Flags of the Sea. Standards : Numbers and Operations, Geometry, Data Analysis and Probability, Problem Solving, Communication, and Connections.

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1 Part 1 Standards : Numbers and Operations, Geometry, Data Analysis and Probability, Problem Solving, Communication, and Connections. There are flags everywhere you go. You see them in front of buildings. At stadiums, in classrooms, on ships, in parades, and many other places. Flags are important symbols of identification and means of communication. But who do flags look the way they do? And what roles do you think mathematics has played in the design of flags? Learn more about flags and mathematics by investigating the question below. International Marine Signal Flags International Marine Signal Flags are special set of flags used by the ships to communicate with each other. Each flag represents a letter with a special meaning. Take a look at these flags by using a search engine to find a Web site about International Marine Signal Flags. Examine the flags carefully and note the key similarities and differences. Pay particular attention to patterns, similarities, and the arrangement of colors. For instance, you might describe the H and K flags as similar because they both are divided in half vertically by their colors. Explain and key similarities here:

2 Look at all the flags and try to find all the geometric figures they contain. Name at least four figures. List each figure you find along with the name where you found it. What is the most common geometric figure you found in the flags? Look at the flag for N and count the total number of squares it contains. How many squares did you find? In the space below make a drawing that shows all of the squares you found. Part 1 Due Date: January 10, 2014

3 Part 2 Fractions and Flags The flag for E could be described using fractions. For instance, the E flag is ½ blue and ½ red. Look through the flags and describe the five flags found in the table below in terms of fractions. Table One: Describing Flags in Terms of Fractions Flag Letter (Example) E D ½ red and ½ blue Fractional Description T U Z C

4 In Table Two, compare flags using fractions. For instance, the blue portions of G when combined, equal the blue portion of K. Explanation: the blue portions of G add up to? As shown here 1/6 + 1/6 + 1/6 = 3/6 = ½. Since the blue portion of K is ½, then the blue portions of G and K are equal. Table Two: Comparing Flags Using Fractions Flags to Compare Flag Comparison Using Fractions (Example) G and K The blue portions of G = 1/6 + 1/6 + 1/6 = 3/8 = ½. Thus, the blue portions of G combine to be one-half of the total flag. Thus, the blue portions of G and K are equal. L and O T and J Z and E Part 2 Due Date: February, 7, 2014

5 Part 3 Flags: Decimals and Percents Using the information from your previous fraction tables, complete the tables below by converting the fractional descriptions into decimal and percent equivalents. For example, E is ½ blue and ½ red; as a decimal it is 0.5 blue and 0.5 red; as a percent E is 50% blue and 50% red. Note: it is helpful to look at your fractional descriptions in Table One. Decimal Equivalent Percentage Equivalent (Example) E D T U Z C Now compare flags in terms of decimals and percentages. Flags to Compare (Example) U and H Flag Comparison Using Decimals and Percentages U and H are both 0.5 red and 0.5 white, as well as 50% red and 50% white. L and O

6 T and J Z and E Flags of the Sea Probability with Flags Math can truly be found everywhere. Believe it or not, flags also offer the chance to think about probability. Imagine you could enlarge each flag to the size of a bulletin board and post it on the wall. If you were to throw ten darts, how many times would you expect to hit it? The orange in the O flag? Explain: The orange in the N flag? Explain: The orange in the Y flag? Explain: The orange in the J flag? Explain: The orange in the C flag? Explain:

7 School Spirit Flag Using Geometric shapes, you will design your own flag that you feel symbolizes the town of Spring Lake. You will be required to hand draw a picture, emblem, or seal that represents Spring Lake, (cannot not use images from the computer) on a poster size 11x14 poster. You will create a flag using at least 4 geometric shapes which consist of correct mathematical measurements. Ex: If your draw a square it must have 4 equal sides and each angle must be 90. Criteria Self-Evaluation Teacher - evaluation Spring Lake needs to be visible on final flag Has to included at least 4 geometric shapes Flag design has to have at least 4 colors A hand drawn picture, emblem or seal that represents Spring Lake All geometric shapes must meet mathematical requirements **This form must be completed and turned in with the extra credit assignment in order to obtain any points. Part 3 Due Date: March 7, 2014