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Common Core for Grade 7

Common Core for Mathematics

More Math Lessons for Grade 7

Videos, solutions, and lessons to help Grade 7 students learn how to 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.

Common Core: 7.G.1

### Suggested Learning Targets

**Solving problems involving scale drawings of geometric figures** (Common Core 7.G.1)

How to determine the scale factor between two similar figures by applying ratios?

**How to calculate actual lengths from a scale drawing by using ratios and proportions?**

Examples:

1. Vincent proposes an idea to the Student Government to install a basketball hoop along with a court marked with all the shooting lines and boundary lines at his school for students to use at recess. He presents a plan to install a half-court design as shown below. After checking with school administration, he is told it will be approved if it will fit on the empty lot that measures 25 feet by 75 feet on the school property. Will the lot be big enough for the court he planned? Explain.

2. The diagram shown represents a garden. The scale is 1 centimeter for every 20 meters. Each square in the drawing measures 1 cm by 1 cm. Find the actual length and width based upon the given drawing.

3. A graphic designer is creating an advertisement for a tablet. She needs to enlarge the picture given here so that 0.25 inches on the scale picture will correspond to 1 inch on the actual advertisement. What will be the length and width of the tablet on the advertisement?

4. Students from the high school are going to perform one of the acts from their upcoming musical at the atrium of the mall. The students want to bring some of the set with them so that the audience can get a better feel for the whole production. The backdrop that they want to bring has panels that measure 10 feet by 10 feet. The students are not sure if they will be able to fit these panels through the entrance of the mall since the panels need to be transported flat (horizontal). They obtain a copy of the mall floor plan, shown below, from the city planning office. Use this diagram to decide if the panels will fit through the entrance. Use a ruler to measure.

Find the actual distance of the mall entrance and determine whether the set panels will fit.

**How to compute perimeter and area from a scale drawing by using ratios and proportions?**

The ratio of the perimeter is equivalent to the scale factor.

The ratio of the area is equal to the square of the scale factor.

Reminder: When squaring fractions, you square both numerator and the denominator.

Examples:

1. The scale drawing below shows an enlarged computer chip. When measured, each side of the scale drawing of the square chip is 4 cm.

a. What is the perimeter of the drawing?

b. What is the perimeter of the actual chip?

c. What is the area of the drawing?

d. What is the area of the actual chip?

2. The scale drawing of the miniature glass mosaic tile helps you to see the detailing on the tile.

a. What are the perimeter and area of the scale drawing?

b. What is the perimeter and area of the actual tile?

3. What are the actual perimeter and area of the master bedroom in the blueprint shown below?**How to make a new scale drawing from a given one by using ratios and proportions?**

Example:

Code is an urban planner. He wants to create a small scale drawing of a city block. The block is a square with an area of 8100 m^{2}.

Create a scale drawing of the block using a scale factor of 0.1.**Scale Drawings and Scale Models**

Examples:

1. The Scale on the map is "1" = 10 mile. You measure the distance from your house to State College, and it measure 3.25". What is the actual ("as th bird flies") distance from your house to State College?

2. Your new room is 10" long by 12" wide. Your father made a scale drawing of the room so you could plan where to put your furniture. On the scale drawing, the width of your room measures 6". What scale did your father use for his drawing?

3. On the scale drawing, the flower bed measures 2" × 4". The scale of the drawing is 1" = 5". What is the area of the real garden?

4. On this scale drawing, each square has a side width of 1/4". What are the actual dimensions of the shape shown in the scale drawing?**Scale Drawings**

Use scale drawings and ratios to find actual distances and lengths.

A scale drawing is an enlarged or reduced drawing of an object that is similar (proportional) to the actual object. For example, a road map is a reduced drawing and cell drawings are enlarged drawings.

Examples:

1. You have a scale drawing of a boat. The length of the boat on the drawing is 3 cm. What is the actual length of the boat?

2. The following are the distances two cities are on the map. Find the actual distance if the map uses the scale 2 cm : 21 km.

a. Chicago and Champaign are 8.2 cm apart on the map. What is their actual distance?

b. Colorado Springs and Breckenridge are 4.8 cm apart on the map. What is their actual distance?

3. The figure on the left is a scale drawing of a doll house. In the drawing, the side of each square represents two and a half feet. Find the actual length of the spaces below.

Height of the house and width of the door

**Scale Drawings and Scale Factors**

Examples:

1. A graphic artist is creating an ad for a new iPod. If she uses a scale of 4 inches = 1 inch (advertisement to actual) what is the length of the iPod on the advertisement?

2. Let 1 unit on the grid paper represent 2 feet. So, 4 units = 8 feet. Convert all your measurements to units.

a) How long are the actual bleachers?

b) What are the actual dimensions of the door?

3. If the distance on the map is 2 cm represents 50 meters, what is the scale factor?

4. Use a Map scale: What is the actual distance between Hagerstown and Annapolis?

5. Use a Blueprint scale: On the blueprint of the deck, each square has a side length of 1/2 inch. What is the actual width of the deck?

6. Find a scale factor: Find the scale factor of a model sailboat if the scale is 1 ich = 6 feet.**Scale Modeling**

NASA Connect segment exploring what it means to scale and why scientists use scale models and drawings. The video also explores math terms that are associated with scale models and drawings.

