Unit 10 Geometry-Measuring Angles Grade 4 5E Lesson Plan Math Grade Level: 4th Subject Area: Math Lesson Title: Geometry-Measuring Lesson Length: 11 Days Angles THE TEACHING PROCESS Lesson Overview: This unit bundles student expectations that address skills necessary to solve problems involving angles less than or equal to 180 degrees, including drawing and measuring angles with a protractor. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace. During this unit, students illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. They also illustrate degrees as the units used to measure an angle, where of any circle is one degree and an angle that "cuts" out of any circle whose center is at the angle's vertex has a measure of n degrees. Using a protractor, students determine the approximate measures of angles in degrees to the nearest whole number and also draw angles of a specified measure. Given one or both angle measures, students determine the measure of an unknown angle formed by two non-overlapping adjacent angles. The concepts of complementary and supplementary angles are embedded within the study of adjacent angles. Within this unit, all angle measures are limited to whole numbers. Unit Objectives: Students will: illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. illustrate degrees as the units used to measure an angle, where of any circle is one degree and an angle that "cuts" out of any circle whose center is at the angle's vertex has a measure of n degrees. use a protractor to determine the approximate measures of angles in degrees to the nearest whole number and also draw angles of a specified measure. determine the measure of an unknown angle formed by two non-overlapping adjacent angles. 1 Unit 10 Geometry-Measuring Angles Grade 4 Standards addressed: TEKS: 4.1A Apply Mathematics to problems arising in everyday life, society, and the workplace. 4.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. 4.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental Math, estimation, and number sense as appropriate, to solve problems. 4.1D Communicate Mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, and language as appropriate. 4.1E Create and use representations to organize, record, and communicate Mathematical ideas. 4.1F Analyze Mathematical relationships to connect and communicate Mathematical ideas. 4.1G Display, explain, and justify Mathematical ideas and arguments using precise Mathematical language in written or oral communication. liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate. 4.7A Illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle. Angle measures are limited to whole numbers. (NA) 4.7B Illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers. (NA) 4.7C Determine the approximate measures of angles in degrees to the nearest whole number using a protractor. (RS) 4.7D Draw an angle with a given measure. (SS) 4.7E Determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures. (SS) ELPS: ELPS C.1.A use prior knowledge and experiences to understand meanings in English ELPS C.2.D monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed ELPS C.3.B expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication ELPS C.3.H narrate, describe, and explain with increasing specificity and detail as more English is acquired ELPS C.4.E read linguistically accommodated content area material with a 2 Unit 10 Geometry-Measuring Angles Grade 4 decreasing need for linguistic accommodations as more English is learned ELPS C.4.H read silently with increasing ease and comprehension for longer periods ELPS C.5.B write using newly acquired basic vocabulary and content-based gradelevel vocabulary ELPS C.5.F write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired ELPS C.5.G narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired. Misconceptions: Some students may think that the angle size is determined by the length of the rays rather than by the size of the turn. Some students may think that the orientation of the angle on a drawing will affect the measurement of the angle. Some students may not have made the connection between estimating the size of an angle before measuring and the appropriate scale on the protractor. Some students may think that degree measure for angles is read from only one side of a protractor (e.g., An angle with a measure of 30° may be at the markings of 30° and 150° on the protractor). Some students may think that when measuring with a protractor, one of the two rays must always align with zero rather than recognizing that an accurate measure is dependent upon the difference in the beginning and ending measure (e.g., An angle with a measure of 30° can be determined by beginning