Using a Full-Circle. Protractor

Transcription

1 Using a Full-Circle Protractor Objective To provide practice using a full-circle protractor to measure and draw angles less than epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Draw and measure angles with a full-circle protractor. [Measurement and Reference Frames Goal ] Use ray and line segment vocabulary. [Geometry Goal ] Describe a circle as having 60. [Geometry Goal ] Rotate objects a given number of degrees. [Geometry Goal ] Key Activities Students use transparent protractors to measure and draw angles. Ongoing Assessment: Informing Instruction See page. Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, page 89). [Measurement and Reference Frames Goal ] Key Vocabulary angle ( ) sides (of an angle) vertex (of an angle) clockwise rotation counterclockwise rotation full-circle protractor Materials Math Journal, p. 55 Student Reference Book, pp. 9 and Study Link 6 5 Math Masters, p. 89 (optional) transparency of Math Masters, p. 9 drinking straw for demonstration purposes straightedge Playing Division Dash Student Reference Book, p. Math Masters, p. 7 per partnership: each of number cards 9 (from the Everything Math Deck, if available) Students practice dividing - or -digit dividends by -digit divisors. Math Boxes 6 6 Math Journal, p. 56 Students practice and maintain skills through Math Box problems. Study Link 6 6 Math Masters, p. 90 full-circle protractor Students practice and maintain skills through Study Link activities. READINESS Making and Using a Waxed-Paper Protractor Math Masters, p. 9 waxed paper scissors Students make and use a waxed-paper protractor. ENRICHMENT Playing Angle Add-Up Math Masters, pp per partnership: of each of number cards 8 and of each of number cards 0 and 9 (from the Everything Math Deck, if available) full-circle protractor (transparency of Math Masters, p. 9) dry-erase markers straightedge Students draw angles and then use addition and subtraction to find the measures of unknown angles. EXTRA PRACTICE Playing Angle Tangle Student Reference Book, p. 0 Math Masters, p. 57 full-circle protractor straightedge Students practice estimating and measuring angles. ELL SUPPORT Building Background for Mathematics Words colored pencils dictionary Students discuss the meanings of the terms clockwise and counterclockwise. Advance Preparation For Part and the optional Enrichment activity in Part, make enough transparencies of Math Masters, page 9 so each student will have a full-circle protractor and there will be a reserve supply for future activities. Teacher s Reference Manual, Grades 6 pp , 5 Lesson 6 6

2 Getting Started Mental Math and Reflexes Students make different angle openings with their arms. Have students begin each angle with arms in the o clock position and use clockwise movement. Suggestions: 90 less than more than more than Math Message Read the top half of page 9 in your Student Reference Book. Be prepared to tell some things that all angles have in common. Study Link 6 5 Follow-Up Consider having a student go through the motions as you go over the answer. Find an empty space on the classroom floor. Mark a starting point. The student should step heel-to-toe while following the directions. Teaching the Lesson Math Message Follow-Up (Student Reference Book, p. 9) ELL WHOLE-CLASS Geometry and Constructions Angles Student Page An angle is formed by rays or line segments that share the same endpoint. Draw an angle on the board. As you review the parts of an angle, label them. To support English language learners, leave this drawing on the board throughout the lesson as a visual reference. An angle is formed by rays or line segments that have the same endpoint. The rays or line segments are called the sides of the angle. The endpoint is called the vertex of the angle. is the symbol for angle. If the vertex of an angle is point T, the angle can be named T, or angle T. Tell students that in this lesson they will learn how to measure angles of varying degrees. angle formed by rays angle formed by segments The endpoint where the rays or segments meet is called the vertex of the angle. The rays or segments are called the sides of the angle. Naming Angles The symbol for an angle is. An angle can be named in two ways:. Name the vertex. The angle shown above is angle T. Write this as T.. Name points: the vertex and one point on each side of the angle. The angle above can be named angle ATC ( ATC) or angle CTA ( CTA). The vertex must always be listed in the middle, between the points on the sides. Measuring Angles The protractor is a tool used to measure angles. Angles are measured in degrees. A degree is the unit of measure for the size of an angle. The degree symbol is often used in place of the word degrees. The measure of T above is 0 degrees, or 0. Sometimes there is confusion about which angle should be measured. The small curved arrow in each picture shows which angle opening should be measured. full-circle protractor Demonstrating Angles and Rotations WHOLE-CLASS In Lesson 6-5, angles were used to represent clockwise rotations. Angles can also be used to represent counterclockwise rotations. To demonstrate, ask a student to fold a straw in half and hold it against the board. Rotate one half of the straw counterclockwise about _ of a turn. Ask another student to draw a line along each side of the straw to form an angle. Measure of A is 60º Measure of B is 5º Measure of C is 00º Student Reference Book, p. 9 half-circle protractor Unit 6 Division; Map Reference Frames; Measures of Angles

