Unit 4 Common Core Mathematical Practices (MP) Domains Number and Operations in Base Ten (NBT) Measurement and Data (MD) Geometry (G) INVESTIG ATION 1 Linear Measurement Teach this Investigation as is. Day Session Common Core Adaptation Common Core Standards 1 1.1 Measurement Benchmarks MP5 4.NBT.4, 4.MD.1, 4.MD.3 2 1.2 Measurement Tools MP5 4.NBT.4, 4.MD.1 3 1.3 Assessment: How Long Is Our Classroom? MP5 4.NBT.4, 4.MD.1, 4.MD.2, 4.MD.3 4 1.4 Measuring Length MP5, MP6 4.NBT.4, 4.MD.1, 4.MD.3 5 1.5 Measuring Length, continued MP5 4.NBT.4, 4.MD.1, 4.MD.2, 4.MD.3 INVESTIG ATION 2 Polygons of Many Types Day Session Common Core Adaptation Common Core Standards 6 2.1 Is It a Polygon? MP6 4.G.1, 4.G.2 7 2.2 Making Polygons MP6 4.G.1 8 2.3A Identifying Geometric See p. CC16. MP5, MP6 Figures 4.NBT.4, 4.MD.5.a, 4.G.1, 4.G.2 9 2.3 Sorting Polygons MP5, MP6 4.MD.3, 4.G.1, 4.G.2 CC UNIT 4
INVESTIG ATION 2 Polygons of Many Types, continued Day Session Common Core Adaptation Common Core Standards 2.4 Sorting Quadrilaterals MP3, MP6 4.G.1, 4.G.2 MATH WORKSHOP 2A Teaching Note Guess My Rule with Parallel and Perpendicular Lines Suggest that students Quadrilaterals use parallel lines and perpendicular lines as rules in Guess My Rule with Quadrilaterals. Discussion All Quadrilaterals Some Quadrilaterals 2.5 Assessment: What Is a Quadrilateral? MATH WORKSHOP 3A Guess My Rule (with Power Polygons or Shape Cards) Teaching Note Parallel and Perpendicular Lines as Attributes of Quadrilaterals Use the terms perpendicular lines and parallel lines as you create the All Quadrilaterals and Some Quadrilaterals chart with students. Teaching Note Parallel and Perpendicular Lines in Guess My Rule Suggest that students use parallel lines, perpendicular lines, and right triangles as rules in Guess My Rule. MP3, MP6 4.G.1, 4.G.2 INVESTIG ATION 3 Measuring Angles Day Session Common Core Adaptation Common Core Standards 3.1 Making Right Angles MP5 4.NBT.4, 4.MD.6, 4.MD.7 Discussion Teaching Note How Many Degrees? Equations for Making Right Angles Write equations on the board that represent what students found out about the measures of the angles. After students state the measure of the small angles in shape E, write on the board: 45 + 45 = 90. After students state the measure of the angles in shape O, write on the board: 30 + 30 + 30 = 90. Instructional Plan CC
INVESTIG ATION 3 Measuring Angles, continued Day Session Common Core Adaptation Common Core Standards 3.2 More or Less Than 90 Degrees? 2A MATH WORKSHOP How Many Degrees? SESSION FOLLOW-UP Daily Practice and Homework 3.3 Assessment: Building Angles DISCUSSION More Strategies for How Many Degrees DISCUSSION How Do You Know It Is 0 Degrees? MP5 4.NBT.4, 4.MD.6, 4.MD.7 Teaching Note Equations for How Many Degrees? Tell students that for each problem on Student Activity Book pages 39 40, they should write an equation that shows how they knew how many were in each unknown angle. Tell students for each problem on Student Activity Book pages 41 43, they should also write addition equations that represent the smaller angles they added together to make the larger angle. Daily Practice: In addition to Student Activity Book page 44, students complete Student Activity Book page 46 or C (Sides and Angles) for reinforcement of the content of this unit. MP5 4.NBT.4, 4.MD.6, 4.MD.7 Teaching Note Addition and Subtraction Equations As students share their ideas about how to find the measurement of the unknown angle in Problem 1, record equations that represent their thinking. For example: 30 + 30 = 60 or 90 30 = 60. Teaching Note Equations for Angles That Make 0 Degrees As students share how they combined angles to make 0, write addition equations that represent the angles they added together to make 0. For example: 60 + 30 + 30 = 0. 15 3.4A Lines and Angles See p. CC21. MP5 4.NBT.4, 4.MD.5.a, 4.MD.5.b, 4.MD.6, 4.G.1 CC UNIT 4
