Mrs. Lopez’s Lesson Plans 7th Grade CMP Math Week of November 2 - 6, 2009 | Monday/November 2, 2009 | Objective (Student will…) | • Apply knowledge of similar triangles and similar quadrilaterals • Develop a technique for indirect measurement | Teacher Activities & Strategies | SS Problem 5.3: Finding Lengths with Similar Triangles Launch: Describe the problem to the class. Ask how it is the same and how it is different from the previous two problems. Ask the class to identify the similar triangles and the corresponding angles and sides. Explore: Monitor the students as they work in groups, using higher order questioning strategies to redirect their thinking. Be sure the groups have identified the similar triangles and correct parts to measure. | Student Activities Make Up Work! | Class Work: SS 5.3: Finding Lengths with Similar Triangles Homework: SS ACE 5.3 #5, 32 Pg. 85 | Assessment/Evaluation | Summary: When all groups have made their estimates, give each group a chance to share their work. Make a line plot showing the estimates that were found by each of the groups. Ask the class what they would give as the estimate of the distance across the pond if they can only give one number to represent the work of the class. Most will suggest that the estimates be averaged which is a good suggestion. Then ask what else they would report if they could give more information about what the class found. Here it is reasonable to give the average distance found along with the spread of the estimates. | Academic Vocabulary | KIM: None | Additional Resources | CMP Book, notebook, calculators, Labsheet 5.3 | | Tuesday/November 3, 2009 | Objective (Student will…) | • Apply knowledge of similar figures. | Teacher Activities & Strategies | Additional Practice, Pg. 31-33 Launch: Pass out student workbooks. Students will tear out pages 31-33. Give directions on the Additional Practice pages. Explore: Monitor and assist the students as they work on the practice pages. Ask questions to redirect the students as needed. | Student Activities Make Up Work! | Class Work: SS: Additional Practice, pages 31-33 Homework: Finish Additional Practice packet | Assessment/Evaluation | Summary: Will grade Additional Practice pages | Academic Vocabulary | KIM: None | Additional Resources | CMP Book, notebook, calculators, Additional Practice Workbooks | Class Name | Wednesday/November 4, 2009 | Objective (Student will…) | • Demonstrate mastery level of mathematical concepts learned in Stretching and Shrinking. | Teacher Activities & Strategies | SS Unit Test Launch: Pass out the Unit Test. Go over directions and answer any questions the students may have. Explore: Monitor the students as they complete the Unit Test | Student Activities Make Up Work! | Class Work: SS Unit Test Homework: None | Assessment/Evaluation | Summary: None | Academic Vocabulary | KIM: none | Additional Resources | CMP Book, notebook, calculators, Unit Test | Class Name | Thursday/November 5, 2009 | Objective (Student will…) | • Demonstrate master level of concepts learned in Stretching and Shrinking | Teacher Activities & Strategies | SS Unit Test, cont’d (½ day, students dismissed at 11:30) Launch: Pass out tests and answer questions as needed. Explore: Monitor the students as they complete the test. | Student Activities Make Up Work! | Class Work: SS Unit Test, cont’d Homework: None | Assessment/Evaluation | Summary: None | Academic Vocabulary | KIM: none | Additional Resources | CMP Book, notebook, calculators, Unit Test | Class Name | Friday/November 6, 2009 | Objective (Student will…) | • Define KIM vocabulary words for Stretching and Shrinking • Organize and empty CMP notebooks | Teacher Activities & Strategies | SS: KIM vocabulary/Binder Check Launch: Give directions for KIM vocabulary sheets. Students will define the vocabulary words in their own words and create a memory clue for each word. Explore: Assist the students as needed. | Student Activities Make Up Work! | Class Work: SS KIM vocabulary Homework: None | Assessment/Evaluation | Summary: Share out definitions and memory clues. | Academic Vocabulary | KIM: None | Additional Resources | CMP Book, notebook, KIM sheets |
