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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 1

Scale Drawings

Lesson 4: Scaled Relationships

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Math Clip Art--Applications of Proportions--Exchange Rates 8 Math Clip Art--Applications of Proportions--Exchange Rates 8 Math Clip Art--Applications of Proportions--Exchange Rates 8

This is a collection of clip art images that show an application of proportional reasoning in the context of currency exchange rates.

Ratios and Rates and Proportions
Math Clip Art--Applications of Proportions--Exchange Rates 9 Math Clip Art--Applications of Proportions--Exchange Rates 9 Math Clip Art--Applications of Proportions--Exchange Rates 9

This is a collection of clip art images that show an application of proportional reasoning in the context of currency exchange rates.

Ratios and Rates and Proportions
Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 1 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 1 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 1

This is a collection of clip art images that show an application of proportional reasoning in the context of carbon dating.

Ratios and Rates and Proportions
Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 2 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 2 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 2

This is a collection of clip art images that show an application of proportional reasoning in the context of carbon dating.

Ratios and Rates and Proportions
Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 3 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 3 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 3

This is a collection of clip art images that show an application of proportional reasoning in the context of carbon dating.

Ratios and Rates and Proportions
Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 4 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 4 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 4

This is a collection of clip art images that show an application of proportional reasoning in the context of carbon dating.

Ratios and Rates and Proportions
Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 5 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 5 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 5

This is a collection of clip art images that show an application of proportional reasoning in the context of carbon dating.

Ratios and Rates and Proportions
Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 6 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 6 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 6

This is a collection of clip art images that show an application of proportional reasoning in the context of carbon dating.

Ratios and Rates and Proportions
Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 7 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 7 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 7

This is a collection of clip art images that show an application of proportional reasoning in the context of carbon dating.

Ratios and Rates and Proportions
Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 8 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 8 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 8

This is a collection of clip art images that show an application of proportional reasoning in the context of carbon dating.

Ratios and Rates and Proportions
Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 9 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 9 Math Clip Art--Applications of Ratios and Proportions--Carbon Dating 9

This is a collection of clip art images that show an application of proportional reasoning in the context of carbon dating.

Ratios and Rates and Proportions
Math Clip Art--Geometry Concepts--Scale Drawing, Image 1 Math Clip Art--Geometry Concepts--Scale Drawing--01 Math Clip Art--Scale Drawing--01

Topic

Geometry Concepts

Description

This image depicts a scale drawing of a square that has been scaled up by a factor of 1:2. This means that each side of the square in the drawing is twice the length of the corresponding side in the actual object. Scale drawings are essential for accurately representing objects in a manageable size while maintaining proportionality.

Teacher's Script: "Observe this scale drawing of a square. How does the 1:2 scale factor help us understand the relationship between the drawing and the actual square? What are some real-world applications of scaling up objects, such as in architecture or design?"

Proportions
Math Clip Art--Geometry Concepts--Scale Drawing, Image 2 Math Clip Art--Geometry Concepts--Scale Drawing--02 Math Clip Art--Scale Drawing--02

Topic

Geometry Concepts

Description

This image illustrates a scale drawing of a square that has been scaled up by a factor of 1:3. Each side of the square in the drawing is three times the length of the corresponding side in the actual object. This scaling helps in visualizing larger versions of objects while maintaining accurate proportions.

Teacher's Script: "Look at this scale drawing of a square. How does the 1:3 scale factor affect the dimensions of the drawing compared to the actual square? What are some mathematical concepts you can explore using scale drawings, such as ratios or proportions?"

Proportions
Math Clip Art--Geometry Concepts--Scale Drawing, Image 3 Math Clip Art--Geometry Concepts--Scale Drawing--03 Math Clip Art--Scale Drawing--03

Topic

Geometry Concepts

Description

This image shows a scale drawing of a rectangle that has been scaled up by a factor of 1:4. Each side of the rectangle in the drawing is four times the length of the corresponding side in the actual object. This scaling is useful for enlarging objects while maintaining their proportional dimensions.

Teacher's Script: "Examine this scale drawing of a rectangle. How does the 1:4 scale factor influence the size of the drawing compared to the actual rectangle? What are some real-world applications of scaling up objects, such as in engineering or construction?"

