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Drawing Angles Objective To guide children as they draw angles as records of rotations. o www.everydaymathonline.com ePresentations eToolkit Algorithms Practice EM Facts Workshop Game™ Teaching the Lesson Family Letters Assessment Management Common Core State Standards Ongoing Learning & Practice Key Concepts and Skills Practicing with ×, ÷ Fact Triangles • Use straws and twist-ties to model angles. ×, ÷ Fact Triangles Children use Fact Triangles to practice multiplication facts. [Geometry Goal 1] • Use quarter-turns to describe right angles. [Geometry Goal 1] • Identify the vertex and sides of an angle. [Geometry Goal 2] • Model, draw, and name angles in terms of turns (rotations). [Measurement and Reference Frames Goal 1] Key Activities Children show angles with connected straws. They record straw rotations by drawing angles. Key Vocabulary rotation vertical Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, p. 398). [Operations and Computation Goal 3] Math Boxes 6 7 Math Journal 1, p. 142 Children practice and maintain skills through Math Box problems. Curriculum Focal Points Interactive Teacher’s Lesson Guide Differentiation Options READINESS Finding Right Angles magazines scissors glue or tape index card blank paper stapler (optional) Children create Right Angle books. ENRICHMENT Making and Comparing Right Triangles per group: paper scraps in a variety of sizes, ruler, yardstick or meterstick Children construct and compare a variety of right triangles. Home Link 6 7 Math Masters, p. 181 Children practice and maintain skills through Home Link activities. Materials Math Journal 1, p. 141 Home Link 66 straws and twist-ties meterstick straightedge 4 pieces of large paper Advance Preparation Label and display four posters to indicate the directions north, south, east, and west. Place two 2" straws and a twist-tie for each child in separate containers near the Math Message. Connect two 8" straws with a twist-tie to use in a demonstration. 438 Unit 6 Geometry 438_EMCS_T_TLG1_G3_U06_L07_576809.indd 438 2/23/11 11:46 AM Getting Started Mental Math and Reflexes Math Message Have children perform turn calisthenics. Children identify the direction they face after each turn. Have them refer to the cardinal direction posters. Take two straws and a twist-tie. Use them to form an angle that shows a quarter-turn. Face north. Do a full turn clockwise. north Do a full turn counterclockwise. north Face south. Do a half-turn clockwise. north Do a half-turn counterclockwise. south Face north. Do a half-turn clockwise. south Do a quarter-turn counterclockwise. east Do a three-quarter turn counterclockwise. south Home Link 6 6 Follow-Up Children share some of their named polygons. Briefly review why the letters that name a polygon cannot be repeated. Each label must be distinct so that all parts of the polygon can be named without any confusion. 1 Teaching the Lesson NOTE To introduce acute and obtuse angles, go to www.everydaymathonline.com. Math Message Follow-Up WHOLE-CLASS ACTIVITY Check that children have made right angles out of their straws. Making Angles with Straws WHOLE-CLASS ACTIVITY Have children place their connected straws on their desks with both sides touching and pointing up, like the hands of a clock showing 12 o’clock as you demonstrate on the overhead. Have them make angles, keeping one straw stationary while rotating the other straw clockwise or counterclockwise. After each turn, children return both straws to the 12 o’clock position. Use the term rotation to describe the motion of the straws. Adjusting the Activity ELL Draw these turns on the board so that children can refer to them as you give turning directions. left turn counterclockwise A U D I T O R Y K I N E S T H E T I C right turn clockwise T A C T I L E V I S U A L Lesson 6 7 EM3cuG3TLG1_439-443_U06L07.indd 439 439 1/20/11 8:48 AM Suggestions: 1 _ 2 ● Show a full-turn rotation. Describe what happened. What are the positions of the straws? They are back to where they started. ● Make a half-turn rotation. Describe the positions of the straws. One is pointing straight up; the other is pointing straight down. ● Make a quarter-turn rotation, either clockwise or counterclockwise. What kind of an angle did you make? A right