NCTM Measurement Standard for Grades 3 5: Understand measureable attributes:

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1 Title Description Source Grade Level/Content Area Materials Needed Mathematical Knowledge Link to Standards Flagging Down Angles By relating the positions of the flagger s arms (the students will create these flaggers) to acute, right, obtuse, and straight angles, students can spell out their initials and send messages to each other. In this activity, there are clear distinctions between the angles. The acute angle is approximately 45 degrees, right (the standard to which others are compared) is 90 degrees, the obtuse angle is 135 degrees and the straight angle is 180 degrees. There will also be situations in which the angle is zero degrees no angle at all. Students will relate each flag to the hand that holds it and the side of the body on which it appears. The base ray will be a line running from the paper fastener down the leg of the flagger figure. Aims Education Foundation ( pdf) 3-5 Geometry/Measurement (best for 4 th grade) - Flagger figure (included in activity) - Paper fasteners - Yellow and red paper squares, 5 cm2 - Glue or tape - Scissors - Student pages (included in activity) - Protractor (if extension is done) - What an acute angle is - What an obtuse angle is - What a straight angle is - How to measure angles - How to use a protractor (if you do extension) NCTM Process standards - Communication - Representation NCTM Measurement Standard for Grades 3 5: Understand measureable attributes: - Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute Common Core Standards for Math - Geometric measurement: understand concepts of angle and measure angles. (4.MD)

2 Content background for teachers Specific Learning Outcomes: Misconception s identified: - Draw and identify lines and angles, and classify shapes by properties of their lines and angles. (4.G) Teachers need to have a solid understanding of: - What acute, obtuse, and straight angles are - How to describe the differences between acute, obtuse, and straight angles - How to use a protractor - How to measure angles Students will learn to - Write their initials using the semaphore flag signaling system - Look for patterns in the flag signaling system - Relate the positions of the flags to acute, right, obtuse, and straight angles - Measure the angles that the flagger creates (if extension is done) - Students might not know what acute, obtuse, and straight angles are - Students might confuse acute, obtuse, and straight angles - Students might not know how to measure angles (if this is the case, don t do the extension or come back to the extension once students know how to or use this as the launch to measuring angles) - Students might not know how to use a protractor - Students might use a protractor the wrong way - Students might not know what a zero degree angle is Various Solution Paths Questions - Encourages students to explore the difference between acute, obtuse, and straight angles - Encourages students to explore different angle measures - Encourages students to find patterns - Encourages students to use a protractor - Encourages students to learn about a code - Encourages students to communicate to classmates in a new way Students who are struggling: - What makes an acute angle different from an obtuse? - Are you starting one side of the angle at zero (when using the protractor) - What are your initials? - Is the angle that your flagger creates bigger or smaller than 90 degrees (perhaps show them what a 90 degree angle is) Students who are getting it: - What patterns can you see with some of the letters? - How many degrees are in a straight angle?

3 Prepared by: - What is your definition of an acute/obtuse/straight angle? - Which of the letters makes acute/obtuse/straight angles? - How can you determine if something is an acute/obtuse Ali Rizzo Explanation as why this is a worthwhile task: This is a worthwhile task because it had important and useful math embedded in a fun, hands on way. Measuring angles and knowing the difference between acute, obtuse, and straight angles is an important skill that students we reencounter again and again in their math careers. While working on this problem, students are making a skillful use of mathematics. Originally, this problem did not include the extension of measuring the angles that each letter creates. I added this in so that way students could take away more from the activity, if the class the class is at the point of measuring angles (I know that when I was in 4 th and even 5 th grade, I was not measuring angles yet so it depends on the school s curriculum). This task connects to other important mathematical ideas like measuring angles in geometric shapes. If this activity, and other activities like it, are mastered, then the teacher can move on to the measurement of geometric shape angles. This activity engages students because it has them make a fun little flagger guy that they can use to learn about angles. They can later use their flaggers and communicate with others in the classroom as a fun side activity. The whole class also comes together at the end to talk about what they have discovered through their flaggers. The teacher can assess students by observing where the class is at with measuring angles and determine if this idea needs to be revisited through another activity.