Proportions
Math Clip Art--Geometry Concepts--Scale Drawing, Image 4 Math Clip Art--Geometry Concepts--Scale Drawing--04 Math Clip Art--Scale Drawing--04

Topic

Geometry Concepts

Description

This image illustrates a scale drawing of a rectangle that has been scaled up by a factor of 1:5. Each side of the rectangle in the drawing is five times the length of the corresponding side in the actual object. Scale drawings like this are crucial for visualizing larger versions of objects while maintaining accurate proportions.

Teacher's Script: "Observe this scale drawing of a rectangle. How does the 1:5 scale factor affect the dimensions of the drawing compared to the actual rectangle? What are some mathematical concepts you can explore using scale drawings, such as ratios or proportions?"

Proportions
Math Clip Art--Geometry Concepts--Scale Drawing, Image 5 Math Clip Art--Geometry Concepts--Scale Drawing--05 Math Clip Art--Scale Drawing--05

Topic

Geometry Concepts

Description

This image depicts a scale drawing of a right triangle that has been scaled down by a factor of 5:1. This means each side of the triangle in the drawing is one-fifth the length of the corresponding side in the actual object. Scaling down is useful for creating manageable representations of larger objects.

Teacher's Script: "Examine this scale drawing of a right triangle. How does the 5:1 scale factor help us understand the relationship between the drawing and the actual triangle? What are some real-world applications of scaling down objects, such as in model making or map creation?"

Proportions
Math Clip Art--Geometry Concepts--Scale Drawing, Image 6 Math Clip Art--Geometry Concepts--Scale Drawing--06 Math Clip Art--Scale Drawing--06

Topic

Geometry Concepts

Description

This image illustrates a scale drawing of a right triangle that has been scaled down by a factor of 4:1. Each side of the triangle in the drawing is one-fourth the length of the corresponding side in the actual object. This scaling helps in visualizing smaller versions of objects while maintaining accurate proportions.

Teacher's Script: "Observe this scale drawing of a right triangle. How does the 4:1 scale factor affect the dimensions of the drawing compared to the actual triangle? What are some mathematical concepts you can explore using scale drawings, such as ratios or proportions?"

Proportions
Math Clip Art--Geometry Concepts--Scale Drawing, Image 7 Math Clip Art--Geometry Concepts--Scale Drawing--07 Math Clip Art--Scale Drawing--07

Topic

Geometry Concepts

Description

This image depicts a scale drawing of a right triangle that has been scaled down by a factor of 3:1. Each side of the triangle in the drawing is one-third the length of the corresponding side in the actual object. Scaling down is useful for creating manageable representations of larger objects.

Teacher's Script: "Examine this scale drawing of a right triangle. How does the 3:1 scale factor help us understand the relationship between the drawing and the actual triangle? What are some real-world applications of scaling down objects, such as in model making or map creation?"

Proportions
Math Clip Art--Geometry Concepts--Scale Drawing, Image 8 Math Clip Art--Geometry Concepts--Scale Drawing--08 Math Clip Art--Scale Drawing--08

Topic

Geometry Concepts

Description

This image illustrates a scale drawing of a right triangle that has been scaled down by a factor of 2:1. Each side of the triangle in the drawing is one-half the length of the corresponding side in the actual object. This scaling helps in visualizing smaller versions of objects while maintaining accurate proportions.

Teacher's Script: "Observe this scale drawing of a right triangle. How does the 2:1 scale factor affect the dimensions of the drawing compared to the actual triangle? What are some mathematical concepts you can explore using scale drawings, such as ratios or proportions?"

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 1 Math Clip Art--Ratios, Proportions, Percents--Proportions 01 Math Clip Art--Ratios, Proportions, Percents--Proportions 01

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 2 Math Clip Art--Ratios, Proportions, Percents--Proportions 02 Math Clip Art--Ratios, Proportions, Percents--Proportions 02

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 3 Math Clip Art--Ratios, Proportions, Percents--Proportions 03 Math Clip Art--Ratios, Proportions, Percents--Proportions 03

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 4 Math Clip Art--Ratios, Proportions, Percents--Proportions 04 Math Clip Art--Ratios, Proportions, Percents--Proportions 04

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 5 Math Clip Art--Ratios, Proportions, Percents--Proportions 05 Math Clip Art--Ratios, Proportions, Percents--Proportions 05

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 6 Math Clip Art--Ratios, Proportions, Percents--Proportions 06 Math Clip Art--Ratios, Proportions, Percents--Proportions 06