Common Core for Grade 7

Common Core for Mathematics

More Math Lessons for Grade 7

Videos, solutions, and lessons to help Grade 7 students learn how to 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.

Common Core: 7.G.1

- I can solve problems involving scale drawings, when given scale.
- I can compute lengths and area from a scale drawing.
- I can reproduce the drawing of a different scale
using a given scale drawing.

The following diagram shows an example of scale drawing. Scroll down the page for more examples and solutions on how to use scale drawings.

How to determine the scale factor between two similar figures by applying ratios?

Examples:

1. Vincent proposes an idea to the Student Government to install a basketball hoop along with a court marked with all the shooting lines and boundary lines at his school for students to use at recess. He presents a plan to install a half-court design as shown below. After checking with school administration, he is told it will be approved if it will fit on the empty lot that measures 25 feet by 75 feet on the school property. Will the lot be big enough for the court he planned? Explain.

2. The diagram shown represents a garden. The scale is 1 centimeter for every 20 meters. Each square in the drawing measures 1 cm by 1 cm. Find the actual length and width based upon the given drawing.

3. A graphic designer is creating an advertisement for a tablet. She needs to enlarge the picture given here so that 0.25 inches on the scale picture will correspond to 1 inch on the actual advertisement. What will be the length and width of the tablet on the advertisement?

4. Students from the high school are going to perform one of the acts from their upcoming musical at the atrium of the mall. The students want to bring some of the set with them so that the audience can get a better feel for the whole production. The backdrop that they want to bring has panels that measure 10 feet by 10 feet. The students are not sure if they will be able to fit these panels through the entrance of the mall since the panels need to be transported flat (horizontal). They obtain a copy of the mall floor plan, shown below, from the city planning office. Use this diagram to decide if the panels will fit through the entrance. Use a ruler to measure.

Find the actual distance of the mall entrance and determine whether the set panels will fit.

The ratio of the perimeter is equivalent to the scale factor.

The ratio of the area is equal to the square of the scale factor.

Reminder: When squaring fractions, you square both numerator and the denominator.

Examples:

1. The scale drawing below shows an enlarged computer chip. When measured, each side of the scale drawing of the square chip is 4 cm.

a. What is the perimeter of the drawing?

b. What is the perimeter of the actual chip?

c. What is the area of the drawing?

d. What is the area of the actual chip?

2. The scale drawing of the miniature glass mosaic tile helps you to see the detailing on the tile.

a. What are the perimeter and area of the scale drawing?

b. What is the perimeter and area of the actual tile?

3. What are the actual perimeter and area of the master bedroom in the blueprint shown below?

Example:

Code is an urban planner. He wants to create a small scale drawing of a city block. The block is a square with an area of 8100 m

Create a scale drawing of the block using a scale factor of 0.1.

Examples:

1. The Scale on the map is "1" = 10 mile. You measure the distance from your house to State College, and it measure 3.25". What is the actual ("as th bird flies") distance from your house to State College?

2. Your new room is 10" long by 12" wide. Your father made a scale drawing of the room so you could plan where to put your furniture. On the scale drawing, the width of your room measures 6". What scale did your father use for his drawing?

3. On the scale drawing, the flower bed measures 2" × 4". The scale of the drawing is 1" = 5". What is the area of the real garden?

4. On this scale drawing, each square has a side width of 1/4". What are the actual dimensions of the shape shown in the scale drawing?

Use scale drawings and ratios to find actual distances and lengths.

A scale drawing is an enlarged or reduced drawing of an object that is similar (proportional) to the actual object. For example, a road map is a reduced drawing and cell drawings are enlarged drawings.

Examples:

1. You have a scale drawing of a boat. The length of the boat on the drawing is 3 cm. What is the actual length of the boat?

2. The following are the distances two cities are on the map. Find the actual distance if the map uses the scale 2 cm : 21 km.

a. Chicago and Champaign are 8.2 cm apart on the map. What is their actual distance?

b. Colorado Springs and Breckenridge are 4.8 cm apart on the map. What is their actual distance?

3. The figure on the left is a scale drawing of a doll house. In the drawing, the side of each square represents two and a half feet. Find the actual length of the spaces below.

Height of the house and width of the door

Examples:

1. A graphic artist is creating an ad for a new iPod. If she uses a scale of 4 inches = 1 inch (advertisement to actual) what is the length of the iPod on the advertisement?

2. Let 1 unit on the grid paper represent 2 feet. So, 4 units = 8 feet. Convert all your measurements to units.

a) How long are the actual bleachers?

b) What are the actual dimensions of the door?

3. If the distance on the map is 2 cm represents 50 meters, what is the scale factor?

4. Use a Map scale: What is the actual distance between Hagerstown and Annapolis?

5. Use a Blueprint scale: On the blueprint of the deck, each square has a side length of 1/2 inch. What is the actual width of the deck?

6. Find a scale factor: Find the scale factor of a model sailboat if the scale is 1 ich = 6 feet.

NASA Connect segment exploring what it means to scale and why scientists use scale models and drawings. The video also explores math terms that are associated with scale models and drawings.

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