INVESTIG ATION 4 Finding Area Day Session Common Core Adaptation Common Core Standards 16 4.1 Symmetry MP5 TEN-MINUTE MATH Also ask students: 4.MD.3, 4.G.2, 4.G.3 Quick Images: 2-D Are there parallel lines, perpendicular lines, or right triangles in this image? If so, where are they? 17 4.2 Symmetry and Area MP5 TEN-MINUTE MATH Quick Images: 2-D 18 4.3 Finding Halves of Crazy Cakes TEN-MINUTE MATH Quick Images: 2-D SESSION FOLLOW-UP Daily Practice and Homework Also ask students: Are there parallel lines, perpendicular lines, or right triangles in this image? If so, where are they? Also ask students: Are there parallel lines, perpendicular lines, or right triangles in this image? If so, where are they? Daily Practice: In addition to Student Activity Book page 60, students complete Student Activity Book page 62 or C16 (More Lines and Angles) for reinforcement of the content of this unit. 4.MD.3, 4.G.2, 4.G.3 MP5 4.MD.3, 4.G.2, 4.G.3 19 4.4 Decomposing Shapes MP5 TEN-MINUTE MATH Also ask students: 4.MD.3, 4.G.2, 4.G.3 Quick Images: 2-D Are there parallel lines, perpendicular lines, or right triangles in this image? If so, where are they? 20 4.5 Area of Rectangles MP5 4.NBT.4, 4.MD.3 21 4.6 Area of Polygons MP5 4.NBT.4, 4.MD.3, 4.G.3 22 4.7 End-of-Unit Assessment MP1, MP2, MP6 4.NBT.4, 4.MD.3, 4.G.1, 4.G.2 Instructional Plan CC15
s e s s i o n 2. 3 A Identifying Geometric Figures Math Focus Points Identifying parallel lines and perpendicular lines Identifying right angles, acute angles, and obtuse angles Identifying right triangles Today s Plan activity Parallel and Perpendicular Lines 30 Min Class Pairs Vocabulary point line ray line segment perpendicular lines parallel lines angle right angle acute angle obtuse angle right triangle Materials Student Activity Book, p. 22A or C9, Parallel and Perpendicular Lines Make copies. (as needed) Power Polygons Activity Kinds of Angles Activity Right Triangles SESSION FOLLOW-UP Daily Practice 15 Min Class Pairs 15 Min Class Pairs Power Polygons Student Activity Book, p. 22B or C, Angles and Right Triangles Make copies. (as needed) T47 Power Polygons Student Activity Book, p. 22D or C, Sorting Shapes Make copies. (as needed) Ten-Minute Math Today s Number: Broken Calculator Students create five expressions that equal 925. They must use both addition and subtraction in their expressions. The 5 and 9 keys are broken. Have two or three students share their equations and explain how they know that the answer is correct. (Examples: 1,000 80 + 2 + 3 = 925 or 200 + 700 + 26 1 = 925) CC16 INVESTIGATION 2 Polygons of Many Types
1 Activity 2 Activity 3 Activity 4 Session Follow-Up A C T I V I T Y Parallel and Perpendicular Lines 30 Min class pairs Begin by discussing points, lines, rays, and line segments. As you do so, draw and label examples on the board. You may want to draw and label the geometric figures presented on chart paper and keep the chart posted in the classroom throughout the unit for student reference. A point is an exact location. You ll see it drawn as a dot. A line goes on and on forever in a straight path in two directions. The arrowheads remind you that a line keeps going. Rays and line segments are parts of lines. A ray has one endpoint and goes on forever in one direction. A line segment has two endpoints. Point Line Ray Line Segment We can use pencils to model lines. You need to imagine that they go on forever. [Use two pencils to show two lines intersecting to form square corners.] I am modeling perpendicular lines. Two perpendicular lines intersect to form square corners. Have students model perpendicular lines with pencils. On the board, draw two perpendicular lines. Now use your two pencils to show two lines that will never intersect. [Have students show this with their pencils.] We are modeling parallel lines. Parallel lines do not intersect. Draw two parallel lines on the board. Perpendicular Lines Parallel Lines Session 2.3A Identifying Geometric Figures CC17