3 Draw a directional arc to show that this angle represents a counterclockwise rotation. Name the vertex. Then use the angle symbol to name the angle. (See below.) Write counterclockwise rotation next to the angle. Measurement Student Page Measuring an Angle with a Full-Circle Protractor Use the full-circle protractor to measure angle A. Step : Place the hole in the center of the protractor over the vertex of the angle, point A. Step : Line up the 0 mark with the side of the angle so that you can measure the angle clockwise. Make sure that the hole stays over the vertex. Step : Read the degree measure at the mark on the protractor that lines up with the second side of the angle. This is the measure of the angle. The measure of A is 5. M M Use your full-circle protractor to measure angles B and C to the nearest degree... Using a straw to demonstrate a counterclockwise rotation B measures about. C measures about. Using a Full-Circle Protractor (Math Journal, p. 55; Student Reference Book, p. ; Math Masters, p. 9) ELL WHOLE-CLASS Student Reference Book, p. Check your answers on page. Distribute the squares from the transparencies of Math Masters, page 9. Explain that full-circle protractors are tools used to measure angles. Write full-circle protractor on the board. Show students how to use the full-circle protractor to measure angle B on page of the Student Reference Book. Point out that the marks on the edge are labeled from 0 to 60 in a clockwise direction. Therefore, students must be careful to measure the angle in a clockwise direction. Ask them to measure reflex angle C. To support English language learners, write reflex angle on the board and discuss its meaning. Student Page Date Time LESSON 6 6 Measuring Angles Use your full-circle protractor to measure each angle D C degrees C. C measures D measures Try This F Angle C measures 70. Students work in partnerships to measure the angles on journal page 55.. F measures E measures. E 5. Without using your full-circle protractor, give the measure of the reflex angle in Problem (the part not marked by the blue arrow). Explain your answer. Sample answer: A full turn corresponds to 60. Angle F measures 50 so the reflex angle measures Math Journal, p. 55 Lesson 6 6

4 Ongoing Assessment: Informing Instruction Watch for students who line up the 0 mark on the full-circle protractor with the right-hand side of the angle and incorrectly read the protractor in a counterclockwise direction. degrees degrees Incorrect Correct do not place the center of the full-circle protractor at the vertex of the angle. have difficulty measuring angles like angle A below that do not have one side of the angle parallel to the bottom of the page. [ART: EM007TLG_G_U06_L06_T_007: angle A] A Discuss Problem 5 with students. Explain that angle measures can be added and subtracted to find unknown angle measures. For example, suppose you want to know the measure of the reflex angle in Problem. Angle C measures 60 and a full turn measures 60. If a stands for the measure of the reflex angle, then 60 + a = 60, or = a. So, a = 00. Drawing an Angle WHOLE-CLASS Step Step Step degrees 6 5 R Using a full-circle protractor and a straightedge to draw an angle Have students use a straightedge and their full-circle protractors to draw a 60 angle. (See margin.) Ask someone to describe how he or she drew the angle. Step : Draw a ray. Step : Place the center of the full-circle protractor on the endpoint of the ray, and align the 0 mark with the ray. Make a dot on the paper at the 60 mark. Step : Draw a second ray from the endpoint of the first ray through the dot. Unit 6 Division; Map Reference Frames; Measures of Angles

