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Scaling Up!

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Haley Sammons

Tier 1
For Schools

Lesson Plan

Scaling Up!

Students will be able to identify and apply scale factors to solve problems involving proportional relationships.

Understanding scale factors helps us understand how models relate to real-world objects, like maps, blueprints, and even resizing images on a screen. It's a fundamental skill for many careers and everyday tasks.

Audience

7th Grade

Time

15 minutes

Approach

Hands-on practice with guided examples.

Materials

Whiteboard or projector, Scale Factor Practice Worksheet, and Scale Factor Practice Answer Key

Prep

Review Materials & Setup

5 minutes

Review the Scaling Up! Lesson Plan, Scale Factor Practice Worksheet, and Scale Factor Practice Answer Key to ensure familiarity with the content and solutions. Prepare the whiteboard or projector for displaying examples.

Step 1

Introduction to Scale Factor

3 minutes

Begin by asking students if they've ever seen a model car or a map. How do these small versions relate to the real thing? Introduce the concept of 'scale factor' as the number that scales, or multiplies, original sizes to new sizes. Use the Scaling Up! Slide Deck to introduce the topic.

Step 2

Guided Practice

7 minutes

Work through 1-2 examples from the Scale Factor Practice Worksheet together as a class. Emphasize how to set up the ratio to find the scale factor (new length / original length) or to find a new dimension (original dimension * scale factor). Encourage students to ask questions and discuss their reasoning.

Step 3

Independent Practice

5 minutes

Distribute the remaining Scale Factor Practice Worksheet for students to complete independently. Circulate around the room to provide support and answer questions. If time permits, review a few answers using the Scale Factor Practice Answer Key.

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Slide Deck

Scaling Up: What's Your Factor?

Have you ever looked at a map? Or maybe a model airplane? How do these small versions relate to the real thing? Today, we're going to learn about scale factors – the secret to understanding how things grow or shrink proportionally!

Welcome students and get them ready to learn about scale factors. Ask them if they've ever built a model car or seen a dollhouse. How are those different from the real thing? Introduce the idea of scaling up or down.

What is a Scale Factor?

A scale factor is a number that tells us how much an object has been enlarged (made bigger) or reduced (made smaller).

Think of it like zooming in or out on a picture! If the scale factor is greater than 1, the object gets bigger. If it's less than 1 (a fraction), the object gets smaller.

Explain what a scale factor is. Emphasize that it's a number that tells us how much an object has been enlarged or reduced. Give a simple example like doubling a recipe or looking at a photograph.

Finding the Scale Factor

To find the scale factor, we compare the new measurement to the original measurement.

Scale Factor = New Length / Original Length

Let's say a toy car is 2 inches long, and the real car is 100 inches long. What's the scale factor?

Introduce the formula for finding the scale factor. It's always 'new measurement' divided by 'original measurement'. Do a quick mental math example or two with the class.

Example 1: Finding Missing Measurements

A photograph is 4 inches wide and 6 inches tall. If you enlarge it with a scale factor of 2, what will the new dimensions be?

  • Original Width: 4 inches

  • Original Height: 6 inches

  • Scale Factor: 2

  • New Width = Original Width × Scale Factor

  • New Height = Original Height × Scale Factor

Solution: New Width = 4 × 2 = 8 inches. New Height = 6 × 2 = 12 inches.

Walk through an example. A rectangle with sides 3cm and 5cm is enlarged to 6cm and 10cm. What's the scale factor? Guide students to see that 6/3 = 2 and 10/5 = 2. So the scale factor is 2. Then, reverse it: if you know the scale factor, how do you find the new dimensions?

Ready for Action!

Now that we've explored scale factors, it's your turn to put your skills to the test!

We're going to work on the Scale Factor Practice Worksheet to practice finding scale factors and applying them to new measurements.

Remember: New / Original to find the scale factor, and Original * Scale Factor to find new dimensions!

Introduce a slightly more complex example with a different scale factor, perhaps a fraction or decimal, to get them thinking about reduction. Then transition to the worksheet.

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Worksheet

Scale Factor Practice

Directions: Read each problem carefully and use your knowledge of scale factors to solve them. Show your work!

Part 1: Finding the Scale Factor

  1. A model car is 4 inches long. The real car is 160 inches long. What is the scale factor of the real car to the model car?






  2. A photograph is 8 cm wide. It is reduced to fit into a locket, and the new width is 2 cm. What is the scale factor of the reduction?






  3. A map shows a distance of 3 cm between two towns. The actual distance between the towns is 30 km. If 1 cm on the map represents 10 km, what is the scale factor of the map to the actual distance?






Part 2: Using the Scale Factor

  1. A drawing of a house has a scale factor of 1/50. If the actual height of the house is 10 meters, what is the height of the house in the drawing (in centimeters)? (Hint: 1 meter = 100 centimeters)











  2. A garden design is drawn with a scale factor of 3. If a flower bed in the design is 5 inches long, what will its actual length be?






