Lesson 1Lots of Flags

Let’s explore the U.S. flag.

Learning Targets:

  • I can find dimensions on scaled copies of a rectangle.
  • I remember how to compute percentages.

1.1 Scaled or Not?

  1. Which of the geometric objects are scaled versions of each other?
  2. 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.
“US flag clip art” via OpenClipArt. Public Domain.
  1. Choose one of the four options and decide on a size that would be appropriate for this flag. Find the size of the union.
  2. 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.

  1. What percentage of the flag is taken up by the union?
  2. What percentage of the flag is red? Be prepared to share your reasoning.

Are you ready for more?

The largest U.S. flag in the world is 225 feet by 505 feet.

  1. Is the ratio of the length to the width equivalent to 1:1.9 , the ratio for official government flags?
  2. If a square yard of the flag weighs about 3.8 ounces, how much does the entire flag weigh in pounds?

Lesson 1 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.

Lesson 1 Practice Problems

  1. A rectangle has a height to width ratio of 3 : 4.5 . Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.

  2. One rectangle measures 2 units by 7 units. A second rectangle measures 11 units by 37 units. Are these two figures scaled versions of each other? If so, find the scale factor. If not, briefly explain why.

  3. Ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the number of ants, a , to the number of ant legs l . Elena writes a = 6 \boldcdot l and Andre writes l = \frac{1}{6} \boldcdot a . Do you agree with either of the equations? Explain your reasoning.

  4. On the grid, draw a scaled copy of quadrilateral ABCD with a scale factor \frac{2}{3} .

    Quadrilateral ABCD is on a grid. Point a is 2 units right and 4 units down from the edge of the grid. Point B is 2 units right and 2 units up from point A. Point C is 6 units right from point A. Point D is 2 units right and 4 units down from point A.
  5. Solve each equation mentally.

    1. \frac{5}{2} \boldcdot x=1
    2. x \boldcdot \frac{7}{3}=1
    3. 1\div \frac{11}{2}=x
  6. Lin has a scale model of a modern train. The model is created at a scale of 1 to 48.

    1. The height of the model train is 102 millimeters. What is the actual height of the train in meters? Explain your reasoning.

    2. On the scale model, the distance between the wheels on the left and the wheels on the right is 1\frac14 inches. The state of Wyoming has old railroad tracks that are 4.5 feet apart. Can the modern train travel on those tracks? Explain your reasoning.