Lesson 1
Lots of Flags
Let’s explore the U.S. flag.
1.1: Scaled or Not?
- Which of the geometric objects are scaled versions of each other?
- Pick two of the objects that are scaled copies and find the scale factor.
1.2: Flags Are Many Sizes
One standard size for the United States flag is 19 feet by 10 feet. On a flag of this size, the union (the blue rectangle in the top-left corner) is \(7\frac58\) feet by \(5\frac38\) feet.
There are many places that display flags of different sizes.
- Many classrooms display a U.S. flag.
- Flags are often displayed on stamps.
- There was a flag on the space shuttle.
- Astronauts on the Apollo missions had a flag on a shoulder patch.
![An image of a United States flag.](https://cms-im.s3.amazonaws.com/buL8zgHSQn5tusfy4QiT7wXk?response-content-disposition=inline%3B%20filename%3D%227-7.4.US.flag.png%22%3B%20filename%2A%3DUTF-8%27%277-7.4.US.flag.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T141904Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=553434c7b7b02125ccc56ed0a1464f23abc31c1a6195c21f30dd84a80333d947)
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Choose one of the four options and decide on a size that would be appropriate for this flag. Find the size of the union.
- Share your answer with another group that used a different option. What do your dimensions have in common?
1.3: What Percentage Is the Union?
On a U.S. flag that is 19 feet by 10 feet, the union is \(7\frac58\) feet by \(5\frac38\) feet. For each question, first estimate the answer and then compute the actual percentage.
- What percentage of the flag is taken up by the union?
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What percentage of the flag is red? Be prepared to share your reasoning.
The largest U.S. flag in the world is 225 feet by 505 feet.
- Is the ratio of the length to the width equivalent to \(1:1.9\), the ratio for official government flags?
- If a square yard of the flag weighs about 3.8 ounces, how much does the entire flag weigh in pounds?
Summary
Imagine you have a painting that is 15 feet wide and 5 feet high. To sketch a scaled copy of the painting, the ratio of the width and height of a scaled copy must be equivalent to \(15:5\). What is the height of a scaled copy that is 2 feet across?
width | height |
---|---|
15 | 5 |
2 | \(h\) |
We know that the height is \(\frac13\) the width, so \(h=\frac13 \boldcdot 2\) or \(\frac23\).
Sometimes ratios include fractions and decimals. We will be working with these kinds of ratios in the next few lessons.
Glossary Entries
- percentage
A percentage is a rate per 100.
For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.