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The CROSSROADS Project Summer 2004 UNIT COVER PAGE Subject: Mathematics Grade Level: 5 Unit Title: Angle Me This, Angle Me That Description: This unit contains 4 lessons, a pretest, and a post-test. The lessons are designed to teach the measurement indicator dealing with the topics of benchmark angles, estimating angle measurement, and use of a protractor to measure and draw angles. Math Standard: Measurement Grade Level Indicator: Use benchmark angles (e.g. 45ď‚°, 90ď‚°, 120ď‚°) to estimate the measure of angles, and use a tool to measure and draw angles. Duration: This unit consists of 4 lessons requiring 5 days. Creators (Design Team Members): Steve Hrynko, Brett Hughes, Katerina McCullough-Lombardi, Mary Sanders, Amy York-Wagner Unit Title: Angle Me This, Angle Me That Grade Level : 5 Math Standard: Measurement Indicator Number: 7 Teacherâ€™s Name ________________________________ Building _________________________ District ________________________________________ Date of Testing ___________________ NOTE: Student protractors required for this test. Skills & Concepts: Pre-Test Studentâ€™s Name ____________________________________ Total Score: _____/20 A. Multiple Choice (2 points each; 10 points total) Directions to the student: Show how you solve each problem in the box provided. Use words, pictures, or numbers. Then circle the LETTER of the correct answer. 1. Estimate the angle created by the hands of a clock when the time is 3:10. How did you find your answer? a. 70ď‚° b. 30ď‚° c. 90ď‚° d. 120ď‚° 2. Choose the best estimate for this angle. How did you find your answer? a. 80ď‚° b. 55ď‚° c. 93ď‚° d. 21ď‚° 3. Choose the best estimate for this angle. a. 180ď‚° How did you find your answer? b. 95ď‚° c. 35ď‚° d. 135ď‚° 4. Use your protractor to measure the angle and choose the best answer. How did you find your answer? a. 49ď‚° b. 28ď‚° c. 37ď‚° d. 144ď‚° 5. Use your protractor to measure the angle and choose the best answer. How did you find your answer? a. 63ď‚° b. 148ď‚° c. 33ď‚° d. 162ď‚° Objective Test Sub-Score: _____/10 B. Multiple-Step Problem Solving (3 points) Directions to the student: Find the answer to this question. Be sure to finish the WHOLE question. You may use words, pictures, or numbers. Be sure to show your work. Using your protractor, draw two angles. One must measure 80ď‚° and the other must measure 120ď‚°. Label the angles Score: _____/3 C. Try It Another Way! (3 points) Directions to the student: Read the question below. Then draw, write about, or show with number sentences TWO DIFFERENT ways to find the answer. Describe or show two ways you could draw a 45ď‚° angle. Method #1 Method #2 Score: _____/3 D. Extended Response (4 points) Directions to the student: Use sentences to answer this question. Using the angle on the right: 1. Estimate the angleâ€™s measurement. Then explain how you determined your estimate. 2. Use your protractor to find the exact measurement. Explain the steps that you used to arrive at your answer. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Score: _____/4 Unit Pre-Test ANSWER KEY Multiple Choice (2 points each; 10 possible) 1. B 2. A 3. D 4. C 5. B Multi-Step Problem Solving (3 points each) Scoring Rubric: 3= Both angles are drawn within plus or minus 3° for the given measurements. Angles are labeled correctly. 2= One angle is drawn within plus or minus 3°. The other angle is drawn within plus or minus 7°. 1= Both angles drawn within plus or minus 7° of the given measurements. 0= Angles drawn measure greater than plus or minus 7° of the given measurements or no drawing is attempted. Try It Another Way! (3 points) Scoring Rubric: 3= Method 1 and Method 2 show or describe a correct way to draw the angle. 2= Both methods shown or described are correct, but contain some inaccuracies. 1= Only one method is accurately shown or described. 0= No attempt was made to answer the question or both methods described or shown are inaccurate. Extended Response (4 points) Scoring Rubric: 4= The estimate written is within plus or minus 10° of 143°. The explanation contains logical deductions using real life references or using benchmark angles. The actual measurement written is 143° (plus or minus 3°). The explanation of the steps used to arrive at the actual measurement contains a correct method for measuring angles. 