1 Activity 2 Activity 3 Activity 4 Session Follow-Up Teaching Note 1 Working With Angles Right, acute, and obtuse angles are studied further in Investigation 3. Name Date Parallel and Perpendicular Lines In Problems 1 4, write point, line, ray, or line segment. 1. 2. 3. Can you describe examples of some things in the real world that look like perpendicular lines or parallel lines? Students might say: Perpendicular lines could be two streets that cross each other and make four square corners. Parallel lines would be two streets that never meet. 4. For Problems 5 and 6, use the polygon at the right. 2 Hold up a sheet of paper and point out parallel sides and perpendicular sides of the rectangle. Give each pair of students a set of Power Polygons and have students look for parallel sides and perpendicular sides in each shape. Then have students complete Student Activity Book page 22A or C9. 3 1 4 5 5. Give the numbers for a pair of parallel sides. 6. Give the numbers for a pair of perpendicular sides. For Problems 7 and 8, use the map below. 7. Name a pair of parallel streets. 8. Name a pair of perpendicular streets. ce AC TIVIT Y 22A Law Unit 4 Session 2.3A Student Activity Book, Unit 4, p. 22A; Resource Masters, C9 INV_SE04_U4.indd Kinds of Angles Pearson Education 4 ren Lincoln Ford Howard Evans 1 6/1/ 9:04 AM 15 Min class pairs Let s imagine your two pencils are rays, and the erasers are the endpoints. Hold them so they touch just at their endpoints. [Demonstrate with your own pencils.] We are modeling an angle. Hold your pencils so that the angle looks like a square corner. That s a right angle. Now close up the opening. That s an acute angle. It s smaller than a right angle. Now make an opening bigger than a right angle. That s an obtuse angle. Draw examples on the board. Right Angle Acute Angle Obtuse Angle Give each pair of students a set of Power Polygons. Have them take turns choosing a polygon and describing each of the angles. For example, shape J has one obtuse angle and two acute angles. 1 Ongoing Assessment: Observing Students at Work Do students recognize right angles, acute angles, and obtuse angles? Do they use a square corner on a Power Polygon or the corner of a sheet of paper to check? CC18 INVESTIGATION 2 Polygons of Many Types INV_TE04_U04_S2.3A.indd 18 6/2/ 4:48 PM
1 Activity 2 Activity 3 Activity 4 Session Follow-Up Name AC TIVIT Y Right Triangles Date 15 Min class Shape Cards (page 1 of 2) pairs 1 1 1 1 On the overhead, display Shapes 1 and 3 of Shape Cards (T47). Take a look at Shape 1 and Shape 3. How are these shapes the same? How are they different? 99 99 99999 9 99999 9 Display the other triangles from T47. Ask students to identify those triangles that are right triangles and those triangles that are not right triangles. Students should recognize Shapes 1, 4, 5, and 8 as right triangles. Ask volunteers to point to the right angle in each of these triangles. Students may show that an angle is a right angle or is not a right angle by using the corner of a piece of paper, a strategy they may remember from third grade, or by using a Power Polygon, such as shape A. 88 88 88888 8 88888 8 1515 15 15 15 15 15 15 15 15 15 15 15 15 15 15 1717 17 17 17 17 17 17 17 17 17 17 17 17 17 17 44 44 44444 4 44444 4 Pearson Pearson Education Education 4 4 [Derek] said Shape 1 has a right angle. A triangle that has a right angle in it is called a right triangle. 77 77 77777 7 77777 7 66 66 66666 6 66666 6 55 55 55555 5 55555 5 Students should recognize both shapes as triangles, and notice the differences in the angles. 