American Flag Three-Act Math

Student Activities

If you are not familiar with Three Act Mathematics, I recommend you learn a little about it from some of the leaders, Dan Meyers, Andrew Stadel, and Graham Fletcher.

Three-act math problems are inquiry-based, collaborative, constructivist problem solving exercises. In each act, more information is revealed to the students, until in Act Three the results are revealed.

Before Act 1: Distribute the Three-Act Math Template, or use your own. I have provided one in the supporting files. Discuss the importance of flags and their representation with students. If you are not in America, you may choose to use your own flag. Ask students what patterns they notice in their flag?

I group my students into small groups to solve these problems, usually 3-4 children per group. Groups are used for collaborating during each act.

Act 1: Show the screen shot of the Flag. Ask students to generate questions based on observations of what they notice and wonder. These questions should be mathematical in nature. Allow students time to think and share. In a small group, they should generate questions. Examples: What is the area of the flag? How many blocks is the flag? How heavy would the flag be? How much would it cost to make that flag? Ultimately, we want to guide students to "What fraction (or percent) of the flag is red/white/blue?" This should go in the main question.

Have students make an estimate/guess for each color. I also have them do a high/low estimate as well. Students then draw a picture.

Act 2: Give the kids more information. You may ask them what information they need, or you may let them explore the world file. I will reveal a lot of information here, some of it should not be revealed until Act 3. One suggestion is to let kids simply count blocks to determine length and width of various objects. Another option is to let them build their own American Flag somewhere in the grassy plains nearby.

Stripes: Each stripe is 3 blocks wide.

Red: 4 Rows of 50 Blocks, 3 Rows of 75 Blocks. ((50 x 3) x 4) + ((75 x 3) x 3) = (150 x 4) + (225 x 3) = 600 + 675.

White: 50 Stars, 3 Rows of 50 Blocks, 3 Rows of 75 Blocks. 50 + ((50 x 3) x 3) + ((75 x 3) x 3) = 50 + (150 x 3) + (225 x 3) = 50 +450 + 675.

Blue: The field of Blue is 25 by 21 Blocks less 50 stars. (25 x 21) - 50 = 525 - 50.

Act 3: The Reveal. At this point, I allow children to share their results and compare them to their original estimates.

The total number of blocks and their fractions or percentages of each color.

Red = 1,275 blocks. White = 1,175 blocks. Blue = 475 blocks. Total = 2,925 blocks.

Red = 1,275/2,925 or 51/117 in simplest form or 44% (when rounded to nearest whole number.

White = 1,175/2,925 or 47/117 in simplest form or 40%

White = 475/2,925 or 19/117 in simplest form or 16%

Act 4: Allow students time to construct their own version of a flag. You may determine the maximum number of colors (IE: 3) and size, or simply set a time limit. Then allow children time to solve each other's flag problems.