3= The estimate written is within plus or minus 15° of 143°, and the explanation given used real life references or benchmark angles to arrive at the estimate. The actual measurement is within plus or minus 7° of 143°. The explanation of the steps used contains a correct method for measuring angles. 2= The estimate written is within plus or minus 15° of 143°, but the explanation given is difficult to understand because of some inaccuracies. The actual measurement of the angle is within plus or minus 10° of 143°, but the explanation is not clear and/or contains some inaccuracies. 1= The estimate written is more than plus or minus 15° from 143°, and the explanation is difficult to understand or are not there. The actual measurement of the angle is more than plus or minus 10° from 143°, and the explanation is either diffuclut to understand or itâ€™s not there. 0= No attempt was made LESSON PLAN #1 Unit Title: Angle Me This, Angle Me That Math Standard: Measurement Math Indicator: #7 Use benchmark angles (e.g., 45ď‚°, 90ď‚°, 120ď‚°) to estimate the measurement of angles, and use a tool to measure and draw angles. Objective: Each 5th grade mathematics student will create benchmark angles and use them to find benchmark angles in objects around them. Benchmark angles used are 45ď‚°, 90ď‚°, 120ď‚°, 135ď‚°, and 180ď‚°. Materials: Straight edge for each student blank paper *** MUST BE PREPARED AHEAD OF TIME: - 5 coffee filters per student (prefold one filter per student into thirds) - wall chart that is a replica of the student chart (in attachments) crayons or markers chart paper chart markers copy of student benchmark angles chart for each student (in attachments) copy of activity paper for each student (in attachments) Procedures: 1. Identify todayâ€™s goal: to discover the measurement of several special angles, which shall be called benchmark angles. These benchmark angles will be used to estimate the measure of other angles. (Benchmark angles can be defined as easy to identify reference angles used to estimate unknown measures of angles.) 2. Pass out one coffee filter. Fold it in half and then in half again. (fourths) Unfold. 3. Teacher can use a folded coffee filter or circle on board as model. Ask the students to tell you how many right angles they see. (4) Tell the students that there are 360ď‚° in these four angles. (360ď‚° in a circle) If these four anglesâ€™ measurements total 360ď‚°, how much would just one right angle measure? (90ď‚°â€¦360/4=90) This is the first benchmark angle. Have students use a marker and straight edge to draw on two of the fold lines to create a 90ď‚° angle. Have them mark it 90ď‚°. Put in a vertex also. As you add information to the wall chart, have students add information to their personal chart. 4. With another coffee filter, have the students fold them in half and then half again. Do not unfold. Review where the 90ď‚° angle is. Pose the question: if we fold the 90ď‚° in half, what will we create? (another angle, a 45ď‚°) Have students fold the filter in half. This is the second benchmark angle. Have students unfold the filters and use their marker and straight edge to draw on the two fold lines that create the 45ď‚° angle. Create a vertex. Label the angle with 45ď‚°. Add the information to the wall chart as students add to their own charts. 5. Using a third coffee filter, see if students can fold it to create a 90ď‚° (right) angle. Have students help each other. Pose this question: if you unfold the paper once, what have you created? Some students will say a straight line. Have them discover that it is indeed an angle by reviewing the definition of an angle (the intersection of two rays â€“ center of the circle is vertex of angle, rays come out from that pointâ€¦.in opposite directions). Ask what would be the measure of this angle? (180ď‚°) This is called a straight angle, and it is the third benchmark angle. Have students trace over the folds that create this angle, make a vertex, and label the angle 180ď‚°. Add information to wall chart. 6. Use a fourth filter. Have students fold to create a 90ď‚°. Then fold to create a 45ď‚° angle. Unfold the filter. On your model, go over the lines that will create a 135ď‚° angle (hint: 90 plus 45). Have students do the same. Ask what the measure of this angle might be? (135ď‚°). How did they get their answer? Create the vertex and label it 135ď‚°. Add the information to charts. 