33 33 33333 3 33333 3 22 22 22222 2 22222 2 1818 18 18 18 18 18 18 18 18 18 18 18 18 18 18 1616 16 16 16 16 16 16 16 16 16 16 16 16 16 16 2020 20 20 20 20 20 20 20 20 20 20 20 20 20 20 1919 19 19 19 19 19 19 19 19 19 19 19 19 19 19 Sessions 2.3, 2.4, 2.5 M19 Unit 4 T47 First Pass 24084_001-029_RM_G4-U04 19 Transparencies, T47 6/2/ 5:05 PM Second First PassPass Confirming Second PassPass 24084_42-52_OHT_G4_U4.indd 47 6/16/ :23 PM PDF Proof Pass Confirming PDF Proof Name Date Angles and Right Triangles In Problems 1 3, write right angle, acute angle, or obtuse angle. 1. 2. 3. Have students complete Student Activity Book page 22B or C. 4. Complete the chart. Number of Right Angles Differentiation: Supporting the Range of Learners Some students may have difficulty recognizing right triangles especially when one side of the right angle is not horizontal. Encourage them to use the corner of a sheet of paper to check for right angles. 5. Circle each right triangle. Session 2.3A Unit 4 22B Student Activity Book, Unit 4, p. 22B; Resource Masters, C INV_SE04_U4.indd 2 Session 2.3A INV_TE04_U04_S2.3A.indd 19 Number of Obtuse Angles Pearson Education 4 Students may confuse right angle and right triangle. You might want to work with students in small groups. Provide drawings to help them distinguish between angle and triangle. Number of Acute Angles 6/2/ 4:07 PM Identifying Geometric Figures CC19 6/16/ :25 PM
Pearson Education 4 1 Activity 2 Activity 3 Activity 4 Session Follow-Up Name Date Sorting Shapes Write the numbers of all the shapes that belong in each category. 2 3 1 6 5 7 Daily Practice note Students identify parallel sides, perpendicular sides, and obtuse angles in polygons. 4 9 8 S E S S I O N F O L L O W - U P Daily Practice Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page 22D or C. 1. Which shapes have at least one pair of parallel sides? 2. Which shapes have at least one pair of perpendicular sides? 3. Which shapes have at least one obtuse angle? Session 2.3A Unit 4 22D Student Activity Book, Unit 4, p. 22D; Resource Masters, C CC20 INVESTIGATION 2 Polygons of Many Types
s e s s i o n 3. 4 A Lines and Angles Math Focus Points Drawing lines, parts of lines, and angles Understanding the relationship between the degree measure of an angle and circular arcs Measuring angles using a protractor Today s Plan activity Drawing Lines and Angles 20 Min Class Individuals activity Using a Protractor 40 Min Class Pairs Session Follow-Up Daily Practice Vocabulary protractor Materials Student Activity Book, p. 51A or C, Drawing Lines and Angles Make copies. (as needed) Student Activity Book, p. 51B or C, Using a Protractor Make copies. (as needed) 6-inch paper circles (1 per student) Protractors (1 per student) Student Activity Book, p. 51C or C15, Lines and Angles Make copies. (as needed) Student Math Handbook, pp. 1 2 Ten-Minute Math Today s Number: Broken Calculator Students create five expressions that equal 722. They must use only subtraction in their expressions. The 2 and 7 keys on their calculators are broken. Have two or three students share their equations and explain how they know that the answer is correct. (Examples: 838 6 722 or 1,361 639 722) Session 3.4A Lines and Angles CC21
1 Activity 2 Activity Name 3 Session Follow-Up Date AC TIVIT Y Drawing Lines and Angles Draw an example of the figure. 1. 2. Line Segment 4. Line 5. Perpendicular Lines Pearson Education 4 7. class Individuals Begin by reviewing lines, line segments, and rays, and discuss how to draw them. As you do so, draw and label examples on the board. Ray When you draw a line, you can t show all of it. So you draw part of it and add two arrowheads. To draw a ray, be sure to show a dot for its one endpoint and draw just one arrowhead. For a line segment, you need to show its two endpoints. Angle Parallel Lines 9. Acute Angle Session 3.4A Obtuse Angle Unit 4 51A Student Activity Book, Unit 4, p. 51A; Resource Masters, C INV_SE04_U4.indd 20 Min 6. 8. Right Angle Drawing Lines and Angles 3. 