Graphing Real-Life Situations

Grade Level: 7th Grade

Curriculum Area: Mathematics - Ratios and Proportional Relationships

Duration: 10 minutes

Standards:

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

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Objective

Students will be able to identify and differentiate between proportional and non-proportional relationships through real-life graphing scenarios.

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Materials

• Graph paper
• Colored pencils
• Whiteboard and markers

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Introduction (2 minutes)

Engage:

• Begin with a quick storytelling to capture attention: "Imagine you're at a candy store. You love jellybeans, and the store offers a deal—10 jellybeans for $1. However, for chocolate bars, each one costs $2 regardless of how many you buy. Let's explore how these deals look on a graph!"

• Share the lesson objective: "Today, we'll learn how to use graphs to represent situations like buying candies and understand how to tell if these relationships are proportional or not."

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Activity (5 minutes)

1. Proportional Scenario:

• Context: Walking with friends. Introduce the concept of walking a trail where every 1 mile takes 20 minutes.
• Graph it: With students' help, sketch the relationship on the whiteboard (x-axis: Miles, y-axis: Time in minutes). Point out that this is a straight line through the origin (0,0), indicating proportionality.
• Think Prompt: Ask students if they would walk at the same rate forever, leading to insights into constant speed.

2. Non-Proportional Scenario:

• Context: Explain a scenario where you have a membership fee of $5 for a local pool, and each visit costs an additional $3.
• Graph it: Again, with student interaction, graph this relationship on the whiteboard (x-axis: Number of visits, y-axis: Total Cost). Highlight that the line does not pass through the origin, showing it's non-proportional.
• Think Prompt: Have students consider how the initial fee affects cost, reinforcing the concept of being non-proportional.

Hands-on Task: Provide each pair of students with graph paper and colored pencils. Ask them to sketch one proportional and one non-proportional scenario from their lives, like buying apps with/without an initial charge.

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Conclusion (3 minutes)

• Recap Quiz: Quickly ask, "Which graph did we just sketch for walking—a proportional or non-proportional one?" and "How did the pool charges graph differ?"

• Reflection: Encourage students to share their graph scenarios and discuss why each is proportional or not.

• Wrap-Up: Reinforce understanding with a closing statement: "Remember, proportional relationships are like our walking path—steady and constant over time. Non-proportional ones, like our pool membership, have extra costs to consider."

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Teacher’s Note

• Personalize examples. Use scenarios relevant to students' interests like video game purchases or family road trips.
• Encourage students to bring real-life scenarios for the next class to enhance engagement.
• Differentiate by using rulers for graphing to support students struggling with drawing straight lines.

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This short, dynamic lesson seamlessly embeds understanding of proportional and non-proportional relationships through real-world applications, creating an inclusive and engaging math experience for special education students.