  3. A science experiment involves a microscopic organism that is 0.05 mm long. If you magnify it under a microscope with a scale factor of 200, how long will it appear?






Part 3: Challenge!

  1. A poster is 2 feet wide and 3 feet tall. You want to make a miniature version for a diorama that is 6 inches wide. What will be the height of the miniature poster? (Hint: 1 foot = 12 inches)












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Answer Key

Scale Factor Practice Answer Key

Part 1: Finding the Scale Factor

  1. A model car is 4 inches long. The real car is 160 inches long. What is the scale factor of the real car to the model car?

    • Thought Process: The scale factor is calculated as New Length / Original Length. In this case, the real car is the 'new' length, and the model car is the 'original' length from the perspective of scaling up from the model to the real car.
    • Calculation: Scale Factor = 160 inches / 4 inches = 40
    • Answer: The scale factor is 40.

  2. A photograph is 8 cm wide. It is reduced to fit into a locket, and the new width is 2 cm. What is the scale factor of the reduction?

    • Thought Process: Again, Scale Factor = New Length / Original Length. Here, the reduced width is the 'new' length, and the original photograph width is the 'original' length.
    • Calculation: Scale Factor = 2 cm / 8 cm = 1/4 or 0.25
    • Answer: The scale factor of the reduction is 1/4 or 0.25.

  3. A map shows a distance of 3 cm between two towns. The actual distance between the towns is 30 km. If 1 cm on the map represents 10 km, what is the scale factor of the map to the actual distance?

    • Thought Process: We need to ensure units are consistent. If 1 cm on the map is 10 km, then 3 cm on the map is 30 km. The question asks for the scale factor of the map (new) to the actual distance (original). Convert kilometers to centimeters.
      • 1 km = 1000 meters
      • 1 meter = 100 centimeters
      • 1 km = 1000 * 100 cm = 100,000 cm
      • 30 km = 30 * 100,000 cm = 3,000,000 cm
    • Calculation: Scale Factor = Map Distance (new) / Actual Distance (original)
      • Scale Factor = 3 cm / 3,000,000 cm = 1/1,000,000
    • Answer: The scale factor is 1/1,000,000.

Part 2: Using the Scale Factor

  1. A drawing of a house has a scale factor of 1/50. If the actual height of the house is 10 meters, what is the height of the house in the drawing (in centimeters)? (Hint: 1 meter = 100 centimeters)

    • Thought Process: We are given the actual size and the scale factor (drawing to actual). We need to find the drawing size. First, convert the actual height to centimeters, then apply the scale factor.
      • Actual height in cm = 10 meters * 100 cm/meter = 1000 cm
    • Calculation: Drawing Height = Actual Height * Scale Factor
      • Drawing Height = 1000 cm * (1/50) = 20 cm
    • Answer: The height of the house in the drawing is 20 cm.

  2. A garden design is drawn with a scale factor of 3. If a flower bed in the design is 5 inches long, what will its actual length be?

    • Thought Process: This question implies the design is enlarged to create the actual garden. So, 'design length' is the original, and 'actual length' is the new. We need to find the actual length.
    • Calculation: Actual Length = Design Length * Scale Factor
      • Actual Length = 5 inches * 3 = 15 inches
    • Answer: The actual length of the flower bed will be 15 inches.

  3. A science experiment involves a microscopic organism that is 0.05 mm long. If you magnify it under a microscope with a scale factor of 200, how long will it appear?

    • Thought Process: The original length is the organism's actual length, and the scale factor tells us how much it is magnified (enlarged). We need to find the new, apparent length.
    • Calculation: Apparent Length = Original Length * Scale Factor
      • Apparent Length = 0.05 mm * 200 = 10 mm
    • Answer: The organism will appear 10 mm long.

Part 3: Challenge!

  1. A poster is 2 feet wide and 3 feet tall. You want to make a miniature version for a diorama that is 6 inches wide. What will be the height of the miniature poster? (Hint: 1 foot = 12 inches)
    • Thought Process: First, convert all measurements to the same unit (inches). Then, find the scale factor from the original poster to the miniature poster using the widths. Finally, apply that scale factor to the original height to find the miniature height.
      • Original Poster Width = 2 feet * 12 inches/foot = 24 inches
      • Original Poster Height = 3 feet * 12 inches/foot = 36 inches
      • Miniature Poster Width = 6 inches
    • Step 1: Find the Scale Factor (Miniature to Original)
      • Scale Factor = Miniature Width / Original Width = 6 inches / 24 inches = 1/4
    • Step 2: Apply the Scale Factor to the Height
      • Miniature Height = Original Height * Scale Factor
      • Miniature Height = 36 inches * (1/4) = 9 inches
    • Answer: The height of the miniature poster will be 9 inches.
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