1 5/4/ 1:31 PM Line Ray Line Segment Next, discuss parallel lines and perpendicular lines and show how to draw them. Ask volunteers to explain why each of your examples shows either perpendicular or parallel lines. Perpendicular Lines Parallel Lines Now, turn your attention to angles. Be sure students remember that angles are formed by two rays that share a common endpoint. Show how to draw angles and provide a variety of examples on the board. Review right angles, acute angles, and obtuse angles. Ask students to classify the angles you drew. Right Angle Acute Angle Obtuse Angle Have students complete Student Activity Book page 51A or C. CC22 Investigation 3 INV_TE04_U04_S3.4A.indd 22 Measuring Angles 6/3/ 1:17 PM
1 Activity 2 Activity 3 Session Follow-Up A C T I V I T Y Using a Protractor 40 Min class Pairs In this activity, students relate circular arcs to angle measures before they use a protractor to measure angles. Give each student a paper circle. Ask students to fold the circle in half and crease the paper. Then have them fold it in half again. Open your circle. What kind of angles do the creases make? What s the measure of each of those angles? How many is the sum of the four angles? Students might say: The creases look perpendicular, so those are right angles. Each right angle measures 90. So all four of them add up to 360. Let s pretend your circle is a clock. Draw the, 3, 6, and 9 on your clock. Then draw two rays on your circle pointing straight up like the hands of a clock pointing to the. 9 6 3 If one of the rays turns all the way around the circle, it has gone through the four right angles, so it has gone 360. Suppose it only goes halfway around and stops at the 6. How many is that? What about a quarter of the way around? Suppose it goes only 360 1 of the way around? Can you describe what kind of angle this would make? How many would it have? Talk to a partner about your ideas. Students might say: 360 1 of the way around is a really teensy part of the whole way around. It s like a little sliver. 360 1 of the way around is 1 of 360 360. So, it s only 1 degree. Session 3.4A Lines and Angles CC23
1 Activity 2 Activity Name 3 Session Follow-Up That s right. It has a very tiny opening. When we measure angles, we find how many are in them. How many would be in a right angle? Look at your circle. If the ray travels 41_ of the way around the circle, it has traveled 90. The creases in the paper show a right angle. A right angle has a measure of 90. Date Using a Protractor In Problems 1 4, use a protractor to measure each angle. 1. 2. 3. Give each student a protractor and explain that it is used to measure an angle in. Point out that each tick mark represents one degree. Demonstrate how to measure an angle. Discuss the two scales and be sure students understand which scale to use. 4. 5. How many are in a full circle? 6. What fraction of a circle does the angle in Problem 3 turn through? Have students complete Student Activity Book page 51B or C. 51B Unit 4 Pearson Education 4 7. The angle at the right cuts off _18 of the circle. Without using a protractor, give the measure of the angle. Ongoing Assessment: Observing Students at Work Session 3.4A Student Activity Book, Unit 4, p. 51B; Resource Masters, C INV_SE04_U4.indd 2 6/1/ 9:04 AM Students determine the degree measures of angles. Do students understand that an angle that turns through n one-degree angles is said to have an angle measure of n? Differentiation: Supporting the Range of Learners Some students may have difficulty reading the correct scale on the protractor. Encourage them to identify the angle they are measuring as acute, right, or obtuse before they measure it. Then have them measure the angle and check to see whether their numerical answer agrees with the type of angle they identified. If it does not, they likely used the wrong scale. Challenge students to use a protractor to draw angles with given measures. CC24 Investigation 3 Measuring Angles INV_TE04_U04_S3.4A.indd 24 6/3/ 1:20 PM