5 Remind students to draw an arc with an arrowhead to identify the direction of the rotation and use a letter to name the vertex point. Have partners take turns: One partner names a degree measure; the other draws an angle with that degree measure. Ongoing Assessment: Recognizing Student Achievement Exit Slip Use an Exit Slip (Math Masters, page 89) to assess students ability to draw angles with measures less than or greater than 90. Ask students to draw one angle that measures less than 90 and one angle that measures more than 90. Students should then use the full-circle protractor to measure the angles and record their measures. Students are making adequate progress if they are able to draw angles measuring less and more than 90. Some students may be able to correctly measure the angles to within a few degrees. [Measurement and Reference Frames Goal ] Date LESSON 6 6 Math Boxes Time. Ms. Kawasaki s fourth grade class made a circle graph to show students favorite days of the week. a. Which day of the week is the least favorite in Ms. Kawasaki s classroom? Monday b. About what fraction of the students prefer Saturday? _. Juan talked on the phone an average of minutes per week for whole year. About how many minutes did Juan spend on the phone in year? Number model with unknown: 5 = m Answer:,768 minutes Summary number model: 5 =,768. Write <, >, or = to make each number sentence true. a. 0,000,000 = four hundred twenty million Student Page 8 9 Favorite Day of the Week Saturday Sunday Friday. Divide with a paper-and-pencil algorithm. Write the remainder as a fraction. 88 / 7 = 6 _ 7 Tuesday Thursday Monday Wednesday For this spinner, what color would you be most likely to land on? white b. 65,000,000 < 9,000,000 red c. four hundred thousand > 0 blue d. 0 <,000 white Ongoing Learning & Practice Math Journal, p. 56 Playing Division Dash (Student Reference Book, p. ; Math Masters, p. 7) PARTNER Students play Division Dash to practice dividing - or -digit dividends by -digit divisors. See Lesson 6- for additional information. Math Boxes 6 6 (Math Journal, p. 56) INDEPENDENT Study Link Master Name Date Time Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-9. The skill in Problem 5 previews Unit 7 content. Writing/Reasoning Have students write a response to the following: Winnona said there isn t enough information provided in Problem to answer the question. Do you agree or disagree? Explain your answer. Sample answer: I disagree. There are 5 weeks in year, so I multiplied by 5 to get the number of minutes Juan spends on the phone in year. STUDY LINK 6 6 Measuring Angles First estimate and then use your full-circle protractor to measure each angle. > 0. This angle measures (>, <) 90. measure of G: G >. This angle measures (>, <) 90. measure of I: < 5. This angle measures (>, <) 90. measure of H: H < 85. This angle measures (>, <) 90. measure of J: Study Link 6 6 (Math Masters, p. 90) INDEPENDENT I J Try This 5. On the back of this page, draw and label angles with the following degree measures: Home Connection Students use a full-circle protractor to measure angles. ABC 78 DEF 5 GHI JKL Practice 6. = = = = 8 R 85 R Math Masters, p. 90 Lesson 6 6 5

