Illustrative Math Alignment: Grade 7 Unit 1

Topic

Ratios

Description

The video explains how proportions are used to create scale drawings, ensuring geometric figures remain proportional. Examples include finding dimensions in similar triangles, scaling architectural models, and solving geometric problems. The concept of proportional relationships is key to accurate scaling.

Topic

Ratios, Proportions, and Percents

Definition

A scale drawing is a representation of an object or structure with dimensions proportional to the actual object or structure.

Description

Scale drawings are essential in fields like architecture, engineering, and cartography, where accurate representations of large objects or areas are needed. For example, an architect might create a scale drawing of a building where 1 inch on the drawing represents 10 feet in reality. This allows for detailed planning and visualization without needing a full-sized model.

This hands-on activity is a companion to the video segment from the Geometry Applications: Angles and Planes video. In particular, it supports the segment on the architecture of Himeji Castle.

Library of Instructional Resources

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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?"

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?"

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?"

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?"

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?"

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?"

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?"

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?"

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

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

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

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

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

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

This is the transcript that goes with the video segment entitled Video Tutorial: Ratios and Proportions: Scale Drawings.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.