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 7 Math Clip Art--Ratios, Proportions, Percents--Proportions 07 Math Clip Art--Ratios, Proportions, Percents--Proportions 07

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 8 Math Clip Art--Ratios, Proportions, Percents--Proportions 08 Math Clip Art--Ratios, Proportions, Percents--Proportions 08

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 9 Math Clip Art--Ratios, Proportions, Percents--Proportions 09 Math Clip Art--Ratios, Proportions, Percents--Proportions 09

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Proportions, Image 10 Math Clip Art--Ratios, Proportions, Percents--Proportions 10 Math Clip Art--Ratios, Proportions, Percents--Proportions 10

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models, Image 1 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 01 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 01

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models, Image 2 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 02 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 02

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models, Image 3 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 03 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 03

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models, Image 4 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 04 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 04

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models, Image 5 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 05 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 05

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models, Image 6 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 06 Math Clip Art--Ratios, Proportions, Percents--Scale Drawings and Scale Models 06

This is part of a collection of math clip art images that explain different aspects of ratios, proportions, and percents.

Proportions
Math Example--Ratios and Rates--Example 1 Math Example--Ratios and Rates--Example 1 Math Example--Ratios and Rates--Example 1

Topic

Ratios and Rates

Description

This math example focuses on understanding ratios using colored socks. The image displays a collection of red and blue socks, and students are asked to determine the ratio of red socks to blue socks. The solution demonstrates that there are 4 pairs of red socks and 4 pairs of blue socks, resulting in a ratio of 4 : 4, which simplifies to 1 : 1.

Ratios and Rates
Math Example--Ratios and Rates--Example 10 Math Example--Ratios and Rates--Example 10 Math Example--Ratios and Rates--Example 10

Topic

Ratios and Rates

Description

This example focuses on finding equivalent ratios using a collection of socks in various colors. The image shows socks arranged in rows, with black, green, white, and other colors present. Students are asked to find a ratio among three colors that is equivalent to 1 : 3 : 1.

Ratios and Rates
Math Example--Ratios and Rates--Example 11 Math Example--Ratios and Rates--Example 11 Math Example--Ratios and Rates--Example 11

Topic

Ratios and Rates

Description

This example focuses on finding equivalent ratios using a collection of socks in various colors. The image shows socks arranged in rows, with black, green, white, and other colors present. Students are asked to find a ratio among three colors that is equivalent to 1 : 4 : 1.

Ratios and Rates
Math Example--Ratios and Rates--Example 12 Math Example--Ratios and Rates--Example 12 Math Example--Ratios and Rates--Example 12

Topic

Ratios and Rates

Description

This example explores the concept of similar triangles using ratios. The image shows a right triangle with sides labeled as 9, 12, and 15 units. Students are asked to determine if this triangle is similar to a standard 3-4-5 Pythagorean triplet triangle.

Understanding similar triangles is an important application of ratios in geometry. This example demonstrates how ratios can be used to compare the sides of triangles and determine similarity. By scaling the sides of a known triangle (3-4-5) and comparing them to the given triangle, students can see how ratios maintain proportionality in similar shapes.

Ratios and Rates
Math Example--Ratios and Rates--Example 13 Math Example--Ratios and Rates--Example 13 Math Example--Ratios and Rates--Example 13

Topic

Ratios and Rates

Description

This example focuses on verifying the similarity of triangles using ratios. The image shows a right triangle with sides labeled 25, 60, and 65 units. Students are guided through a step-by-step process to determine if this triangle is similar to a 5-12-13 right triangle.

Ratios and Rates
Math Example--Ratios and Rates--Example 14 Math Example--Ratios and Rates--Example 14 Math Example--Ratios and Rates--Example 14

Topic

Ratios and Rates

Description

This example explores the concept of special right triangles using ratios. The image shows a right triangle with sides labeled 3, 3 2 2 ​ , and 6 units. Students are guided through a step-by-step process to verify if this triangle is similar to a 30°-60°-90° triangle.

