Scaling and Similarity

Grade Level

8th Grade

Duration

60 minutes

Standards Alignment

Common Core State Standards - Mathematics (Grades 6-8):

• CCSS.MATH.CONTENT.7.G.A.1 – Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
• CCSS.MATH.CONTENT.7.RP.A.2 – Recognize and represent proportional relationships between quantities.
• CCSS.MATH.PRACTICE.MP1 – Make sense of problems and persevere in solving them.
• CCSS.MATH.PRACTICE.MP4 – Model with mathematics.
• CCSS.MATH.PRACTICE.MP7 – Look for and make use of structure.

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Learning Objectives

By the end of this lesson, students will be able to:

• Understand the concept of scaling as it relates to similarity in figures.
• Use ratios to determine scale factors between similar figures.
• Create similar figures by applying scale factors to dimensions.

I can...

• I can explain what scaling means and how it changes a figure’s size while preserving shape.
• I can calculate scale factors between two similar figures.
• I can create similar figures by appropriately scaling their dimensions.

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Success Criteria

Students will demonstrate understanding by:

• Accurately identifying scale factors in given problems.
• Successfully constructing similar figures using scaling techniques.
• Explaining the relationship between the original figure and its scaled image using ratio language.

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Materials

• Graph paper (dyslexia-friendly: wider spacing and higher contrast colors in print if possible)
• Rulers and protractors
• Dry erase boards and markers for student groups
• Pre-prepared example posters with colorful visuals and dyslexia-friendly fonts
• Handouts with dyslexia-friendly formatting (sans-serif fonts, larger spacing, and bullet lists)
• Projector or smartboard for digital demonstrations

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Lesson Outline

1. Warm-up and Review (10 minutes)

Goal: Activate prior knowledge on ratios and proportions.

• Begin with a brief interactive review quiz on ratios and proportions using dry erase boards.
• Pose questions like "If you have a ratio of 3:4, what happens if you multiply both sides by 2?"
• Use simple real-world examples (e.g., recipe adjustments, map scales).
• Dyslexia-friendly option: Provide printed question cards with clear, simple fonts and ample spacing.
• Wrap up by connecting ratios and proportions to scaling and similarity that will be the focus today.

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2. Direct Instruction: Scaling and Similar Figures (15 minutes)

Goal: Explain the concept of scaling and similar figures aligned with the CCSS standards.

• Use a projector or smartboard to show an original figure (e.g., triangle or rectangle) side-by-side with a scaled version.
• Demonstrate how all side lengths multiply by the same scale factor (e.g., scale factor = 2).
• Define key vocabulary: scale factor, similar figures, corresponding sides.
• Show visual ratio comparisons of side lengths and discuss how ratios express similarity.
• Use color coding on figures and their sides to reinforce correspondence visually—supporting dyslexic learners with visual clues.
• Use the statement: "I can understand scaling and its effects on figures" to frame the concept clearly.

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3. Guided Practice: Calculate and Create Scale Figures (20 minutes)

Goal: Practice calculating scale factors and creating similar figures.

• Activity 1 (10 min): In pairs, students are given pairs of figures and asked to:

  • Identify corresponding sides.
  • Calculate the scale factor between figures (both enlargement and reduction).
  • Write the ratio of side lengths in simplest form.

• Provide scaffolded worksheets with visuals and numbered steps for students who need support.

• Circulate and provide prompts for students who struggle, such as “What do you multiply the original side length by to get the new length?”

• Activity 2 (10 min): Using rulers and graph paper, students will:

  • Draw an original geometric figure (choose a simple polygon like a triangle or rectangle).
  • Apply a given scale factor (e.g., 1.5 or 0.5) to create a similar figure by measuring and plotting points.
  • Shade or color the figures, emphasizing the same orientation but different size.

• Use dyslexia-friendly formatting on instruction sheets and provide number lines or visual ratio models as needed.

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4. Class Discussion and Reflection (10 minutes)

Goal: Reinforce understanding through explanation and peer feedback.

• Volunteers share their scaled figures and scale factor calculations with the class using document camera or smartboard.
• Teacher guides discussion about what stayed the same (shape, angles) and what changed (side lengths, area).
• Introduce how area changes by the square of the scale factor (teasing for later lessons).
• Students articulate an “I can” statement aloud:
  • "I can explain how scaling changes the size but not the shape of a figure."
• Encourage students to use mathematical vocabulary including “proportion,” “scale factor,” and “similar.”

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5. Exit Ticket / Assessment (5 minutes)

Goal: Formative assessment to check mastery.

• Each student completes a quick exit ticket:
  • Given two similar polygons with side lengths, calculate the scale factor.
  • Draw a side of length 3 scaled by 2.5 inches long.
  • Write an "I can" statement reflecting what they learned.
• Collect exit tickets to inform instruction for next lesson.

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Differentiation and Accessibility

• Use varied modalities: visual (color-coded diagrams), kinesthetic (drawing), verbal (class discussion).
• Present all instructions and materials in dyslexia-friendly fonts (e.g., OpenDyslexic or Comic Sans) with increased spacing and bullet points.
• Pair stronger students with peers who need support for peer tutoring.
• Provide sentence starters for explanations (e.g., "The scale factor is ____ because...").
• Allow oral responses or drawings for students with fine motor difficulties.

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Reflection for Teachers

• Were students able to connect scale factors with proportional reasoning?
• Did the hands-on drawing help solidify the concept of similarity?
• How did dyslexia-friendly formatting impact student engagement and understanding?
• Plan to extend understanding of scaling to areas and volumes in subsequent lessons.

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By making use of direct engagement, visual supports, and scaffolded practice, this lesson will build a strong foundational understanding in scaling and similar figures aligned with Common Core standards, helping students master ratios and proportions concepts through hands-on application and reflection.