at 0° and ending at 30° or by finding the difference between other ending and starting points, such as 180° – 150°, 100° – 70°, etc.). Vocabulary: Acute – an angle that measures less than 90° Adjacent angles – angles that share a common vertex and side Angle – two rays with a common endpoint (the vertex) Angle congruency marks – angle marks indicating angles of the same measure Center of the circle – the point equidistant from all points on the circle Complementary angles – two angles whose sum of angle measures equals 90 degrees Congruent angles – angles whose angle measurements are equal Degree – the measure of an angle where each degree represents of a circle Obtuse – an angle that measures greater than 90° but less than 180° Protractor – a tool used to determine the measure of an angle Ray – part of a line that has one endpoint and continues without end in one direction 3 Unit 10 Geometry-Measuring Angles Grade 4 Right – an angle (formed by perpendicular lines) that measures exactly 90° Straight – an angle that measures 180° (a straight line) Supplementary angles – two angles whose sum of angle measures equals 180 degrees Related Vocabulary: Approximate Interval Circle Parallel Congruent Perpendicular Cut out Rotation List of Materials: Protractors What’s your angle? document Angle anchor chart Using a protractor power point Measuring Angles is EEEasy chart Measuring Angles Coloring Sheet Measuring Angles Using A Protractor Pinwheel Angle Measurement Angles Measurement Cards Baggies or Paper Bags Angle Star activity Colored pencils Complementary Angles picture Angles Complementary worksheet Supplementary Angles picture Angles Supplementary worksheet Graph Paper Angle Relationship Foldable Adding Angle Measures activity Paper Plates Tissue Paper Glue Rulers Scissors Clock Angles Cardstock INSTRUCTIONAL SEQUENCE Phase One Engage, Explore 4 Semi-circle Turn Unit Vertex Unit 10 Geometry-Measuring Angles Grade 4 Day One Activity – Angles and Protractors Materials: Angle anchor chart, Using a protractor power point, protractors Give the angles pre-assessment in the What’s Your Angle document.. Recall Information: Ask students to recall the four angles types discussed and properties of each. Students: obtuse more than 90◦, acute less than 90◦, right 90◦, straight 180◦. Bring out anchor chart or other class chart from angle lesson. Clear up any misconceptions from the preassessment. Ask: How do we know how many degrees an angle is if it is not labeled for us? Give students hints, like how do we tell temp, time. Students: answers may vary, we must measure it. Tell students today we will learn how to use a special tool, called a protractor, to measure angles. Pass out protractors and let students explore with them for 5 minutes. Ask students what they see on protractor. numbers, lines, circle, ruler What do you think the numbers represent with regards to measuring angles? degrees of the angles How do you think we can use this to measure an angle? Answers will vary Display the Angle Anchor Chart to show students parts of an angle. Tell them these vocabulary terms will be important when using a protractor. What part of an angle will you put on the circle of the protractor? vertex What line of the angle will you read to measure the angle? side Show students the video below about using protractors. Follow up with the Using a Protractor Powerpoint (if necessary). https://learnzillion.com/lessons/2973-measure-angles-to-the-nearest-degreewith-protractors Practice reading a protractor at this website. http://www.mathplayground.com/measuringangles.html Add this information to math journal. 5 Unit 10 Geometry-Measuring Angles Grade 4 What’s the teacher doing? Facilitating the discussion regarding angles and measurements. What are the students doing? Recalling previously taught information on angles. Allowing students to explore using the protractor tool and leading the discussion regarding how to read and use it. Exploring the protractor and understanding how to use it. Using the examples on the website to help students use a protractor to measure different angles. Phase Explore, Explain 6 Unit 10 Geometry-Measuring Angles Grade 4 Day Two Activity - Practice Measuring Angles with a Protractor Materials: Protractors, Measuring Angles is EEEasy chart, Measuring Angles Coloring Sheet, Measuring Angles Using a Protractor sheet, Pinwheel Angle Measurement Sheet Lead a discussion about where we see angles. Students should mention things like corners of cabinets, windows, doors. Lead students to name letters, clock hands, sports fields, houses, roofs, etc. Point out different angles around the classroom . Ask: Are the angles acute, obtuse, right or straight? How may