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Scale Up, Scale Down!

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Haley Sammons

Tier 1
For Schools

Lesson Plan

Scale Up, Scale Down!

Students will be able to define scale factors, apply them to enlarge or reduce geometric figures, and solve real-world problems involving scale.

Understanding scale factors helps us interpret maps, blueprints, models, and even resize images, making it a crucial skill in everyday life and future careers.

Audience

7th Grade

Time

30 minutes

Approach

Interactive review, guided practice, and independent application through a review sheet.

Materials

Whiteboard or Projector, Scale Up, Scale Down! Slide Deck, Scale Factors Guided Notes, Scale Factors Review Sheet, Scale Factors Answer Key, and Pencils and paper for students

Prep

Review Materials

10 minutes

  • Review the Scale Up, Scale Down! Slide Deck and Scale Factors Guided Notes to familiarize yourself with the content and flow.
    - Print copies of the Scale Factors Guided Notes and Scale Factors Review Sheet for each student.
    - Have the Scale Factors Answer Key ready for quick reference during student support and review.
    - Ensure whiteboard or projector is set up and ready to display the slide deck.

Step 1

Warm-Up & Introduction (5 minutes)

5 minutes

  • Begin by projecting the first slide of the Scale Up, Scale Down! Slide Deck.
    - Ask students: "What does it mean to 'scale something up' or 'scale something down'? Think about maps or models."
    - Briefly introduce the concept of scale factors as the number that multiplies the original dimensions to get the new dimensions. Explain that today's lesson will be a review of this concept.

Step 2

Guided Review (10 minutes)

10 minutes

  • Distribute the Scale Factors Guided Notes to each student.
    - Progress through the Scale Up, Scale Down! Slide Deck, reviewing key concepts: defining scale factor, calculating scale factor, enlarging figures, reducing figures, and real-world applications. Encourage students to fill in their guided notes as you go.
    - Use the examples on the slides to facilitate a quick discussion and check for understanding. Encourage students to share their thinking processes.

Step 3

Independent Practice: Review Sheet (10 minutes)

10 minutes

  • Distribute the Scale Factors Review Sheet to each student.
    - Explain that this is an opportunity to practice what they've reviewed independently.
    - Circulate around the room, providing support and answering questions as students work. Remind them to show their work.

Step 4

Review & Cool-Down (5 minutes)

5 minutes

  • After 10 minutes, gather students' attention.
    - Project the Scale Factors Answer Key or go over the answers orally, allowing students to check their work and ask questions.
    - Facilitate a brief discussion about common misconceptions or challenging problems.
    - Conclude by asking students to summarize one new thing or one reinforced idea they gained from the review.
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Slide Deck

Scale Up, Scale Down!

Understanding Scale Factors in the Real World!

Welcome students and introduce the topic. Ask them to think about everyday examples of scaling.

What is a Scale Factor?

A scale factor is a number that scales, or multiplies, quantities. It's used to enlarge or reduce the size of an object while maintaining its proportions.

  • Enlargement: Scale factor > 1
  • Reduction: Scale factor < 1

Define scale factor clearly. Emphasize it's a ratio.

Calculating Scale Factor

To find the scale factor, we use this simple ratio:

Scale Factor = (New Dimension) / (Original Dimension)

Example: A photo is 4 inches wide. You enlarge it to 12 inches wide. What is the scale factor?

Scale Factor = 12 / 4 = 3

Explain how to calculate the scale factor using corresponding side lengths.

Enlarging Figures

When you enlarge a figure, every dimension (length, width) is multiplied by the scale factor.

Example: A rectangle has a length of 2 cm and a width of 3 cm. If it's enlarged by a scale factor of 4, what are the new dimensions?

  • New Length = 2 cm * 4 = 8 cm
  • New Width = 3 cm * 4 = 12 cm

Provide an example of enlarging a figure. Guide students through applying the scale factor to all dimensions.

Reducing Figures

When you reduce a figure, every dimension is multiplied by a scale factor less than 1 (a fraction or decimal).

Example: A map has a scale factor of 1/100. If a real-life distance is 500 meters, what is its length on the map?

  • Map Length = 500 m * (1/100) = 5 meters

Provide an example of reducing a figure. Guide students through applying the scale factor to all dimensions.

Scale Factors in Real Life

  • Maps: Represent large areas on a small piece of paper.
  • Models: Create smaller versions of cars, airplanes, or buildings.
  • Blueprints: Detailed drawings of buildings, scaled down.
  • Photography: Resizing images while keeping proportions.

Discuss real-world examples to connect the concept to students' experiences.

Time for Practice!

Now, let's put your knowledge of scale factors to the test with our review sheet!

Remember to show your work and think carefully about each problem.

Transition to the review sheet. Encourage students to apply what they've learned.

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Worksheet

Scale Factors Guided Notes

Introduction: Scale Up, Scale Down!

  1. What does it mean to "scale something up" or "scale something down"? Think about maps or models.


What is a Scale Factor?

  1. A scale factor is a number that ___________, or multiplies, quantities. It's used to ___________ or ___________ the size of an object while maintaining its proportions.
    • Enlargement: When the scale factor is ___________ 1.
    • Reduction: When the scale factor is ___________ 1.

Calculating Scale Factor

  1. To find the scale factor, we use this simple ratio:
    Scale Factor = (___________ Dimension) / (___________ Dimension)

    Example: A photo is 4 inches wide. You enlarge it to 12 inches wide. What is the scale factor?

