Mathematics Success Level D

Transcription

1 T782 [OBJECTIVE] The student will explore concepts of angles and be able to use a protractor to measure angle degrees. [PREREQUISITE SKILLS] multiplying multi-digit whole numbers [MATERIALS] Student pages S259 S271 Transparencies T794, T796, T797, T799, T801, T803, T805, T807, T809, and T811 Copy Master T796 (1 per student pair) Fraction strips (2 per student pair) Protractor (1 per student pair) [ESSENTIAL QUESTIONS] 1. When the two hands of a clock are on numbers next to each other, for example 1 and 2, how many degrees are in the angle they make? 2. How many one-degree angles are in a circle? 3. Describe how to use a protractor to measure an angle. [WORDS FOR WORD WALL] degree, protractor, ray, angle, vertex, acute angle, obtuse angle, right angle (90 ), straight angle (180 ) [GROUPING] Cooperative Pairs (CP), Whole Group (WG), Individual (I) *For Cooperative Pairs (CP) activities, assign the roles of Partner A and Partner B to students. This allows each student to be responsible for designated tasks within the lesson. [LEVELS OF TEACHER SUPPORT] Modeling (M), Guided Practice (GP), Independent Practice (IP) [MULTIPLE REPRESENTATIONS] SOLVE, Verbal Description, Graphic Organizer, Pictorial Representation, Concrete Representation

2 T783 [WARM-UP] (5 minutes IP, WG, I) S259 (Answers are on T793.) Have students turn to S259 in their books to begin the Warm-Up. Students will work with adding fractions with like denominators. Monitor students to see if any of them need help during the Warm-Up. Give students 3 minutes to complete the problems and then spend 2 minutes reviewing the answers as a class. {Verbal Description} [HOMEWORK] (5 minutes) Take time to go over the homework from the previous night. [LESSON] Day 1: (60 minutes M, GP, IP, WG, CP) Day 2: (60 minutes M, GP, IP, WG, CP) Day 1 Understanding Concepts of Angles SOLVE Problem (3 minutes WG, GP) T794, S260 (Answers on T795.) Have students turn to S260 in their books, and place T794 on the overhead. The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during the lesson they will learn how to measure angles. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE, Graphic Organizer} Exploring Angles - Concrete (27 minutes WG, M, GP, CP) T794, T796, T797, S260, S261 (Answers on T795, T798.) 27 minutes M, GP, WG, CP: Have students turn to S260 in their books, and place T794 on the overhead. Distribute two fraction strips, a protractor, and copy of T796 to each student pair. Have students work in partners and designate the roles of Partner A and Partner B. {Verbal Description, Concrete Representation, Pictorial Representation}

3 T784 MODELING Exploring Angles - Concrete Step 1: Direct students attention to the protractor in the middle of the page. Partner A, identify what part of a circle is represented by the protractor. (half of a circle) Partner B, explain what you notice about the numbers on the protractor. (There are two numbers for each mark.) Partner A, determine if there is a place on the protractor where the values are the same? (Yes, 90.) Have students discuss possible reasons why there are two sets of numbers? (Some angles open to the right, and others open to the left.) Step 2: Have students turn to S261, and place T796 on the overhead. Partner A, identify the shape of the clock. (circle) Partner B, identify how many numbers are on the clock. (12) Step 3: Tell students that you are now going to use the fraction strips as hands on the clock to create angles. Partner A, place a fraction strip so that one end is at the middle of the clock, and the other end is at the 12. Tell students that the fraction strip represents a ray. Partner B, place a fraction strip so that one end is at the middle of the clock, and the other end is at the 3. Partner A, identify what the two fraction strips form. (angle) Step 4: Model how to place the protractor on top of the clock, aligning the dot in the protractor with the point where the two hands meet. Have partners identify the measure of the angle. (90 )

4 T785 Step 5: Have Partner A move the fraction strip on the 12 to the 6. Partner B, place the protractor over the hands and determine the number of degrees in this angle. (90 ) Step 6: Have Partner B move the fraction strip on the 3 to the 9. Partner A, place the protractor over the hands and determine the number of degrees in this angle. (90 ) Step 7: Have Partner A move the fraction strip on the 6 to the 12. Partner B, place the protractor over the hands and determine the number of degrees in this angle. (90 ) Step 8: Have both partners draw all of the 90 angles in the clock in Question 7. The point where the rays meet in each angle is called the vertex. (Record and label the drawing.) Each hand on the clock represents one ray of the angle. (Record and label the drawing.)