Pearson Education 4 1 Activity 2 Activity 3 Session Follow-Up S E S S I O N F O L L O W - U P Daily Practice Name Lines and Angles In Problems 1 3, draw an example of the figure. Date Daily Practice note Students draw geometric figures and use a protractor to measure angles. 1. 2. 3. Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page 51C or C15. Line Segment Parallel Lines Obtuse Angle In Problems 4 and 5, use a protractor to measure the numbered angle. 4. 5. 2 Student Math Handbook: Students and families may use Student Math Handbook pages 1 2 for reference and review. See pages 170 174 in the back of Unit 4. 1 Session 3.4A Unit 4 51C Student Activity Book, Unit 4, p. 51C; Resource Masters, C15 Session 3.4A Lines and Angles CC25
Name Date Parallel and Perpendicular Lines In Problems 1 4, write point, line, ray, or line segment. 1. 2. 3. 4. For Problems 5 and 6, use the polygon at the right. 2 1 4 3 5 5. Give the numbers for a pair of parallel sides. 6. Give the numbers for a pair of perpendicular sides. For Problems 7 and 8, use the map below. 7. Name a pair of parallel streets. 8. Name a pair of perpendicular streets. Ford Lincoln Howard Lawrence Evans Unit 4 Session 2.3A C9 Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Name Date Angles and Right Triangles In Problems 1 3, write right angle, acute angle, or obtuse angle. 1. 2. 3. 4. Complete the chart. Number of Right Angles Number of Acute Angles Number of Obtuse Angles 5. Circle each right triangle. Unit 4 Session 2.3A C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Name Date Daily Practice Sorting Shapes Write the numbers of all the shapes that belong in each category. note Students identify parallel sides, perpendicular sides, and obtuse angles in polygons. 1 2 3 4 9 5 6 7 8 1. Which shapes have at least one pair of parallel sides? 2. Which shapes have at least one pair of perpendicular sides? 3. Which shapes have at least one obtuse angle? Unit 4 Session 2.3A C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Name Date Daily Practice Sides and Angles For Problems 1 and 2, use the polygon at the right. 1 2 3 note Students identify parallel sides, perpendicular sides, and special types of angles in polygons, and they identify right triangles. 4 1. Give the numbers for a pair of parallel sides. 2. Give the numbers for a pair of perpendicular sides. 3. Circle each right triangle. 4. Complete the chart. Number of Right Angles Number of Acute Angles Number of Obtuse Angles Unit 4 Session 3.2 C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Name Date Drawing Lines and Angles Draw an example of the figure. 1. 2. 3. Line Segment Line Ray 4. 5. 6. Perpendicular Lines Parallel Lines Angle 7. 8. 9. Right Angle Acute Angle Obtuse Angle Unit 4 Session 3.4A C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Name Date Using a Protractor In Problems 1 4, use a protractor to measure each angle. 1. 2. 3. 4. 5. How many are in a full circle? 6. What fraction of a circle does the angle in Problem 3 turn through? 7. The angle at the right cuts off 1_ 8 of the circle. Without using a protractor, give the measure of the angle. Unit 4 Session 3.4A C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Name Lines and Angles In Problems 1 3, draw an example of the figure. Date Daily Practice note Students draw geometric figures and use a protractor to measure angles. 1. 2. 3. Line Segment Parallel Lines Obtuse Angle In Problems 4 and 5, use a protractor to measure the numbered angle. 4. 5. 2 1 Unit 4 Session 3.4A C15 Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Name Date Daily Practice More Lines and Angles In Problems 1 3, draw an example of the figure. note Students draw geometric figures and use a protractor to measure angles. 1. 2. 