6 Name Date Time LESSON 6 6 A Waxed-Paper Protractor. Follow the steps below to make a waxed-paper protractor. Step : Take a sheet of waxed paper. Step : Fold it in half again. Step 5: Cut off the top. Teaching Master fold Step : Fold the paper in half. Be sure to crease it tightly. fold Step : Bring the folded edges together and fold it in half. Repeat this step again. Step 6: Unfold. fold fold Differentiation Options READINESS Making and Using a Waxed-Paper Protractor (Math Masters, p. 9) SMALL-GROUP 5 0 Min py g g p. Use your waxed-paper protractor to measure the angles below. a. b. M R Angle M measures about _ wedges. Angle R measures about 7 wedges.. Use a straightedge to draw more angles on the back of this sheet. Measure the angles and record the numbers of wedges. Math Masters, p. 9 To explore the use of a protractor to measure angles, have students make and then use a waxed-paper protractor to approximate the measure of angles using standard angles as reference. Have students record the measurements as wedges and fractions of wedges. ENRICHMENT Playing Angle Add-Up (Math Masters, pp. 9 and ) PARTNER 5 5 Min To further explore the idea that angle measures are additive, have students draw angles and then use addition and subtraction to find the measures of unknown angles. Note that Round requires students to use addition to find the unknown angle measure. Rounds and require subtraction. The given measures of 90 and 80 degrees provide practice with complementary and supplementary angles. Before they play the game, tell students that the notation m ABC shown on the record sheet means the measure of angle ABC. Name Date Time Angle Add-Up Game Master EXTRA PRACTICE Playing Angle Tangle (Student Reference Book, p. 0; Math Masters, p. 57) PARTNER 5 5 Min Materials number cards 8 ( of each) number cards 0 and 9 ( of each) dry-erase marker straightedge full-circle protractor (transparency of Math Masters, p. 9) To practice estimating and measuring angles, have students play Angle Tangle. See Lesson 6-8 for additional information. py g g p Angle Add-Up Record Sheet (Math Masters, p. 509) Players Skills Drawing angles of a given measure Recognizing angle measures as additive Solving addition and subtraction problems to find the measures of unknown angles Objective To score the most points in rounds. Directions. Shuffle the cards and place the deck number-side down on the table.. In each round, each player draws the number of cards indicated on the Record Sheet.. Each player uses the number cards to fill in the blanks and form angle measures so the unknown angle measure is as large as possible.. Players add or subtract to find the measure of the unknown angle and record it in the circle on the Record Sheet. The measure of the unknown angle is the player s score for the round. 5. Each player uses a full-circle protractor, straightedge, and marker to show that the angle measure of the whole is the sum of the angle measures of the parts. 6. Players play rounds for a game. The player with the largest total number of points at the end of the rounds wins the game. Math Masters, p. 507 ELL SUPPORT Building Background for Mathematics Words SMALL-GROUP 5 5 Min To provide language support for angle rotations, discuss the meanings of the words clockwise and counterclockwise. Explain that counter can be a noun with many meanings. Ask students to provide some examples. Kitchen counter, using counters to make an array Explain that counter- can also be used as a prefix. Have students look up words in the dictionary that have the prefix counter-. Countermove, counterattack, counterbalance Clarify the meaning of counter in this context. Consider labeling a clock with an arrow arcing to the right labeled clockwise and an arrow arcing to the left labeled counterclockwise. 6 Unit 6 Division; Map Reference Frames; Measures of Angles

7 Name Date Time STUDY LINK 6 6 Measuring Angles First estimate and then use your full-circle protractor to measure each angle.. This angle measures (>, <) 90. measure of G:. This angle measures (>, <) 90. measure of H: G. This angle measures (>, <) 90. measure of I: H. This angle measures (>, <) 90. measure of J: I J Try This 5. On the back of this page, draw and label angles with the following degree measures: ABC 78 DEF 5 GHI JKL Practice Copyright Wright Group/McGraw-Hill 6. = = 8. = = 90

8 Name Date Time Angle Add-Up Materials number cards 8 ( of each) number cards 0 and 9 ( of each) dry-erase marker straightedge full-circle protractor (transparency of Math Masters, p. 9) Angle Add-Up Record Sheet (Math Masters, p. 509) Players Skills Drawing angles of a given measure Recognizing angle measures as additive Solving addition and subtraction problems to find the measures of unknown angles Objective To score the most points in rounds. Directions. Shuffle the cards and place the deck number-side down on the table.. In each round, each player draws the number of cards indicated on the Record Sheet. Copyright Wright Group/McGraw-Hill. Each player uses the number cards to fill in the blanks and form angle measures so the unknown angle measure is as large as possible.. Players add or subtract to find the measure of the unknown angle and record it in the circle on the Record Sheet. The measure of the unknown angle is the player s score for the round. 5. Each player uses a full-circle protractor, straightedge, and marker to show that the angle measure of the whole is the sum of the angle measures of the parts. 6. Players play rounds for a game. The player with the largest total number of points at the end of the rounds wins the game. 507

9 Name Date Time Angle Add-Up Example Example: In Round, Suma draws a, 7,, and 5. She creates the angle measures 5 and 7 and records them on her record sheet. Round : Draw cards = Using addition, Suma finds the sum of the measures of angles ABD and DBC. She records the measure of angle ABC on her record sheet and scores points for the round. Round : Draw cards = Suma uses her full-circle protractor to show that m ABD + m DBC = m ABC. A degrees 0 9 B D Copyright Wright Group/McGraw-Hill C 508

10 Name Date Time Angle Add-Up Record Sheet Game Round : Draw cards. + = Round : Draw cards. Round : Draw cards. + = 90 + = 80 Total Points = Copyright Wright Group/McGraw-Hill Game Round : Draw cards. Round : Draw cards. Round : Draw cards. + = + = 90 + = 80 Total Points = 509