7. Pass out the last filter which should be the one you have already folded into thirds. With a partner or in small groups, have the students try to come up with a measure of one of the three angles created. (60ď‚°) Two of the angles? (120ď‚°) Discuss answers and how the students got the answers. This is the fifth benchmark answer. Have students trace fold lines to create a 120ď‚° angle. Put in a vertex and label the angle with its measure. 8. Optional activity: Using their benchmark angles as models, have pairs of students find objects in the room (hall, building) that have angles with these measures. Discussion afterwards would include which benchmark angles were easiest to find, which were hardest to find. Product: Student will have coffee filter models of five benchmark angles and a chart with benchmark angle information. If optional activity is done, students will also have a list of real objects that have angles with benchmark measures. Assessment Criteria: As students are working with coffee filters, teacher should observe the answers that are produced and the explanation of how they got the answers. Charts can be collected to check for accuracy. Teacher can also show unmarked models to class or individual students for them to say which benchmark measure it is. Attachments Chart instructions: List angle measures from smallest to greatest. Type of angle: acute, right, or obtuse. For the â€śsee itâ€ť: students can place folded angle in box. Trace just as much will fit in the column. Student Name______________________________________ BENCHMARK KIND OF â€śSEE ITâ€ť ANGLE ANGLE MEASURE LESSON PLAN #2 Unit Title: Angle Me This, Angle Me that Math Standard: Measurement Math Indicator: #7 Use benchmark angles (e.g. 45ď‚°, 90ď‚°, 120ď‚°) to estimate the measurement of angles, and use a tool to measure and draw angles. Objective: Each 5th grade mathematics student will use benchmark angles to estimate the measurement of angles. Materials: 3â€ť by 5â€ť cards â€“ 5 per student straight edge piece of paper Procedures: 1. Using a straight edge each student should draw 5 angles, one per card. The angles need to be either acute or obtuse. The angle should be marked on the card. On the back of the card, students should put their name and labeled 1-5. On a separate piece of paper, each student should create an answer key containing an estimate of the anglesâ€™ measurements they drew and the benchmark angle he/she used to help them estimate. They should be prepared to explain their estimate and use of benchmark angle. Teacher should walk the room and check students understanding at this point, by asking them to orally explain one of their angles and their estimates. (15 min.) 2. In pairs, the students take turns estimating each otherâ€™s angles. After each estimate, the students should also offer an explanation using a benchmark angle. If there is a question about a studentâ€™s answer or the studentâ€™s answer key, they may use another pair of students as a resource. If there is still a disagreement, the teacher may be consulted. Teacher should walk the room and listen in to studentsâ€™ estimates and explanations. (15 min.) 3. After students have had a chance to practice estimating, pick some angle cards from the class that are examples of estimating with each of the benchmarks. Discuss as whole class. (10 min.) 4. Use student work sheet for individual check on student understanding of this objective. (See attachment) Product: - Student made angle cards. - Individual student assessment Assessment Criteria: Teacher observation and questioning of student activity to check for understanding of the use of benchmark angles to estimate angle measure. Individual student assessment rubric: 3: Student chooses a benchmark angle and correctly explains how it was used to arrive at the estimate. 2: Student chooses a benchmark angle, but explains his/her estimate with some difficulty. 1: Student chooses a benchmark angle, but cannot explain his/her estimate relationship to the benchmark. 0: No understanding of the relationship between estimating angle measure and the use of benchmark angles. Student Name ________________________________________ Look at each angle. Write an estimate for the measure of each angle. Then write how you arrived at that estimate, making sure you use a benchmark angle in your answer. 