Ratios and Rates
Math Example--Ratios and Rates--Example 15 Math Example--Ratios and Rates--Example 15 Math Example--Ratios and Rates--Example 15

Topic

Ratios and Rates

Ratios and Rates
Math Example--Ratios and Rates--Example 16 Math Example--Ratios and Rates--Example 16 Math Example--Ratios and Rates--Example 16

Topic

Ratios and Rates

Description

This example focuses on converting units of speed and calculating rates. The image shows a car and calculations for converting speed from miles per hour to feet per second, given the distance traveled in miles and time in minutes.

Understanding unit conversions and rate calculations is crucial in many real-world applications, particularly in physics and engineering. This example demonstrates how to use ratios to convert between different units of speed, showcasing the practical application of mathematical concepts in everyday scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 17 Math Example--Ratios and Rates--Example 17 Math Example--Ratios and Rates--Example 17

Topic

Ratios and Rates

Description

This example explores the concept of unit rates using the cost of gasoline. The image shows a red gasoline container, and students are asked to calculate the cost per gallon of gas given the total cost and volume.

Understanding unit rates is a fundamental skill in mathematics with numerous real-world applications. This example demonstrates how to calculate a unit rate by dividing the total cost by the total quantity, illustrating the practical use of division in everyday scenarios like purchasing gasoline.

Ratios and Rates
Math Example--Ratios and Rates--Example 18 Math Example--Ratios and Rates--Example 18 Math Example--Ratios and Rates--Example 18

Topic

Ratios and Rates

Description

This example focuses on calculating unit rates in a restaurant context. The image shows a hamburger, and students are asked to determine the cost per pound of ground beef given the total cost and weight purchased.

Understanding unit rates is essential in various real-world scenarios, particularly in business and economics. This example illustrates how to calculate a unit rate by dividing the total cost by the total quantity, demonstrating the practical application of division in a restaurant supply context.

Ratios and Rates
Math Example--Ratios and Rates--Example 19 Math Example--Ratios and Rates--Example 19 Math Example--Ratios and Rates--Example 19

Topic

Ratios and Rates

Description

This example explores the concept of flow rates using a backyard pool scenario. The image shows a backyard pool, and students are asked to calculate the rate of water flow in gallons per minute given the pool's capacity and the time taken to fill it.

Understanding flow rates is important in various fields, including engineering and physics. This example demonstrates how to calculate a rate by dividing the total volume by the total time, illustrating the practical application of division in real-world scenarios involving fluid dynamics.

Ratios and Rates
Math Example--Ratios and Rates--Example 2 Math Example--Ratios and Rates--Example 2 Math Example--Ratios and Rates--Example 2

Topic

Ratios and Rates

Description

This example explores ratios using purple and black socks. The image shows a collection of socks, and students are asked to determine the ratio of purple socks to black socks. The solution reveals that there is 1 pair of purple socks and 2 pairs of black socks, resulting in a ratio of 1 : 2, which is already in its simplest form.

Ratios and Rates
Math Example--Ratios and Rates--Example 20 Math Example--Ratios and Rates--Example 20 Math Example--Ratios and Rates--Example 20

Topic

Ratios and Rates

Description

This example focuses on unit conversion using the height of the Statue of Liberty. The image shows the Statue of Liberty, and students are asked to convert its height from feet to inches.

Understanding unit conversions is crucial in many fields, including science, engineering, and everyday life. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of multiplication in real-world measurement scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 21 Math Example--Ratios and Rates--Example 21 Math Example--Ratios and Rates--Example 21

Topic

Ratios and Rates

Description

This example focuses on unit conversion, specifically converting the height of the Statue of Liberty from feet to yards. The image shows the iconic Statue of Liberty, providing a real-world context for the mathematical problem.

Understanding unit conversions is crucial in many fields, including engineering, science, and everyday life. This example demonstrates how to use a conversion factor to change units, illustrating the practical application of division and multiplication in real-world measurement scenarios.

Ratios and Rates
Math Example--Ratios and Rates--Example 22 Math Example--Ratios and Rates--Example 22 Math Example--Ratios and Rates--Example 22

Topic

Ratios and Rates

Description

This example explores unit conversion, specifically converting the height of the Statue of Liberty from feet to miles. The image depicts the Statue of Liberty, providing a tangible reference for the mathematical problem.

Understanding unit conversions, especially between widely different scales like feet and miles, is important in various fields such as geography, engineering, and urban planning. This example showcases how to use a conversion factor to change units, demonstrating the practical application of division and multiplication in real-world measurement scenarios.

Ratios and Rates