    • Original Dimension: ___________
    • New Dimension: ___________
    • Calculation:


    • Scale Factor = ___________

Enlarging Figures

  1. When you enlarge a figure, every dimension (length, width) is multiplied by the ___________.

    Example: A rectangle has a length of 2 cm and a width of 3 cm. If it's enlarged by a scale factor of 4, what are the new dimensions?

    • Original Length: ___________, Original Width: ___________
    • Scale Factor: ___________
    • New Length: ___________ * ___________ = ___________ cm
    • New Width: ___________ * ___________ = ___________ cm

Reducing Figures

  1. When you reduce a figure, every dimension is multiplied by a scale factor ___________ than 1.

    Example: A map has a scale factor of 1/100. If a real-life distance is 500 meters, what is its length on the map?

    • Real-Life Distance: ___________
    • Scale Factor: ___________
    • Map Length: ___________ * ___________ = ___________ meters

Scale Factors in Real Life

  1. List three real-world examples where scale factors are used:
    • a) ___________

    • b) ___________

    • c) ___________

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Worksheet

Scale Factors Review Sheet

Part 1: Define It!

  1. In your own words, what is a scale factor? When do we use it?





Part 2: Calculate the Scale Factor

  1. A small toy car is 5 cm long. A larger model of the same car is 20 cm long. What is the scale factor of the enlargement?


  2. A poster is 60 inches tall. You want to make a miniature version that is 10 inches tall. What is the scale factor of the reduction?


Part 3: Scale Up or Down!

  1. A photograph measures 4 inches by 6 inches. If you enlarge it using a scale factor of 2.5, what will be the new dimensions of the photograph?





  2. A rectangular garden plot is 15 meters long and 10 meters wide. You want to create a scaled-down drawing of it using a scale factor of 1/5. What will be the dimensions of the garden in your drawing?





Part 4: Real-World Application

  1. On a map, 1 inch represents 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance between the two cities? What is the scale factor in this scenario? (Hint: You'll need to think about consistent units for the scale factor!)











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Answer Key

Scale Factors Review Sheet - Answer Key

Part 1: Define It!

  1. In your own words, what is a scale factor? When do we use it?
    • Answer: A scale factor is a number that we multiply the dimensions of an object by to either make it larger (enlarge) or smaller (reduce) while keeping its shape and proportions the same. We use scale factors in many real-world situations, like reading maps, making models, designing buildings with blueprints, or resizing images.

Part 2: Calculate the Scale Factor

  1. A small toy car is 5 cm long. A larger model of the same car is 20 cm long. What is the scale factor of the enlargement?

    • Thought Process: To find the scale factor, we use the formula: Scale Factor = New Dimension / Original Dimension. In this case, the new dimension is 20 cm and the original dimension is 5 cm.
    • Calculation: Scale Factor = 20 cm / 5 cm = 4
    • Answer: The scale factor of the enlargement is 4.

  2. A poster is 60 inches tall. You want to make a miniature version that is 10 inches tall. What is the scale factor of the reduction?

    • Thought Process: Again, use the formula: Scale Factor = New Dimension / Original Dimension. The new dimension is 10 inches, and the original dimension is 60 inches.
    • Calculation: Scale Factor = 10 inches / 60 inches = 1/6
    • Answer: The scale factor of the reduction is 1/6.

Part 3: Scale Up or Down!

  1. A photograph measures 4 inches by 6 inches. If you enlarge it using a scale factor of 2.5, what will be the new dimensions of the photograph?

    • Thought Process: To find the new dimensions, multiply each original dimension by the scale factor.
    • Calculation:
      • New Width = 4 inches * 2.5 = 10 inches
      • New Length = 6 inches * 2.5 = 15 inches
    • Answer: The new dimensions of the photograph will be 10 inches by 15 inches.

  2. A rectangular garden plot is 15 meters long and 10 meters wide. You want to create a scaled-down drawing of it using a scale factor of 1/5. What will be the dimensions of the garden in your drawing?

    • Thought Process: Multiply each original dimension by the scale factor (1/5 or 0.2).
    • Calculation:
      • Drawing Length = 15 meters * (1/5) = 3 meters
      • Drawing Width = 10 meters * (1/5) = 2 meters
    • Answer: The dimensions of the garden in your drawing will be 3 meters by 2 meters.

Part 4: Real-World Application

  1. On a map, 1 inch represents 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance between the two cities? What is the scale factor in this scenario? (Hint: You'll need to think about consistent units for the scale factor!)
    • Thought Process (Actual Distance): If 1 inch on the map is 50 miles in real life, then 3.5 inches would be 3.5 times that distance.
    • Calculation (Actual Distance): Actual Distance = 3.5 inches * 50 miles/inch = 175 miles
    • Thought Process (Scale Factor): The scale factor is (New Dimension) / (Original Dimension). Here, the map is the 'new' (scaled) version and the real distance is the 'original'. We need to make the units consistent. Let's convert miles to inches (1 mile = 63,360 inches).
      • 1 inch (map) : 50 miles (real)
      • Convert 50 miles to inches: 50 miles * 63,360 inches/mile = 3,168,000 inches
      • So, 1 inch on the map represents 3,168,000 inches in real life.
    • Calculation (Scale Factor): Scale Factor = (Map distance) / (Real distance) = 1 inch / 3,168,000 inches = 1/3,168,000
    • Answer: The actual distance between the two cities is 175 miles. The scale factor in this scenario is 1/3,168,000.
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