# The Half-Circle Protractor

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1 The Half-ircle Protractor Objectives To guide students as they classify angles as acute, right, obtuse, straight, and reflex; and to provide practice using a half-circle protractor to measure and draw angles. epresentations etoolkit lgorithms Practice EM Facts Workshop Game Family Letters ssessment Management ommon ore State Standards urriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key oncepts and Skills dd and subtract to find unknown angle measures. [Operations and omputation Goal 2] Use reference points to estimate the measures of angles; use a half-circle protractor to measure and draw angles. [Measurement and Reference Frames Goal 1] lassify angles according to their measure. [Geometry Goal 1] Key ctivities Students identify types of angles. They measure and draw angles with a half-circle protractor. They identify an angle as obtuse or acute to help them determine which protractor scale to use. They add and subtract to find unknown angle measures. Ongoing ssessment: Recognizing Student chievement Use Mental Math and Reflexes. [Number and Numeration Goal 1] Ongoing ssessment: Informing Instruction See page 4. Key Vocabulary acute angle obtuse angle reflex angle straight angle half-circle protractor base line Materials Math Journal 1, pp. 157 and 158 Study Link 6 6 half-circle protractor protractor for demonstration purposes straightedge chart paper World Tour Option: Visiting Europe Math Journal 1, p. 171 (optional); pp. 172, 173,, and 181 Student Reference ook, pp. 276, 277, 2, 284, 285, 297, and 2 5 Math Masters, pp (optional) Students resume the World Tour in Europe. Math oxes 6 7 Math Journal 1, p. 159 Students practice and maintain skills through Math ox problems. Study Link 6 7 Math Masters, p. 192 protractor Students practice and maintain skills through Study Link activities. REDINESS Modeling ngles Student Reference ook, p. 93 rope or string Students model angles with a rope. ENRIHMENT Measuring ngles in Triangles Math Masters, p. 193 straightedge protractor glue or tape Students determine that the sum of the measures of the angles of any triangle is. ENRIHMENT Exploring ngles in Literature Math Masters, p. 388 or 389 Students read Sir umference and the Great Knight of ngleland. ELL SUPPORT uilding ackground for Mathematics Words Students create a graphic organizer for the word angle. dvance Preparation For the optional Enrichment activity in Part 3, obtain the book Sir umference and the Great Knight of ngleland by indy Neuschwander (harlesbridge Publishing, 1). Teacher s Reference Manual, Grades 4 6 pp , 178, Lesson

2 Getting Started Mental Math and Reflexes Write decimals on the board and have volunteers read them aloud. Suggestions: sk questions such as: What digit is in the hundredths place? What is the value of the digit x? Math Message omplete the Math Message problems on journal page 157. Study Link 6 6 Follow-Up Students compare answers. Make sure they understand that the directional arc shows the path and direction of the rotation. Ongoing ssessment: Recognizing Student chievement Mental Math and Reflexes Use Mental Math and Reflexes to assess students ability to identify places in decimals and the values of the digits in those places. Students are making adequate progress if they can correctly identify and express the values of digits through thousandths. Some students may correctly identify and express the values of digits through ten thousandths. [Number and Numeration Goal 1] 1 Teaching the Lesson Math Message Follow-Up (Math Journal 1, p. 157) ELL WHOLE-LSS Links to the Future Identifying and describing acute, obtuse, straight, and reflex angles is a Grade 5 Goal. In discussing the answers, talk about the angles in terms of rotations: is less than a 1_ 4 turn, is more than a 1_ turn but 4 less than a 1_ 2 turn, and is between a 1_ turn and 1 full turn. 2 all attention to the names for the various types of angles. To support English language learners, write the names on chart paper next to an example of each. Display the chart paper throughout the unit. n acute angle measures between and 9. n obtuse angle measures between 9 and. reflex angle measures between and 3. Remind students that a 9 angle is called a right angle. omplete the list of angle names by mentioning that a angle is called a straight angle. sk: Why is this a good name for this angle? In a angle, the two sides meet to form a straight line. 438 Unit 6 Division; Map Reference Frames; Measures of ngles