1. Estimate: ___________ Explanation: ____________________ _______________________________ _______________________________ _______________________________ 2. Estimate: _______________ Explanation: _____________________ ________________________________ ________________________________ ________________________________ 3. Estimate: _______________ Explanation: _____________________ ________________________________ _________________________________ _________________________________ 4. Estimate:________________ Explanation: _____________________ ________________________________ _________________________________ __________________________________ LESSON PLAN #3 2 Day Lesson Unit Title: Angle Me This, Angle Me That Math Standard: Measurement Math Indicator: Use benchmark angles (e.g.; 45ď‚°, 90ď‚°, 120ď‚°) to estimate the measure of angles, and use a tool to measure and draw angles. Objective: Each 5th grade mathematics student will: Use a protractor to measure given angles and draw angles to specific degrees Materials: 1. pencils 2. protractors ( one for each student) 3. â€śEstimate Meâ€ť worksheet (one for each group of 4) 4. â€śMeasure Thisâ€ť worksheet (one for each student) â€“ Day 1 5. â€śDraw Partnerâ€ť worksheet (one for each student) â€“ Day 2 Procedures: Day 1 1. Place your students in groups of four. 2. Pass out â€śEstimate Meâ€ť worksheet face down (one to each group). 3. Allow groups 90 seconds to estimate the measurement of each angle and record their estimates on the Estimate Me worksheet. 4. Discuss the estimates with the whole group, using previous vocabulary (right, obtuse, acute). 5. Introduce the tool and the vocabulary that goes with the tool. (protractor, vertex, ray, and degrees). 6. In their groups have the students discuss how they could use the tool to measure angles on â€śEstimate Meâ€ť sheet. Expected response: Put the vertex of the angle in the center of the tool and line up the base line and use the measures to the right or left depending on the opening of the angle write the measure. 7. Place an unmarked 120ď‚° angle on the overhead. Lay the protractor on the angle with one ray at 50ď‚° and one ray at 170ď‚°. Have the groups see if they can measure the angle without moving the protractor. 8. Review the strategies that the groups came up with for measuring angles. 9. Pass out â€śMeasure Thisâ€ť worksheet and complete the first four problems together as a whole. 10. Allow time for the students to complete the remainder of the work sheet on their own to turn in for assessment. Day 2 1. Review the previous days discussion on measuring angles and discuss the ways to measure angles. 2. Have the groups discover a way to use the tool to draw an angle of 55ď‚°. Allow time for groups to discuss. 3. Have groups explain their methods to the class. 4. Pass out the â€śDraw Partnerâ€ť work sheet. 5. Complete the first four problems together as a class. 6. Have the students complete the remainder of the worksheet in class on their own and turn in for assessment. Product: Each fifth grade student will complete two worksheets that involve measuring angles and drawing angles. Assessment Criteria: Each work sheet will be assessed with the following 3 point rubrics Day 1 3= Students show estimate and show proper use of tool within + or - 3ď‚° 2= Students show estimate and use of tool within + or - 7ď‚° 1= Students estimates are inaccurate and no use of tool 0= No attempt made Day 2 3= Angles are drawn and labeled with + or - 3ď‚° 2= Angles are drawn and labeled with + or - 7ď‚° 1= Angles are drawn but inaccurate 0= No attempt made â€śESTIMATE MEâ€ť â€śMEASURE THISâ€ť Name______________________ Date_______________________ Estimate and find the measure of each of the following angles. 1. estimate __________ actual ___________ 2. estimate __________ actual__________ 3. estimate ___________ actual __________ 4. estimate ___________ actual___________ 5. estimate ___________ actual ____________ 6. estimate ___________ actual ___________ 7. estimate ___________ actual __________ 8. estimate ___________ actual __________ â€śDraw Partnerâ€ť Name___________________ Date ____________________ Use your protractor to draw the following angles. Label your answer. 1. 47ď‚° angle 2. 153ď‚° angle 3. 16ď‚° angle 4. 111ď‚° angle 5. 89ď‚° angle 6. 