degrees could that angle measure? Answers will vary; acute angles should be less than 90, right 90, obtuse more than 90, straight angles are 180. Show students the Measuring Angles is EEEasy chart to recall how to use a protractor. Display the Measuring Angles with a Protractor pg. 10 in the What’s Your Angle document. Ask the students what kind of angle each one is. Do the first one in front of the students, talking out how to read the protractor. Guide students to complete the remaining problems. Pass out page 9 in the What’s Your Angle document and protractors. Guide students to measure the different angles and share what kind of angle and what it measures. Tell students they are going to be rotating to three different measuring angles stations. Have the Measuring Angles Coloring Sheet, Measuring Angles-Using a Protractor Sheet and Pinwheel Angle Measurement Sheet at three stations. Another station will be the teacher station, with small group protractor and sorting angle practice. Students will rotate through the four stations practicing measuring with a protractor. As a closing activity, have students share one angle that they measured and the degrees. Sort each angle under acute, obtuse or right in an anchor chart. Make sure that students are able to correctly categorize the angles based on the measurement. What’s the teacher doing? What are the student’s doing? Leading angle discussing and sharing Participating and sharing knowledge of angles and angle measures. Monitoring students use of protractors and classifying angles. Providing small group instruction and reteaching during stations. Working in angle measuring stations and collaborating with other students. ‘ Sharing their findings from stations in whole group. . Phase Explain, Elaborate 7 Unit 10 Geometry-Measuring Angles Grade 4 Day Three Activity – Drawing Angles Materials: Protractors, Angles Measurement Cards, Baggies or Paper Bags Explain to students that today they will practice drawing different angles with a protractor. How do you know by reading a protractor what kind of angle you are drawing? Obtuse are greater than 90 degrees, acute are less than 90 degrees, right are 90 degrees and straight are 180 degrees. Use study jams lesson to practice constructing angles as a class. http://studyjams.scholastic.com/studyjams/jams/math/geometry/constructangles.htm Ask students to give you an angle measure. Answers will vary. Given the measurement, use a protractor to draw it. Talk through the procedure for using a protractor again. What type of angle is it? Answers will vary depending on degrees. Now give the students an angle measure. Together, draw an angle with that measurement. Then label it as acute, obtuse, right or straight. Do this a few more times with different measurements. Make sure the students are identifying the correct angle given the measurement. Tell students that they are going to break up into partners for an angle drawing activity. Give each group a baggie/paper bag with the Angle Measurement Cards in it as well as protractors. Students will take turns drawing out a card, drawing the angle and labeling it. Both students will draw and label every angle and compare answers. What’s the teacher doing? What are the students doing? Facilitating the study jam online lesson. Participating in the study jam lesson. Leading students in drawing different angle measures. Drawing angles with the teacher in the guided lesson. Monitoring the students as they complete the Angle Measurement Card lesson/reteaching as necessary. Collaborating with a partner in the Angle Measurement Card activity. Phase Evaluate, Elaborate 8 Unit 10 Geometry-Measuring Angles Grade 4 Day Four Activity – Performance Assessment Materials: Performance Assessment Question 3, Protractors, Colored Pencils, copy paper Give students this portion of the performance assessment to complete. 3) City officials are looking for entries of designs of skateboard kicker ramps that will be used in a skateboard park. Kyle and Terry both built a ramp using this design a) Kyle built his kicker ramp as shown below. Determine the approximate measure of the angle of incline on the kicker ramp in degrees to the nearest whole number. b) Terry wanted to design a kicker ramp with a 12° angle of incline. Use a protractor to draw a kicker ramp diagram of Terry’s design with the given angle measure. c) Describe the incline of Terry’s kicker ramp as being steeper, as steep as, or less steep than Kyle’s kicker ramp. Provide students with copy of Create an Angle Star directions, protractors and colored pencils. Encourage students to think about the many different kinds of angle measures when they are drawing the dots. Remind them to label the angles as they connect the dots. Display completed angle stars around the classroom. What’s the teacher doing? What are the students doing? Monitoring student performance. Completing performance assessment. Explaining and facilitating Angle Star Activity. Completing Angle Star Activity. 