5 T786 Measuring Angles - Concrete (20 minutes WG, M, GP, CP) T796, T799, S262 (Answers on T800.) 20 minutes M, GP, WG, CP: Have students turn to S262 in their books, and place T799 on the overhead. Students will also be using the clock and fraction strips. Have students work in partners and designate the roles of Partner A and Partner B. {Verbal Description, Concrete Representation, Pictorial Representation} MODELING Measuring Angles - Concrete Step 1: Have Partner B place the fraction strips to show 1:00 on the clock. Partner A, explain the position of the rays. (One starts at the center and points to 12; the other starts at the center and points to 1.) Step 2: Have students measure the angle with the protractor. Tell students they have just made a 30 degree angle. Step 3: Have students choose any two digits on the clock that are next to each other and use the fraction strips to form an angle. Partners should measure the angle formed by the two fraction strips. What is the measure of the angle formed? (30 degrees) Did all students choose the same digits? (No.) Did all the angles have the same measure? (Yes.) What does this mean about the angle formed between each of the digit pairs next to each other on the clock? (Each angle equals 30 ) Have partners determine how many 30 degree angles are in the circle on the clock. (12) Step 4: Have partners discuss how they could determine the total number of degrees in a circle. Partner A, what is the total number of degrees in the circle? (360) Partner B, explain how you could determine this. (Multiply 12 times 30.) (Explain that we can do this by multiplying 12 3 and adding the 0.)

6 T787 Step 5: Have Partner A move the strips so that the clock says 12:25. Partner B, explain the position of the rays. (One starts at the center and points to 12; the other starts at the center and points to 5.) Have the partners measure the angle with the protractor. How many degrees are in the angle you just made? (150 degrees) If you did not have a protractor, is there a way you could figure out the angle? (There are 30 degrees between each digit on the clock, so I could multiply 30 times 5.) Step 6: Have Partner B move the strips so that the clock says 12:30. Partner A, explain the position of the rays. (One starts at the center and points to 12; the other starts at the center and points to 6.) Have partners measure the angle with the protractor. How many degrees are in the angle you just made? (180 ) If you did not have a protractor, is there a way you could figure out the angle? (There are 30 between each digit on the clock, so I could multiply 30 times 6.) Measuring Angles Pictorial (10 minutes CP, WG, M, GP) T801, S263 (Answers on T802.) 10 minutes M, GP, WG, CP: Have students turn to S263 in their books, and place T801 on the overhead. Have students work in partners and designate Partner A and Partner B. {Verbal Description, Graphic Organizer, Pictorial Representation}

7 T788 MODELING Measuring Angles Pictorial Step 1: Direct students attention to the circles at the top of the page. Partner A, explain how these circles differ from the clocks we used. (There are no numbers.) Have partners discuss how they could estimate the angle measure using what they know about the clock. (They could visualize the clock face and use the numbers to determine the position of the rays - 12 and 2.) Partner B, if the rays are at 12 and 2, what is the measure of the angle? (There are 30 between each number, therefore 30 2 = 60.) Have students measure the angle with a protractor to check. Explain to students that there is a term to describe all angles that are less than 90. They are called acute angles. Step 2: Have students look at the second circle. Have partners discuss how they could estimate the angle measure using what they know about the clock. (They could visualize the clock face and use the numbers to determine the position of the rays - 11 and 2.) Partner B, if the rays are at 11 and 2, what is the measure of the angle? (There are 30 between each number, 30 3 = 90.) Have students measure the angle with a protractor to check. Explain to students that there is a term to describe all angles that are exactly 90. They are called right angles. Step 3: Have students look at the third circle. Have partners discuss how they could estimate the angle measure using what they know about the clock. (They could visualize the clock face and use the numbers to determine the position of the rays - 1 and 6.) Partner B, if the rays are at 1 and 6, what is the measure of the angle? (There are 30 between each number, 30 5 = 150.) Have students measure the angle with a protractor to check. Explain to students that there is a term to describe all angles that are greater than 90 but less than 180. They are called obtuse angles.

8 T789 Step 4: Direct students attention to the fourth circle. Have partners discuss how they could estimate the angle measure using what they know about the clock. (They could visualize the clock face and use the numbers to determine the position of the rays - 10 and 4.) Partner B, if the rays are at 10 and 4, what is the measure of the angle? (There are 30 between each number, 30 6 = 180.) Have students measure the angle with a protractor to check. Explain to students that there is a term to describe all angles that measure exactly 180. They are called straight angles Day 2 Measuring Angles with a Protractor One-Degree Angles (20 minutes CP, WG, M, GP, IP) T801, T803, S263, S264 (Answers on T802, T804.) 10 minutes M, WG, CP, GP: Students will work with the concept of 360 degrees in a circle to determine angle measures. {Verbal Description, Pictorial Representation, Graphic Organizer} MODELING One - Degree Angles Step 1: Have students look at Problem 2 on S263. Partner A, explain how many degrees are in a circle. (360 ) Explain to students that they can use that information to determine angle measures in a circle. Partner B, how many one-degree angles are in a circle? (360) Have partners discuss how we could represent a 1-degree angle as a fraction of the circle. ( ) Why? (There are a total of 360 degrees, and each degree measures 1.)