33ď‚° angle 7. 129ď‚° angle 8. 97ď‚° angle LESSON PLAN #4 Unit Title: Angle Me This, Angle Me That Math Standard: Measurement Math Indicator: Use benchmark angles (e.g.; 45ď‚°, 90ď‚°, 120ď‚°) to estimate the measure of angles and use a tool to measure and draw angles. Objective: Each 5th grade mathematics student will: learn how to measure angles using benchmark angles (45ď‚°, 90ď‚°, 120ď‚°). Materials: Computers/laptops for each student in your class or enough to partner students Internet site http;//www.brainpop.com Printer to print documentation of measuring angles worksheets Procedures: This web-based lesson could be used anytime through out the unit because it includes the benchmark angles. Have the students log on to the above web site ( you may want to have it book marked for them to save you time). When the site appears you will see the title screen. At the title screen you will have the students click on the Math icon. When the math movies appear, have the students click on the measuring angles icon. When the measuring angles movie appears, have the students click on â€śplay the movie.â€ť Allow time for the students to observe the movie. When the movie is over, instruct the students to click the â€śtake the quizâ€ť icon, and allow them to take the computer generated quiz. This will allow the student to have instant feedback. Have the students write down their score at the end of the quiz. When the students have finished the quiz, instruct them to scroll down to the activity page icon and click on it. This will bring up an activity sheet that they will need to complete when they have finished this activity. Have the students click on â€śfileâ€ť in the top left corner of the screen and scroll down to print and click â€śprint.â€ť This will print the activity sheet that they need to complete. If you wish for your students to complete the other activities that go with the angles movie you may have the students click on the other icons and enjoy the other activities. Product: Students will print off their activity sheets from the printer, and turn in to be assessed. Assessment Criteria: Students will be assessed on the following 3 point rubric: 3= Worksheet successfully completed 2= Worksheet complete but partially incorrect 1= Worksheet is incomplete 0= No attempt made RECOMMENDED UNIT RESOURCES Print Resources Literature Books 1. Sir Cumference and the Great Knights of Angleland , by C. Neuschwanders 2. The Greedy Triangle, by Marilyn Burns Teacher Resource Geometry and fractions with Tangrams Internet Sites for Teacher Reference www.bbc.co.uk/skillwise matti.usu.edu/ulvm/nav/vlibrary.html www.k111.k12.il.us/king/math.html teams.lacoe.edu/documentation/classrooms/amy/amy.html Internet Sites for STUDENT Use www.k111.k12.il.us/king/math.html teams.lacoe.edu/documentation/classrooms/amy/amy.html www.brainpop.com Additional Resources Geo Boards Pattern Blocks Unit Title: Angle Me This, Angle Me That Grade Level : 5 Math Standard: Measurement Indicator Number: 7 Teacherâ€™s Name ________________________________ Building _________________________ District ________________________________________ Date of Testing ___________________ NOTE: Student protractors required for this test. Skills & Concepts: Post-Test Studentâ€™s Name ____________________________________ Total Score: _____/20 A. Multiple Choice (2 points each; 10 points total) Directions to the student: Show how you solve each problem in the box provided. Use words, pictures, or numbers. Then circle the LETTER of the correct answer. 1. Estimate the angle created by the hands of the clock when the time reads 6:40 How did you find your answer? a. 5ď‚° b. 94ď‚° c. 138ď‚° d. 32ď‚° 2. Choose the best estimate for this angle. How did you find your answer? a. 7ď‚° b. 65ď‚° c. 15ď‚° d. 170ď‚° 3. Choose the best estimate for this angle. How did you find your answer? a. 170ď‚° b. 130ď‚° c. 83ď‚° d. 15ď‚° 4. Use your protractor to measure the angle and choose the best answer. How did you find your answer? a. 40ď‚° b. 63ď‚° c. 110ď‚° d. 19ď‚° 5. Use your protractor to measure the angle and choose the best answer. How did you find your answer? a. 72ď‚° b. 145ď‚° c. 111ď‚° d. 39ď‚° Objective Test Sub-Score: _____/10 B. Multiple-Step Problem Solving (3 points) Directions to the student: Find the answer to this question. Be sure to finish the WHOLE