9 Unit 10 Geometry-Measuring Angles Grade 4 Phase Engage, Explore Day Five Activity – Complementary Angles Materials: Complementary Angles picture, Complementary Angles page, Protractors, Graph Paper Show students the Complementary Angles picture. Ask: What do you notice about the two angles? They are about the same size, they are both acute. What do both angles form together? A right angle Tell students that complementary angles are two acute angles that form a right angle. (if they students didn’t notice, point out that a good way to remember is that the angles are complimenting each other). Make a class chart: What are two angle measures that could be complementary? Answers will vary 45 and 45, 60 and 30, 70 and 20…any measures that add to 90. Using a protractor and graph paper, model for students how to draw a right angle. Give each arm of the angle a letter name. Then draw complementary angles using the protractor. Label the new arm with another letter. Label each angle with the correct measurement. Then write the angle names and the degrees, showing they add up to the original right angle. <AC 60◦ <BC 30◦ = <AB 90◦ Model one or two more examples Using their protractors and graphing paper, have students draw 5 complementary angles, labeling each one as you did together. Click on link to print Angles Complementary handout: http://goo.gl/1hdGTy Have students add complementary angles picture to their math journals. What’s the teacher doing? What are the students doing? Leading the discussion of complementary angles definition and examples. Participating in the discussion of complementary angles. 10 Unit 10 Geometry-Measuring Angles Grade 4 Guiding the practice of drawing complementary angles. Monitoring the independent practice of complementary angles. Observing the modeling of drawing and labeling complementary angles. Practicing independently working with complementary angles. Phase Engage, Explore Day Six Activity – Supplementary Angles Materials: Supplementary Angles picture, Angles Supplementary worksheet, Protractors, Graph Paper Show students Supplementary Angle Picture. Ask: What do you notice about supplementary angles? They form a straight angle. They add up to 180 degrees. How are they similar and different from complementary angles? They are two angles that add together to make up another angle. They are two right angles together. They are larger angles. One of the angles can be obtuse. Make a class chart: What are two angle measures that could be supplementary? Answers will vary 90 and 90, 110 and 70, 140 and 40, etc…any measures that add to 180. Using a protractor and graph paper, model for students how to draw a straight angle. Give each arm of the angle a letter name. Then draw supplementary angles using the protractor. Label the new arm with another letter. Label each angle with the correct measurement. Then write the angle names and the degrees, showing they add up to the original straight angle. <ABC 140◦ <BCD 40◦ = <ABD 180◦ Model one or two more examples Using their protractors and graphing paper, have students draw 5 supplementary angles, labeling each one as you did together. Click on link to print Angles Supplementary handout. http://goo.gl/YgNjc6 Have students add supplementary angles picture to their math journals. 11 Unit 10 Geometry-Measuring Angles Grade 4 What’s the teacher doing? What are the students doing? Leading the discussion of supplementary angles definition and examples. Participating in the discussion of supplementary angles. Guiding the practice of drawing supplementary angles. Monitoring the independent practice of supplementary angles. Phase Elaborate Observing the modeling of drawing and labeling supplementary angles. Practicing independently working with supplementary angles. Day Seven Activity – Adjacent Angles Materials: Angle Relationships Foldable, Adding Angle Measures Document Review complementary and supplementary angles by showing the picture to students. Discuss again the similarities and differences between the two. What does the word adjacent mean? Next to, close to, having a common side Were the complementary and supplementary angles we looked at the last two days adjacent? Yes Why? they were next to each other Define adjacent angles as those angles that have a common side and vertex. Show some of the complementary and supplementary angles from the last days’ lessons and point out the common side and