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?

[math]\frac{1}{5,280\cdot12\cdot\left(2.54\right)}[/math] [math]5,280+12+2.54[/math] [math]\frac{2.54}{12\cdot5,280}[/math] [math]5,280\cdot12\cdot\left(2.54\right)[/math] [math]\frac{5,280\cdot12}{2.54}[/math]

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 Lesson: Units in Scale Drawings

Here are some cards with a scale on each card.

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 scale with the value that makes it equivalent to the scale of 1 to 2,000. Explain your reasoning.

Here is a floor plan of a recreation center.

Information: IM 7.1.12 Lesson: Units in Scale Drawings