaining WHY or WHY NOT the graph shows a proportional relationship.
Encourage use of the “I can” statement and success criteria language in their explanation.

5. Closure & Assessment (8 minutes)

Collect exit tickets with two questions:
1. Does this graph represent a proportional relationship? (Yes/No)
2. Explain your reasoning using at least one success criterion.
Quickly review answers as a class, clarifying any misconceptions.
Re-state “I can” statement and celebrate progress.

Differentiation & Accessibility

Use dyslexia-friendly fonts and spacing on all printed materials.
Pair students strategically for peer support.
Provide color-coded graph axes and grids on graph paper.
Offer verbal and visual explanations.
Allow use of calculators for calculations if needed.
Encourage use of speech-to-text tools for written parts if available.

Reflection for Teacher

Were all students able to identify proportional relationships?
Did the sentence stems support thoughtful explanations?
Which misconceptions were most common and how can next lessons address them?
Adjust future lessons for pace and scaffold based on these reflections.

This lesson combines visual, verbal, and kinesthetic learning to help all students—especially those with dyslexia—confidently analyze graphs and recognize proportional relationships according to Common Core standards.