Units in Scale Drawings: IM 7.1.12
[url=https://im.kendallhunt.com/MS/teachers/2/1/12/preparation.html]“Units in Scale Drawings”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 7.1.12
- IM 7.1.12 Lesson: Units in Scale Drawings
- Practice 7.1.12
- IM 7.1.12 Practice: Units in Scale Drawings
IM 7.1.12 Lesson: Units in Scale Drawings
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?
Here are 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.[br][br]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.
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.
Complete the table. Explain or show your reasoning for how you determined the values in the table.
Complete the scale with the value that makes it equivalent to the scale of 1 to 2,000. Explain 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[br]
What is the area of the actual large version of the Tunisia flag? What is the area of the smaller scaled version of the flag? The area of the large flag is how many times the area of the smaller flag?[br]
Here is 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 cm² on the drawing. What is its actual area? Explain or show your reasoning.
Square A is a scaled copy of Square B with scale factor 2. If the area of Square A is 10 units[sup]2[/sup], what is the area of Square B?
Cube A is a scaled copy of Cube B with scale factor 2. If the volume of Cube A is 10 units[sup]3[/sup], what is the volume of Cube B?
The four-dimensional Hypercube A is a scaled copy of Hypercube B with scale factor 2. If the “volume” of Hypercube A is 10 units[sup]4[/sup], what do you think the “volume” of Hypercube B is?[br]
IM 7.1.12 Practice: Units in Scale Drawings
The Empire State Building in New York City is about 1,450 feet high (including the antenna at the top) and 400 feet wide. Andre wants to make a scale drawing of the front view of the Empire State Building on an [math]8\frac{1}{2}[/math]-inch-by-[math]11[/math]-inch piece of paper. Select a scale that you think is the most appropriate for the scale drawing.
Explain your reasoning.
Elena finds that the area of a house on a scale drawing is 25 square inches. The actual area of the house is 2,025 square feet. What is the scale of the drawing?
Which of these scales are equivalent to 3 cm to 4 km? Select [b]all [/b]that apply. Recall that 1 inch is 2.54 centimeters.
These two triangles are scaled copies of one another. The area of the smaller triangle is 9 square units.
What is the area of the larger triangle? Explain or show how you know.
Water costs $1.25 per bottle. At this rate, what is the cost of:
10 bottles?
20 bottles?
50 bottles?
The first row of the table shows the amount of dish detergent and water needed to make a soap solution. Complete the table for 2, 3, and 4 batches.
[color=#ff0000][color=#000000]How much water and detergent is needed for 8 batches? Explain your reasoning.[/color][/color]