angle ● Make a three-quarter turn rotation, either clockwise or counterclockwise. What are the positions of the straws? One is pointing straight up; the other is pointing at 3:00 or 9:00. What kind of angle did you make? A 270° angle ● Make less than a half-turn but more than a quarter-turn counterclockwise. ● Make less than a quarter-turn clockwise. ● Make more than a half-turn but less than a three-quarter turn clockwise. turn 1 full turn 3 _ 4 1 _ 4 turn turn Drawing Angles to WHOLE-CLASS ACTIVITY Record Rotations (Math Journal 1, p. 141) Ask a child to assist you in demonstrating how to draw an angle to record a turn, or rotation. Less than Less than _12 turn but more than _14 turn 1 More than _2 turn but less 3 than _4 turn 1 _ 4 turn A 1. Draw a dot on the board. Label it A. Explain that it is called Point A. 2. Place the connected straws so that the vertex is on Point A with both straws pointing to 12 o’clock. A 3. Keeping one straw stationary, rotate the other straw clockwise a quarter-turn. 4. Ask your assistant to draw a dot to represent a point at the tip of each straw. 5. Using a meterstick, draw two rays: one from the vertex through each point. Draw a curved arrow to show the direction of the rotation. Call children’s attention to the sides of the angle. The sides of angles are rays with common endpoints at the vertex of the angle. A A NOTE A point is an exact location in space and has no size. Dots, which do have size, are not really points; they are used to represent points. Points are usually named with capital letters. Journal page 141 provides additional practice with drawing angles. Each exercise is done twice (partners trade roles so that work is done in both journals). 440 Unit 6 Geometry EM3cuG3TLG1_439-443_U06L07.indd 440 1/20/11 8:48 AM Student Page Date Part 1 LESSON 6 7 䉬 Present the following directions: Time Drawing Angles Draw each angle as directed by your teacher. Record the direction of each turn with a curved arrow. 1. Each dot on the journal page represents a point, the vertex of an angle. Place the connected straws so the vertex is on point A with both straws pointing to 12 o’clock. Part 1 2. While one partner keeps the left straw stationary, the other partner rotates the other straw less than a quarter-turn clockwise. Sample answers: B A C Part 2 3. One partner marks points along both straws. S 4. Put the straws aside. Using a straightedge, draw a ray from the vertex through each point. Then draw a curved arrow to show the direction of the turn. R Present similar directions for angles B and C. For example: T Draw an angle that shows more than a half-turn counter clockwise but less than a three-quarter turn. Draw an angle that shows more than a quarter-turn clockwise but less than a half-turn. Math Journal 1, p. 141 Part 2 Present directions for drawing angles R, S, and T using the routine outlined above. This time the fixed straw should not be pointing to 12 o’clock. For example: Draw an angle that shows a quarter-turn clockwise. Draw an angle that shows more than a quarter-turn counterclockwise but less than a half-turn. Draw an angle that shows a half-turn clockwise. After children have completed the journal page, emphasize the following ideas: Angle size is determined by the amount of the turn. Neither side needs to be vertical (upright). To record a rotation correctly, draw a curved arrow showing which direction one side was rotated. Adjusting the Activity ELL Model and discuss the meaning of the word vertical. Have children stand in a vertical position, raise their arms in a vertical position, and find vertical line segments in the classroom. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Lesson 6 7 EM3cuG3TLG1_439-443_U06L07.indd 441 441 1/20/11 8:48 AM Student Page Date Time LESSON 2 Ongoing Learning & Practice Math Boxes 67 57 _ 1. The grid is ONE. Shade 100 of 2. Circle the pairs of lines that intersect. the grid. Practicing with ×, ÷ Fact Triangles Write the decimal that tells how much of the grid is shaded. 0.57 99 34 3. Draw an angle that is less than Have children sort their 18 Fact Triangles into 2 piles– multiplication facts they know and multiplication facts they still need to practice. Have them work independently or with a partner to review the facts they still need to practice. 