Connecting Proportions to Functions

Grade Level

7th Grade

Duration

60 Minutes

Unit

Ratios and Proportions Mastery (Lesson 15 of 16)

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Common Core State Standards (CCSS) Alignment

CCSS.MATH.CONTENT.7.RP.A.2
Recognize and represent proportional relationships between quantities.

CCSS.MATH.CONTENT.7.RP.A.2.B
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

CCSS.MATH.CONTENT.7.F.A.1
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

CCSS.MATH.CONTENT.7.F.B.4
Construct a function to model a linear relationship between two quantities.

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Learning Objectives

• I can describe proportional relationships using ratios, tables, and graphs.
• I can explain how a proportional relationship represents a linear function.
• I can write a function rule from a proportional relationship.
• I can interpret the constant of proportionality as the rate of change in a function.

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Success Criteria

• I can identify the unit rate from a ratio table.
• I can create and describe a graph that represents a proportional relationship.
• I can write linear functions that model proportional relationships.
• I can explain how proportional relationships fit the definition of a function.

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Materials Needed

• Whiteboard and markers
• Graph paper (dyslexia-friendly with colored grid lines, e.g., light blue)
• Ratio tables handout (large print, dyslexia-friendly font such as OpenDyslexic)
• Interactive mini-whiteboards for student responses
• Calculators (optional)
• Color-coded function cards for grouping activity
• Visual props: rulers and measuring tape

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Lesson Breakdown

1. Warm-Up (10 minutes)

• Begin with a brief review using a simple, relatable proportional relationship (e.g., recipe ingredient scaling, or speed and time while traveling).
• Display a ratio table representing a proportional relationship (e.g., 1 cup flour : 2 cups sugar scaled up) in dyslexia-friendly font on the board.
• Ask students to identify the unit rate and explain it in their own words.
• Formative Check: Quick whole-class Q&A to ensure understanding.

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2. Introduction to Concepts (10 minutes)

• Explain the connection between proportional relationships and linear functions: every proportional relationship can be represented as a linear function with the equation ( y = kx ).
• Define constant of proportionality (k) as the slope or unit rate.
• Use a graph on the board to illustrate a line that passes through the origin and explain the significance (y-intercept is 0).
• Use color-coded lines on graph paper to differentiate between functions (visual aid).

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3. Guided Practice (15 minutes)

• Distribute ratio tables handout formatted in dyslexia-friendly font and color.
• In pairs (heterogeneous grouping to support diverse learners), students complete tables and then graph the proportional relationship on colored graph paper.
• Students write the function rule using ( y = kx ) notation based on their tables.
• Teacher circulates to scaffold and prompt deeper thinking (e.g., “What happens if the input doubles? What does ( k ) mean here?”).

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4. Activity: Function Card Match-Up (15 minutes)

• Provide groups with cards showing proportional relationships in four formats: verbal description, table, graph, and function rule.
• Students must match four cards that represent the same proportional relationship (e.g., verbal description of speed, corresponding table, graph, and function rule ( y = 5x )).
• Groups explain their matches to the class with one representative speaking.
• This multi-modal activity reinforces diverse learning preferences, supports dyslexic students via repetition and different formats.

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5. Closing Reflection & Exit Ticket (10 minutes)

• Have students complete a brief exit ticket:
  1. Write an "I can" statement about today’s lesson.
  2. Answer: “How is a proportional relationship like a function?”
  3. Identify the constant of proportionality in a provided ratio table, with space for a short explanation.
• Review exit tickets quickly to gauge class understanding and tailor the last lesson.

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Differentiation & Dyslexia-Friendly Supports

• Use dyslexia-friendly font (OpenDyslexic or similar) and spacing in all printed materials.
• Use color overlays and graph paper with subtle colored grids to reduce visual stress.
• Oral instructions paired with visual examples and manipulatives (rulers, measuring tape).
• Pair stronger readers with students who need support for peer-assisted learning.
• Visual aids with consistent color coding for proportional elements (e.g., rate always in blue, input in green).
• Allow response flexibility via oral explanations or drawing instead of written only.

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Assessment

• Informal formative assessments during warm-up discussions and guided practice.
• Group activity observations and explanations.
• Exit ticket responses to check individual understanding.

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Reflection for the Teacher

• Did students connect proportional reasoning to function rules successfully?
• Which students showed difficulty, and how can next lesson address their needs?
• How effective was the multi-sensory approach for engagement and understanding?
• Consider incorporating more technology or interactive graphs for varied learning styles in future lessons.

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This lesson fosters deep conceptual understanding, engaging students through multisensory activities, while meeting key Common Core standards for proportional relationships and linear functions.