vertex. Go through the math is fun lesson on adjacent angles. http://www.mathsisfun.com/geometry/adjacent-angles.html If I know the measure of one adjacent angle, how can I find the measure of the other angle? Subtract it from the total angle measurement, Subtract from 90 if complementary, 180 if supplementary. Pass out the Angle Relationship foldable and complete as a class. As you match the angle name to the correct descriptor card, ask students what they know about each type of angle. How can I tell if my angles are supplementary? They add to 180, they form a straight angle. How can I tell if my angles are complementary? They add to 90, they form a right angle. How can I tell if my angles are adjacent? They share a 12 Unit 10 Geometry-Measuring Angles Grade 4 common vertex and a common side. Model how to find adjacent angles by subtracting the known angle from 180/90. Address any misconceptions about angles. Put foldable in math journals. Work through adjacent angle problems on website below as a class: http://mrnussbaum.com/adjacentangles/ Complete the Adding Angle Measures activity. What’s the teacher doing? What are the students doing? Facilitating the discussion about angles and adjacent angles. Discussing the different types of angles. Completing the angle foldable. Working through the online lessons and foldable together as a class. Completing the adding angle measures activity. Monitoring the completion of the adding angle measures activity. Phase Engage, Explore Day Eight Activity – Circle Angles Materials: Paper plates (3 per student), tissue paper, scissors, glue, ruler, protractors, pen The following activity is modeled in the school tube video below. Watch before hand to be able to model it with students. http://www.schooltube.com/video/e70028466e0b485791d7/Paper%20Plate%20Angles Students will cover two paper plates with tissue paper and create a “moving” circle that can be used to show different measures of a circle. Give each student a paper plate. Fold the paper plate in half two times. Cut a very small circle in the center of the plate while folded. Open it back up and identify the cut as the vertex. What do we recall is the vertex of an angle? Endpoint where two rays (arms) come together. Using a ruler draw a line straight across the vertex horizontally. Look at the angles that you have made. What kind of angle did you make? Straight How many degrees is a straight angle? 180 Point out the straight angles applies to both the bottom and the top of the circle. If you have two straight angles that are each 180 degrees, how many degrees make up the total circle? 360 Now draw another line vertically? What kind of angles are the four angles of the 13 Unit 10 Geometry-Measuring Angles Grade 4 circle? Right angles How many degrees is a right angle? 90 If you have four right angles, each measuring 90 degrees, how many total degrees is a circle? 360 Flatten out and cover two more paper plates with tissue paper. Use the hole in the first plate to mark the vertex in both of the plates. Using a ruler, draw a line from the vertex to the end of the plates. Cut the lines on both plates, then fit them together. Model for students how to rotate/turn the plates to show different angles. Using the protractor, measure out different degrees of angles. If you measured out a 90 degree angle in one color, how much of the other color is left? 360-90=270 Write the angles as n/360, 90/360 or 270/360. If you measured out a 175 degree angle in one color, how much of the other color is left? 360-175=185 . How would I write that like I did the last angle? 175/360 or 185/360. Let students explore with the paper plates and protractors, creating different angles and representing them as n/360. What’s the teacher doing? What are the students doing? Modeling the paper plate construction and measuring of angles. Following directions to create the paper plate circles and practicing with creating different angles in a circle. Phase Explain, Elaborate Day Nine Activity – Clock Hand Angles Materials: Paper plate from yesterday, What’s Your Angle Resource, page 4 Using the paper plates created yesterday, have the students create a 180 degree angle. If the circle represents a clock, what numbers would be at either end of the straight angle? 3 and 9, or 12 and 6 depending on if the angle is vertical or horizontal. Label these numbers, then label the opposite angle, so that 12, 3, 6 and 9 are all labeled. Now create a right angle, with one arm at 12 and one at 3. What numbers should be in between? 