3. Perpendicular Lines Ray Acute Angle 4. Use a protractor to measure each numbered angle. Angle 1 4 Angle 2 Angle 3 3 Angle 4 1 2 Unit 4 Session 4.3 C16 Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Nombre Tamaño, forma y simetría Fecha Rectas paralelas y perpendiculares En los Problemas 1 a 4, escribe punto, recta, semirrecta o segmento de recta. 1. 2. 3. 4. En los Problemas 5 y 6 usa el polígono de la derecha. 2 1 4 3 5 5. Da los números de un par de lados paralelos. 6. Da los números de un par de lados perpendiculares. En los Problemas 7 y 8, usa el mapa de abajo. 7. Nombra un par de calles paralelas. 8. Nombra un par de calles perpendiculares. AYUNTAMIENTO Ford Lincoln Howard Lawrence Evans Unidad 4 Sesión 2.3A C9 Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Nombre Tamaño, forma y simetría Fecha Ángulos y triángulos rectángulos En los Problemas 1 a 3, escribe ángulo recto, ángulo agudo o ángulo obtuso. 1. 2. 3. 4. Completa la tabla. Número de ángulos rectos Número de ángulos agudos Número de ángulos obtusos 5. Encierra en un círculo cada triángulo rectángulo. Unidad 4 Sesión 2.3A C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Nombre Tamaño, forma y simetría Fecha Práctica diaria Agrupar figuras Escribe los números de todas las figuras que pertenecen a cada categoría. nota Los estudiantes identifican lados paralelos, lados perpendiculares y ángulos obtusos en polígonos. 1 2 3 4 9 5 6 7 8 1. Qué figuras tienen por lo menos un par de lados paralelos? 2. Qué figuras tienen por lo menos un par de lados perpendiculares? 3. Qué figuras tienen por lo menos un ángulo obtuso? Unidad 4 Sesión 2.3A C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Nombre Fecha Tamaño, forma y simetría Práctica diaria Lados y ángulos En los Problemas 1 y 2, usa el polígono de la derecha. 1 2 3 nota Los estudiantes identifican lados paralelos, lados perpendiculares y tipos de ángulos en polígonos e identifican triángulos rectángulos. 1. Da los números de un par de lados paralelos. 4 2. Da los números de un par de lados perpendiculares. 3. Encierra en un círculo cada triángulo rectángulo. 4. Completa la tabla. Número de ángulos rectos Número de ángulos agudos Número de ángulos obtusos Unidad 4 Sesión 3.2 C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Nombre Tamaño, forma y simetría Fecha Dibujar rectas y ángulos Dibuja un ejemplo de cada figura. 1. 2. 3. Segmento de recta Recta Semirrecta 4. 5. 6. Rectas perpendiculares Rectas paralelas Ángulo 7. 8. 9. Ángulo recto Ángulo agudo Ángulo obtuso Unidad 4 Sesión 3.4A C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Nombre Tamaño, forma y simetría Fecha Usar un transportador En los Problemas 1 a 4, usa un transportador para medir cada ángulo. 1. 2. grados grados 3. 4. grados grados 5. Cuántos grados hay en un círculo completo? 6. Qué fracción de un círculo atraviesa el ángulo del Problema 3? 7. El ángulo de la derecha corta 1_ del 8 círculo. Sin usar un transportador, da la medida del ángulo. Unidad 4 Sesión 3.4A C Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Nombre Tamaño, forma y simetría Rectas y ángulos En los Problemas 1 a 3, dibuja un ejemplo de cada figura. Fecha Práctica diaria nota Los estudiantes dibujan figuras geométricas y usan un transportador para medir ángulos. 1. 2. 3. Segmento de recta Rectas paralelas Ángulo obtuso En los Problemas 4 y 5, usa un transportador para medir el ángulo numerado. 4. 5. 2 1 grados grados Unidad 4 Sesión 3.4A C15 Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
Nombre Tamaño, forma y simetría Fecha Práctica diaria Más rectas y ángulos En los Problemas 1 a 3, dibuja un ejemplo de cada figura. nota Los estudiantes dibujan figuras geométricas y usan un transportador para medir ángulos. 1. 2. 3. Rectas perpendiculares Semirrecta Ángulo agudo 4. Usa un transportador para medir los ángulos numerados. 4 Ángulo 1 grados Ángulo 2 grados 3 Ángulo 3 grados 1 Ángulo 4 grados 2 Unidad 4 Sesión 4.3 C16 Pearson Education, Inc., or its affiliates. All Rights Reserved. 4