4. Draw a ray, . Draw a line _SO 1 a_ 4 turn. . segment, LA. Draw a line, TI Sample answer: S L O A T I 167 168 100 5. Circle the regular polygons. 6. Complete. ⫻10 104 Ongoing Assessment: Recognizing Student Achievement ⫼5 1 10 2 20 80 8 40 4 200 201 142 Exit Slip Use an Exit Slip (Math Masters, page 398) to assess children’s progress toward demonstrating automaticity with multiplication facts through 10 × 10. Have children record the facts they know from their Fact Triangles. Children are making adequate progress if they record most of the facts represented on the Fact Triangles. Some children may be able to record all of the facts. Math Journal 1, p. 142 EM3MJ1_G3_U06_128-155.indd SMALL-GROUP ACTIVITY 2/10/10 1:48 PM [Operations and Computation Goal 3] Math Boxes 6 7 INDEPENDENT ACTIVITY (Math Journal 1, p. 142) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-5. The skill in Problem 6 previews Unit 7 content. Writing/Reasoning Have children write an answer to the following: Look at the polygons in Problem 5. Draw a different regular polygon and explain why it is regular. Sample answer: The polygon is regular because all of its sides are the same length and all of its angles are the same size. Home Link Master Name Date Time Turns HOME LINK 67 Family Note Home Link 6 7 If your child needs help with the following problems, consider putting up signs in a room in your home to indicate the directions north, south, east, and west. Do the turns with your child. Please return this Home Link to school tomorrow. left turn counterclockwise right turn clockwise INDEPENDENT ACTIVITY (Math Masters, p. 181) Make the turns described below. Show which way you face after each turn. Draw a dot on the circle. Label the dot with a letter. E Example: Face north. 1 turn counterclockwise. Do a _ 2 West On the circle, mark the direction you are facing with the letter A. F E, F, and G are sample answers. 1 _ 1. Face north. Do a 4 turn clockwise. Mark the direction you are facing with the letter B. 1 _ D B You East A South 3 _ 2. Face north. Do a 4 turn clockwise. Mark the direction you are facing with the letter C. 1 _ 3. Face east. Do a 4 turn 4. Face west. Make less than a 4 turn 5. Face north. Make a clockwise turn 6. Face north. Make a counterclockwise. Mark the direction you are facing with the letter D. p g C G Home Connection Children determine which direction they are facing after making certain turns. They record the results on a circle by drawing and labeling a point. North turn, but less that is more than a _ 2 3 than a _ turn. Mark the direction 4 you are facing with the letter F. py g 1 clockwise. Mark the direction you are facing with the letter E. counterclockwise turn that is less 1 than a _ turn, but more than a 2 1 _ turn. Mark the direction you are 4 facing with the letter G. Math Masters, p. 181 EM3MM_G3_U06_167-205.indd 442 181 2/10/10 1:45 PM Unit 6 Geometry EM3cuG3TLG1_439-443_U06L07.indd 442 1/22/11 1:33 PM 3 Differentiation Options READINESS Finding Right Angles SMALL-GROUP ACTIVITY 15–30 Min To provide experience identifying right angles, have children look through magazines for pictures of objects that have right angles. They can verify the angle measurements with the corner of an index card. Children cut out the pictures and tape or glue them on paper. They may staple their papers together to make a Right Angle book. ENRICHMENT Making and Comparing SMALL-GROUP ACTIVITY 15–30 Min Right Triangles To apply children’s understanding that an angle remains the same size regardless of its orientation and the length of its sides, have children make and compare right triangles. First, each child in the group chooses three or more paper scraps and traces the square corner of an index card onto each scrap of paper. Children use rulers or yardsticks to extend the sides of their right angles in order to make right triangles of varying sizes. Encourage the group to make many different looking triangles. They cut out the triangles and display them in a variety of orientations. Using the corners of the index cards, children verify that the right angles match, or are congruent, regardless of the other properties of the triangles. Children share their findings with the class. Lesson 6 7 EM3cuG3TLG1_439-443_U06L07.indd 443 443 1/20/11 8:48 AM