Lesson 12Units in Scale Drawings
Learning Goal
Let’s use different scales to describe the same drawing.
Learning Targets
I can tell whether two scales are equivalent.
I can write scales with units as scales without units.
Lesson Terms
- scale
- scale drawing
Warm Up: Centimeters in a Mile
Problem 1
There are 2.54 cm in an inch, 12 inches in a foot, and 5,280 feet in a mile. Which expression gives the number of centimeters in a mile? Explain your reasoning.
Activity 1: Scales Card Sort
Problem 1
Your teacher will give you some cards with a scale on each card.
Sort the cards into sets of equivalent scales. Be prepared to explain how you know that the scales in each set are equivalent. Each set should have at least two cards.
Trade places with another group and check each other’s work. If you disagree about how the scales should be sorted, work to reach an agreement.
Pause here so your teacher can review your work.
Next, record one of the sets with three equivalent scales and explain why they are equivalent.
Activity 2: The World’s Largest Flag
As of 2016, Tunisia holds the world record for the largest version of a national flag. It was almost as long as four soccer fields. The flag has a circle in the center, a crescent moon inside the circle, and a star inside the crescent moon.
Problem 1
Complete the table. Explain or show your reasoning.
flag length | flag height | height of | |
---|---|---|---|
actual | |||
at 1 to 2,000 scale |
Problem 2
Complete each scale with the value that makes it equivalent to the scale of 1 to 2,000. Explain or show your reasoning.
1 cm to cm
1 cm to m
1 cm to km
2 m to m
5 cm to m
cm to 1,000 m
mm to 20 m
Problem 3
What is the area of the large flag?
What is the area of the smaller flag?
The area of the large flag is how many times the area of the smaller flag?
Activity 3: Pondering Pools
Problem 1
Your teacher will give you a floor plan of a recreation center.
What is the scale of the floor plan if the actual side length of the square pool is 15 m? Express your answer both as a scale with units and without units.
Find the actual area of the large rectangular pool. Show your reasoning.
The kidney-shaped pool has an area of 3.2 cm squared on the drawing. What is its actual area? Explain or show your reasoning.
Are you ready for more?
Problem 1
Square
Problem 2
Cube
Problem 3
The four-dimensional Hypercube
Lesson Summary
Sometimes scales come with units, and sometimes they don’t. For example, a map of Nebraska may have a scale of 1 mm to 1 km. This means that each millimeter of distance on the map represents 1 kilometer of distance in Nebraska. Notice that there are 1,000 millimeters in 1 meter and 1,000 meters in 1 kilometer. This means there are
Sometimes when a scale comes with units, it is useful to rewrite it without units. For example, let’s say we have a different map of Rhode Island, and we want to use the two maps to compare the size of Nebraska and Rhode Island. It is important to know if the maps are at the same scale. The scale of the map of Rhode Island is 1 inch to 10 miles. There are 5,280 feet in 1 mile, and 12 inches in 1 foot, so there are 63,360 inches in 1 mile (because
Here is some information about equal lengths that you may find useful.
Customary Units | Metric Units |
---|---|
1 foot (ft) = 12 inches (in) | 1 meter (m) = 1,000 millimeters (mm) |
Equal Lengths in Different Systems | |
---|---|
1 inch = 2.54 centimeters | 1 centimeter |