3 Date 6 7 Introducing the Half-ircle Protractor WHOLE-LSS Have students examine their half-circle protractors. Students can use either the protractor on the Geometry Template or any other protractor. If some students protractors do not have labels for the and marks, have them write the labels. The marks may smear and disappear later, but they are helpful for this introduction to the half-circle protractor. sk partnerships to decide how the half-circle protractor is different from the full-circle protractor they used in the previous lesson. Review observations. Have students indicate thumbs-up if they had a similar answer. The curved edge of the protractor is a half circle. The edge of the full-circle protractor is a full circle. There are two scales on the half-circle protractor: one scale goes from to in a clockwise direction and the other from to in a counterclockwise direction. To support English language learners, discuss the meaning of scale in this context. ELL The mark on one side of the half-circle protractor is connected with the mark on the other side by a line segment. This segment is the base line of the protractor. The midpoint of the base line is the center of the half-circle protractor. There is often a hole at the center. Math Message Time Drawing and Measuring ngles Use a straightedge to draw the following angles. Do not use a protractor. : any angle that : any angle that measures : any angle that measures less more than 9 and less measures more than 9 than than Sample answers: is called an acute angle. is called an obtuse angle. is called a reflex angle. Measuring ngles with a Protractor Write whether the angle is acute or obtuse. Then measure it as accurately as you can. S D E O SDE is acute. OR is acute. RTV is obtuse. SDE measures 55. OR measures. RTV measures 1. nswers may vary by 3 degrees either way. EM3MJ1_G4_U6_ indd 157 Student Page Math Journal 1, p. 157 R R T V 1/13/11 3:28 PM Measuring ngles with a Half-ircle Protractor (Math Journal 1, p. 157) WHOLE-LSS Draw an angle on the board or overhead projector, but omit the arc that indicates the direction of the rotation. Mention that without the directional arc, this angle could represent a rotation less than or a rotation greater than. Draw directional arcs with arrowheads to show the two possible angles. Explain that if no arc is shown, the smaller of the two angles is intended. (See margin.) Draw another angle on the board or overhead. Use your demonstration protractor to show how to measure the angle. 1. Students should first estimate whether the angle measures more or less than 9. sk: Is the angle acute or obtuse? They can also use 45 and as reference angles to refine their estimate. If students develop this good habit, they will seldom read the wrong scale. 2. Put the center of the protractor over the vertex of the angle. 3. Move the protractor so that one side of the angle is on the base line, as shown in the margin. Make sure the center of the protractor remains over the vertex The arc indicates which angle to consider. 1 baseline 9 center a angle a 115 angle Lesson

4 Ongoing ssessment: Informing Instruction Watch that students are measuring carefully. difference of 3 degrees either way should be enough leeway. 4. Find the place where the other side of the angle crosses a mark on the edge of the protractor. 5. Decide which of the two -to- scales to use to determine the degree measure of the angle. If it is acute, use the smaller number; if it is obtuse, use the larger number. sk students to measure angles SDE, OR, and RTV at the bottom of journal page 157 and compare their measurements. Step 1 Drawing ngles with a Half-ircle Protractor (Math Journal 1, p. 158) INDEPENDENT PROLEM SOLVING Date Steps 2 and Step 4 Student Page Time Have students complete Problem 1 on journal page 158 with a partner or on their own. sk students to describe a procedure for using a half-circle protractor to draw angles while you or a student demonstrates at the board or overhead. One method: 1. Draw a ray. 2. Place the center of the protractor at the endpoint of the ray so that the base line is along the ray. 3. Use the scale that shows where the ray crosses the edge of the protractor. Make a dot where the other ray should cross the edge of the protractor. 4. Draw a ray from the vertex through the dot. Have students complete journal page 158 on their own. Remind students that they can check whether they have chosen the appropriate scale by noting if the angle is acute or obtuse. Share strategies for Problem 5, which requires students to draw a reflex angle. Sample strategy: Subtract 3 from 3 (= ). Draw a angle; then draw an arc on the outside of the angle. 6 7 Drawing ngles 1. Draw a 35 angle, using line segment GH as one of its sides. G H 143 dding and Subtracting to Find Missing ngle Measures WHOLE-LSS 2. Draw a angle, using ray D as one of its sides. D Show students that you can add and subtract angle measures to find unknown angle measures. Draw the diagram below on the board or overhead. 3. Draw a angle, using ray EF as one of its sides. a 4. Draw a 15 angle, using ray as one of its sides. Try This 5. Draw a 3 angle, using ray IJ as one of its sides. F E Point out that a straight angle measures and the smaller angle measures. Let a stand for the measure of the missing angle. Explain to students that the angle measure of the whole is the sum of the angle measures of the parts. Therefore, + a =, so a =. Math Journal 1, p. 158 EM3MJ1_G4_U6_ indd 158 I J 1/13/11 2:28 PM Pose additional problems on the board using either a straight angle or a 9 angle as the main angle. Have students use addition or subtraction to find the missing angle measures. 4 Unit 6 Division; Map Reference Frames; Measures of ngles