4 Topic Geometry: Angles Key Question What angles are used when we form the letters for the initials in our names using the semaphore alphabet? Learning Goals Students will: write their initials using the semaphore flag signaling system; look for patterns in the flag signaling system; and relate the positions of the flags to acute, right, obtuse, and straight angles. Guiding Document Common Core Standards for Math* Geometic measurement: understand concepts of angle and measure angles. (4.MD) Draw and identify lines and angles, and classify shapes by properties of their lines and angles. (4.G) Math Geometry angles right, acute, obtuse, straight Integrated Processes Observing Comparing and contrasting Communicating Interpreting data Materials Flagger figure Paper fasteners Yellow and red paper squares, 5 cm2 Glue or tape Student pages Background Information The semaphore flag signaling system is used when auditory communication is not possible. Students might relate to a catcher s signal to a pitcher as a way to secretly send messages. The semaphore flag signaling system uses the position of the flags to denote letters. There is a distinct pattern in the position

5 of the arms when representing the 26 letters of the alphabet. By relating the positions of the flagger s arms to acute, right, obtuse, and straight angles, students can spell out their initials and send messages to each other. In this activity, there are clear distinctions between the angles. The acute angle is approximately 45 degrees, right (the standard to which others are compared) is 90 degrees, the obtuse angle is 135 degrees and the straight angle is 180 degrees. There will also be situations in which the angle is zero degrees no angle at all. Students will relate each flag to the hand that holds it and the side of the body on which it appears. The base ray will be a line running from the paper fastener down the leg of the flagger figure. Management 1. Copy the flagger figures onto card stock. 2. Each student will need two flaggers, four paper fasteners, and three yellow squares and three red squares. 3. Prepare two flags that are large squares of construction paper to be used to demonstrate the semaphore system. Procedure 1. Ask the Key Question and state the Learning Goals. 2. Demonstrate a letter of your choice. Tell the students that they will be studying the angles used to make up this signaling system. Discuss the need for this type of communication privacy, failure of other technology, etc. 3. Distribute the student pages. Be sure to tell students that the flagger icon is facing them so the flagger s right arm actually appears on the left side of the icon. Give them the example of the letter A. The flag in the flagger s right hand is held at an acute angle (as measured from the flag to the shoulder and the shoulder down the leg). The other flag held in the left hand is at zero degrees, or at no angle. 4. Ask the students to look for patterns in the positions of the flags as they relate to the letters of the alphabet. [They should note that the right hand is the only hand to move for letters A, B, C, and D. The right hand follows a progression of

6 around the clock. Once it reaches the straight angle, the hands switch roles and the left hand continues. The letters E, F, and G are completed this way. The around the clock progression continues with the left hand flag beginning at a different starting point with each sequence. Note that for the letter O, the left hand crosses over the body and for the letters W and X the right hand crosses over the body. If students use these letters, come to a class consensus as to how to describe those angles.] 5. Distribute the card stock flaggers, paper fasteners, and the colored squares. 6. Have students make the two-colored flags as directed on the student page. 7. Direct them to cut out and assemble the flaggers. Have them glue or tape the flags onto the arms of the flaggers. 8. Encourage students to write R for right side and L for left side on their flaggers. This will help them as they describe the angles used to form their initials. 9. Tell students to position the arms of their flaggers to make the initials of their first and last name. 10. Have them describe the angles of the arms for each of the letters. Connecting Learning 1. What is an acute angle? 2. Name a letter made from two acute angles. [N] 3. Which letters have a zero-degree angle (no angle) for one of the flags? [A, B, C, D, E, F, G] 4. Which letters are made from an acute angle and a right angle? [H, M, S, and Z] 5. How can you determine if something is an acute angle? [It is less than a right.] 6. How can you determine if something is an obtuse angle? [It is greater than a right angle.] 7. What angle do the letters D, I, K, P, T, and V have in common? [a straight angle] 8. What are you wondering now? Extension 1. Have students make flags and signal messages to each other. 2. Have the students measure the angles that they have created

7 Using a protractor and recording them under the flagging code sheet Internet Connection Select the Learning Center link Flags. Scroll to the bottom of the page. Click on link Semaphore Flag Signaling System

8 1. Make two small flags. Fold one red square along the diagonal. Cut along the fold line to make two triangles. Glue one red triangle on top of each of two yellow squares.

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11 Semaphore Alphabet

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