question. You may use words, pictures, or numbers. Be sure to show your work. Using your protractor, draw two angles. One must measure 45ď‚° and the other must measure 135ď‚°. Label the angles. Score: _____/3 C. Try It Another Way! (3 points) Directions to the student: Read the question below. Then draw, write about, or show with number sentences TWO DIFFERENT ways to find the answer. Describe or show two different ways to make a 120ď‚° angle. Method #1 Method #2 Score: _____/3 D. Extended Response (4 points) Directions to the student: Use sentences to answer this question. Using the angle on the right: 1. Estimate the angleâ€™s measurement. Then explain how you determined your estimate. 2. Use your protractor to find the exact measurement. Explain the steps that you used to determine the exact measurement. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Score: _____/4 Unit Post-Test ANSWER KEY Multiple Choice (2 points each; 10 possible) 1. D 2. C 3. A 4. B 5. C Multi-Step Problem Solving (3 points each) Scoring Rubric: 3= Both angles are drawn with plus or minus 3° from the given measurement. Angles are labeled correctly. 2= One angle is drawn with plus or minus 3°. The other angle is drawn with plus or minus 7°. 1= Both angles are drawn with plus or minus 7°. 0= Angles are not drawn or they measure greater than plus or minus 7°. Try It Another Way! (3 points) Scoring Rubric: 3= Method 1 and Method 2 show or describe a correct way to draw the angle. 2= Both methods shown or described are correct, but contain some inaccuracies. 1= Only one method is accurately described or shown. 0= No attempt was made to answer the question or both methods described or shown are inaccurate. Extended Response (4 points) Scoring Rubric: 4= The estimate written is within plus or minus 10° of 75°. The explanation contains logical deductions using real life references or using benchmark angles. The actual measurement written is 75° or plus or minus 3° from 75°. The explanation of the steps used to arrive at the actual measurement contains a correct method for measuring angles. 3= The estimate written is within plus or minus 15° of 75°, and the explanation given uses real life references or benchmark angles to arrive at the estimate. The actual measurement given is within plus or minus 7° of 75°. The explanation of the steps used contains a correct method for measuring angles. 2= The estimate written is within plus or minus 15° of 75°, but the explanation given would have been difficult to use because of some inaccuracies. The actual measurement of the angle is within plus or minus 10° of 75°, but the explanation is not clear and/or contains some inaccuracies. 1= The estimate written is more than plus or minus 15° from 75°, and the explanation is difficult to understand or not there. The actual measurement of the angle is more than plus or minus 10° from 75° and the explanation is either difficult to understand or not there. 0= No attempt was made. The CROSSROADS Project Enhancing Mathematics Education, Grades 3-5 Stark County, Ohio UNIT TEST Composite Data Record Unit Title: ______________________________________________ Grade Level : 3 4 5 Math Standard: ___________________________ Indicator Number: __________ Teacherâ€™s Name ________________________________ Building _________________________ District ________________________________________ Date of Pre-Testing ___________________ Date of Post-Testing ___________________ Number of Students Tested _____________ Number of Students Tested __________ POINTS AWARDED Pre-Test Class Average Post-Test Class Average Change (+/-) Part A (Multiple Choice) 10 points possible Part B (Multi-Step Problem Solving) 3 points possible Part C (Variant Methods) 3 points possible Part D (Extended Response) 4 points possible TOTAL Score 20 points possible Please write 1-3 paragraphs describing your experiences with this unit, what the test results suggest to you, and how you plan to use this information in your teaching practices. Attach this response along with the student test set described below to this page for submission. PAYMENT awarded with submission of: (1) this completed form, (2) paragraph(s) as described, and (3) ONE studentâ€™s pre- and post-test set. Please white-out the studentâ€™s last name to protect his/her identity. CROSSROADS Validation ________ Date __________