5 2 Ongoing Learning & Practice SMLL-GROUP World Tour Option: Visiting Europe (Math Journal 1, pp ,, and 181; Student Reference ook, pp. 276, 277, 2, 284, 285, 297, and 2 5; Math Masters, pp ) Social Studies Link If you have chosen to extend the scope of the World Tour for your class, divide students into groups of 4 or 5. Each group visits one of the remaining countries in Europe and records their country data on journal pages and 181, or on Math Masters, pages 419 and 4. Math oxes 6 7 (Math Journal 1, p. 159) INDEPENDENT Date 6 7 Math oxes 1. Insert parentheses to make each number sentence true. ( ) ( ) ( ) ( ) a. 12 = b = c. 49 = Six classrooms collected newspapers for one week. If they collected a total of 582 newspapers by the end of the week, on average about how many newspapers did each class collect? Number model with unknown: = n nswer: 97 newspapers Summary number model: = How many centimeters are in 9.7 meters? ircle the best answer D. 9, Student Page Time 2. Draw a line segment that is 2 inches long. Mark and label the following inch measurements on the line segment: 1_ 4, 3_ 4, 1, 1 1_ 4 and 1 1_ Multiply with a paper-and-pencil algorithm = 2, ircle the square that has 1_ 3 shaded Mixed Practice Math oxes in this lesson are paired with Math oxes in Lesson 6-5. The skill in Problem 6 previews Unit 7 content. Math Journal 1, p. 159 EM3MJ1_G4_U6_ indd 159 1/13/11 3:28 PM Writing/Reasoning Have students write a response to the following: Wei said that both squares in Problem 6 have 1_ 3 shaded. Do you agree or disagree? Explain your answer. Sample answer: I disagree. oth of the squares are divided into three parts and both of the squares have one part shaded. However, only shows 1_ because is divided into equal parts. The three 3 parts in are not equal. Study Link 6 7 (Math Masters, p. 192) INDEPENDENT Home onnection Students measure angles using a half-circle protractor. Some students may prefer to use a full-circle protractor from Lesson 6-6. Name Date Time STUDY LINK 6 7 Measuring ngles with a Protractor First estimate whether the angles measure more or less than 9. Then use a half-circle protractor to measure them. 1. : Three students, acting as points, use rope to represent line segments and form an acute angle. Study Link Master 2. : 3. : Differentiation Options REDINESS Modeling ngles (Student Reference ook, p. 93) SMLL-GROUP 5 15 Min 4. QRS: Q 5 Try This 5. NOP: KLM: K N L O M P To explore estimating angle measures using a concrete model, have students use rope to model angles. (See margin.) sk the vertex to tell the two points the type of angle or the measure of the angle that they should form. Have students use Student Reference ook, page 93 as a guide. R S Practice = ,829 = ,872 = = 3,264 Math Masters, p. 192 EM3MM_G4_U6_177-2.indd 192 1/13/11 2:16 PM Lesson

6 py g g p Name Date Time 6 7 Exploring Triangle Measures You need 2 sheets of paper, a straightedge, and a protractor. 1. Draw a large triangle on each sheet of paper. The 2 triangles should not look the same. 2. Label the vertices of one triangle,, and. Label the vertices of the other triangle D, E, and F. e sure to write the labels inside the triangles. 3. Using your protractor, measure each angle as accurately as you can. Record the degree measures in the tables below. 4. Find the sum of the degree measures in triangle and in triangle DEF. ngle Sum Teaching Master Degree Measure Sample answers: ngle D Degree Measure 5. Write a true statement about the sum of the measures of the 3 angles of a triangle. The sum of the angle measures of a triangle is. E F Sum 143 ENRIHMENT Measuring ngles in Triangles (Math Masters, p. 193) PRTNER 15 Min To apply students understanding of measuring angles, have them draw two triangles, measure the angles, and find the sum of the angle measures for each triangle. The sum of the students measures of the angles of a triangle should range from 1 to 19, with most sums close to. Guide students as they prove that the sum of the measures of the angles of any triangle is. Have them cut off the three corners of one of their triangles and arrange them so that the three angles touch each other but do not overlap. From this, it should be clear that the angles form a straight angle, and so the sum of their measures is. Math Masters, p. 193 ut ut EM3MM_G4_U6_177-2.indd 193 1/13/11 2:13 PM ut Encourage students to extend this exploration to prove that the sum of the measures of the angles of any quadrilateral is 3. Students may reason that since any quadrilateral can be divided into two triangles, the sum of the angles is twice, or 3. ENRIHMENT Exploring ngles in Literature (Math Masters, p. 388 or 389) SMLL-GROUP 15 Min Literature Link To further explore the half-circle protractor and angles, have students read and discuss Sir umference and the Great Knight of ngleland by indy Neuschwander (harlesbridge Publishing, 1). In a Math Log or on an Exit Slip, ask students to summarize what Radius learned on his quest. ELL SUPPORT uilding ackground for Mathematics Words PRTNER 5 15 Min To provide language support for angles, have students create a graphic organizer for the word angle. They may list words and draw pictures that are connected to the word angle. See Differentiation Handbook, page 34 for more information. 442 Unit 6 Division; Map Reference Frames; Measures of ngles

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