9 T790 Step 2: Tell students that if an angle passes through a number of one-degree angles, it has that same number of degrees for a measurement. Partner A, how many one degree angles make up a 30 angle? (thirty) Partner B, how many one degree angles make up a 145 angle? (145) Partner A, what angle passes through sixty-seven one degree angles? (67 ) Step 3: Have students turn to S246 and place T803 on the overhead. Partner A, identify what information is given for the first row. (The number of one degree angles ) Partner B, determine the measure of the angle. (115 ) What type of angle is this? (obtuse) 8 minutes IP, CP: Have partners complete the table on S264 together. Students will use the information given to identify the measure of each angle and the type of angle. {Verbal Description, Pictorial Representation, Graphic Organizer} 2 minutes WG: Have students come back together as a class and share their results. {Verbal Description, Pictorial Representation, Graphic Organizer} Using the Protractor (33 minutes CP, WG, M, GP, IP) T805, T807, T809, S265, S266, S267 (Answers on T806, T808, T810.) 15 minutes M, WG, CP, GP: Have students turn to S265, and place T805 on the overhead. Students will work in partners. Assign the roles of Partner A and Partner B. {Verbal Description, Pictorial Representation, Graphic Organizer}

10 T791 MODELING Using the Protractor Step 1: Point out the two angles marked on the protractor. Partner A, what do you notice about Angle P and Angle S? (They appear to be the same size.) Partner B, are these angles acute or obtuse angles? (acute) How do you know? (They are less than 90.) Look at the angle on the right side of the protractor. (Angle P.) Partner A, identify the location of the vertex of the angle. (in the circle at the bottom of the protractor) One ray is pointing at zero. Where is the other ray pointing? (either 30 or 150 ) Which measurement do you think we should use? Why? (30, because the angle is acute.) Use the same questions about angles to answer Questions 6 9 about Angle S. Step 3: Direct students attention to the protractor at the top of page S266. Partner A, does the angle have a measure of 60 or 120? (120 ) Partner B, explain why. (The angle is an obtuse angle, which means it measures more than 90.) Step 4: Model for students how to place the protractor for the angle in Question 2. Place the vertex in the circle at the bottom of the protractor and line up one ray with zero. (Record for A.) Explain to the students that the protractor does not have to be horizontal, but one ray must line up with zero. Ask students to tell you why you may have a hard time measuring the angle. (because the rays are not long enough) Tell them they can extend the rays by using the side of the protractor, and then reposition the protractor. (Record for B.) Is the angle more or less than a right angle? (less) Explain to students that because the angle is acute they will use the smaller number. () If the angle is obtuse, they will use the larger number. () Where does the ray fall on the protractor? (between 20 and 30) Model how to count the tick marks to get a measurement of 23.

11 T minutes IP, CP: Have students work with their partners to measure the angles on S267. Have Partner A measure the first angle, while Partner B double checks the measurement, and then switch places for every angle. Monitor closely to make sure students are using the protractor correctly. {Verbal Representation, Concrete Representation, Pictorial Representation} 4 minutes WG: Have students come back together as a class and share their results. {Verbal Representation, Concrete Representation, Pictorial Representation} SOLVE Problem (5 minutes WG, GP) T811, S268 (Answers on T812.) Remind students that the SOLVE problem is the same one from the beginning of the lesson. Complete the SOLVE problem with your students. Ask them for possible connections from the SOLVE problem to the lesson. (Students will be using a clock to find the number of degrees in an angle.) {SOLVE, Graphic Organizer, Verbal Description} If time permits (10 minutes IP, CP) S269 (Answers on T813.) Have students measure angles on S269 and around the classroom. [CLOSURE] (2 minutes) To wrap up the lesson, go back to the essential questions and discuss them with students. When the two hands of a clock are on numbers next to each other, for example 1 and 2, how many degrees are in the angle they make? (30 ) How many one-degree angles are in a circle? (360) Describe how to use a protractor to measure an angle. (1. Place the vertex in the circle at the bottom of the protractor; one ray points to a line marked 0 or If necessary, extend the rays with a ruler so they go past the outer portion of the protractor. 3. Read the degrees where the second ray hits the protractor. If the angle is acute, use the smaller number. If the angle is obtuse, use the larger number.) [HOMEWORK] Assign S270 and S271 for homework. (Answers on T814 and T815.) [QUIZ ANSWERS] T816 T818 The quiz can be used at anytime as extra homework or to assess how students progress on understanding the concepts of angles and how to measure them.