1. Which of the geometric objects are scaled versions of each other?

   

   12 shapes on a grid. Shape A, triangle with base 5 units and height 4 units. Shape B, traingle with base 3 units and height 2 units. Shape C, square with sides 5 units. Shape D, rectangle with length 4 units and width 2 units. Shape E, square with sides 2 units. Shape F, rectangle with length 6 units and width 2 units. Shape G, circle with diameter 6 units. Shape H, triangle with base 5 units and height 3 units. Shape I, rectangle with length 6 units and width 3 units. Shape J, circle with diameter a little over 2 units. Shape K, square with sides 3 units. Shape L, circle with diameter a little over 4 units.

2. Pick two of the objects that are scaled copies, and find the scale factor.

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 about  feet by 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.

1. Choose one of the four options, or invent another example of your own. Decide on a size that would be appropriate for this flag. Then, 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?

Here are some flags that use the colors red, white, and blue.

Chile

Puerto Rico

Czech Republic

Liberia

Malaysia

Samoa

1. Take turns with your partner to match each flag with a description. The description gives the percentage of the flag’s area that is each color.

   • For each match that you find, explain to your partner how you know it’s a match.

   • For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking, and work to reach an agreement.

   1. 36% red, 33% white, 24% blue

   2. 37% red, 37% white, 26% blue

   3. 46% red, 27% white, 27% blue

   4. 48% red, 42% white, 10% blue

   5. 50% red, 35% white, 15% blue

   6. 75% red, 1% white, 24% blue

2. Here is an image of the flag of France. The three color bands are each the same width.

   

   What percentage of this flag is:

   1. red?

   2. white?

   3. blue?

3. Here is an image of the flag of Laos. The white circle has a diameter of 8 units.

   

   What percentage of this flag is red?​​​​​​

On a U.S. flag that is 19 feet by 10 feet, the union is about  feet by feet. For each question, first estimate the answer, 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.