1 and 2 How many angles will it make to the angles between 12 and 1, 1 and 2 and 2 and 3? Three angles If the entire space is 90 degrees and I need to divide it into 3 angles, how many degrees should each angle be? 90/3 = 30 Using the protractors, draw a 30 degree angle from 12:00. Label it 1:00 and 30 degrees. Then draw a 30 degree angle and label it 2:00. How many degrees are at 2:00? 30 + 30=60 degrees. 14 Unit 10 Geometry-Measuring Angles Grade 4 Continue on labeling the times on the clock and the corresponding degrees as you turn your angle until you reach 11:00 – 330 degrees. 12:00 will be labeled both 0 degrees and 360 degrees. Go through the below lesson, reinforcing the measurements of a circle. http://www.mathsisfun.com/activity/clocks-angles.html Pass out a copy of page 4 in the What’s Your Angle Document. Model labeling the first clock 2:00. Then show how you use your paper plate clock to determine what the angle of the 2:00 time is, and what the remaining angle represents, by subtracting from 360. If the 2:00 angle represents 60 degrees, then the adjacent angle represents what? 360-60 = 300 degrees. Describe how to find the measurement of any angle in a circle using the angle given as the hands of a clock. Answers will vary, but should include subtracting from 360, each turn of the angle measuring 30 degrees, etc. Continue using the remaining clocks on the resource and measuring the angles. What’s the teacher doing? What are the students doing? Facilitating the hands of a clock discussion. Using the hands of the clock and the paper plate activity to identify different angle measures. Modeling using the turn of the clock hands to represent 30 degrees of the 360 degree circle. Monitoring students using the clock hands to determine angle measures. Phase Elaborate Day Ten Activity – precut circles on cardstock, cardstock, scissors, protractor Tell students today they will practice labeling angles in a circle. Using the circle precut on cardstock, trace 3 circles on another sheet of cardstock. Cut out each circle. Fold the circle in fourths and cut out a small circle in the middle, the vertex. Using the protractor label one or two angles. If angle AB is 80 degrees, what is the measure of the rest of the circle? 360-80=280 15 Unit 10 Geometry-Measuring Angles Grade 4 Draw another 90 degree angle in the same circle and label it. What is the measure of the circle now? 360-80-90 =190 Continue this until all of the angles of the circle have been labeled and add up to 360. Tell students to follow the same process measuring angles in a circle. They will work with a partner, each time they draw an angle, the partner will have to figure out the remaining measure of the circle. Once the students are finished, put one of the circles in the math journals and display the rest of the circles on a class chart. What’s the teacher doing? What are the students doing? Modeling how to use the protractor and the circles to model angles in a circle and finding unknown measures. Monitoring the students as they work with a partner on the circle measuring activity. Phase Evaluate Observing the teacher working with angles in a circle. Working collaboratively on their circles to find measures of angles in a circle. Day Eleven Activity – Performance Assessment Materials: Performance Assessment Handout, Protractor Provide students with a protractor. Analyze the situation(s) described below. Organize and record your work for each of the following tasks. Using precise mathematical language, justify and explain each mathematical process. The town of Pineville is building a new sports park that will be circular in shape. The three main sections of the park will contain a football field, a tennis court, and a skate park. 1) The fourth grade students at Pine Elementary are looking at a diagram of the plans 16 Unit 10 Geometry-Measuring Angles Grade 4 for the park. They notice that the circular shape that outlines the park has a football field in one of the sections. a) Determine the measure of the angle represented by the “cut-out” or section of the circle where the football field is located. Describe how the measure of an angle can be illustrated as a part of a circle using the terms turn, center, vertex, rays, and angle. b) Identify the angle the football field section represents as a portion of a circle in terms of . 2) The diagram shown below illustrates how the park will be divided. The largest section will contain a skate park and the smallest section will have equipment and apparel shops. a) Given the angle measure of the section for the equipment and apparel shops, determine the measure of the angle for the section for the skate park. What’s the teacher doing? What are the students doing? Monitoring students during assessment Completing performance assessment using knowledge from lesson. 17
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