Mrs. S. Lopez’s Lesson Plans 7th Grade CMP Math Week of October 26-30, 2009 | Monday/October 26, 2009 | Objective (Student will…) | • Use ratios of corresponding sides or scale factors to find missing lengths in similar figures | Teacher Activities & Strategies | SS Problem 4.3: Using Similarity to Find Measurements Launch: Show the students the pair of similar triangles in Question B. • Which sides are corresponding? Compare the angles. Label the angles in some way to show which ones correspond. This might help them determine the correct corresponding side lengths. • How can you find the missing side length? Then ask students for another method. Students should be able to describe how they can use either scale factors or internal ratios to find the missing side lengths. Have students work in pairs. Explore: Establishing which sides correspond may still be problematic for students. Guide students by asking questions. • Which side does this side correspond to in the other triangle? How do you know? You could also have students trace one of the triangles, cut it out and turn it to match the orientation of the other one. | Student Activities Make Up Work! | Class Work: SS Problem 4.3 Homework: SS ACE 4.3 #9-11 Pg. 68 | Assessment/Evaluation | Summary: Discuss the answers. Be sure to let different groups share their strategies, particularly for Question E. Be sure that students are using the concept of equivalent fractions to find the missing lengths. Use the Check for Understanding. | Academic Vocabulary | KIM: none | Additional Resources | CMP Book, notebook, calculators | | Tuesday/October 27, 2009 | Objective (Student will…) | • Demonstrate masterly level of concepts developed in Stretching and Shrinking, Investigations 1-4 | Teacher Activities & Strategies | SS Partner Quiz Launch: Pass out quizzes and go over the directions for the quiz. Answer any questions that the students may have Explore: Monitor the partners as they complete the Partner Quiz | Student Activities Make Up Work! | Class Work: SS Partner Quiz Homework: None J | Assessment/Evaluation | Summary: Will grade the Partner Quiz | Academic Vocabulary | KIM: none | Additional Resources | CMP Book, notebook, calculators, Partner Quiz | Class Name | Wednesday/October 28, 2009 | Objective (Student will…) | • Summarize findings of the concepts practiced in SS 4 (ratios, similarity, and missing side lengths) | Teacher Activities & Strategies | SS Mathematical Reflection 4 Launch: Instruct the students to discuss the reflection questions in their groups for 5-7 minutes. Have a whole-class share-out for 5-8 minutes Explore: Students will write their reflection. | Student Activities Make Up Work! | Class Work: SS Mathematical Reflection 4 Pg. 77 Homework: None J | Assessment/Evaluation | Summary: Will grade the mathematical reflections | Academic Vocabulary | KIM: none | Additional Resources | CMP Book, notebook, KIM vocabulary sheets | Class Name | Thursday/October 29, 2009 | Objective (Student will…) | • Apply knowledge of similar triangles. • Develop a technique for indirect measurement • Practice measuring lengths to solve problems | Teacher Activities & Strategies | SS Problem 5.1: Using Shadows to Find Heights Launch: Have students practice one or two simple missing parts problems. Talk to the students about the situation. Explain that you need to have a pretty good estimate of the height of a tower, a building, a pole, etc. but there does not seem to be any way to measure it directly. The task is to find out how you can use mathematics to make such measurements. • From your experiences, hat can you say about the shadows that the sun casts? • At the same time of day, how will the shadows of two objects that are not the same height compare? • This means that the length of the shadow depends on the height of the object. Imagine that you are looking at a tall pole when the sun casts a shadow for the pole. In your mind, move around until you are standing so that you see the pole and its shadow from the side. Sketch on your paper what you think this would look like. • Add to your sketch a line to show the triangle formed by the pole, the shadow, and the line from the top of the pole to the tip of the shadow. Continue to guide students through the set-up of the problem, being sure that they understand what is being measured, what is being compared, and how they are to use their knowledge of similar triangles. Have students work in groups of four. Have each group make their own measurements. Explore: Usually, students have so little opportunity to make actual measurements of distances larger than a desktop that some groups may need help in getting started. One of the important goals of this problem is to give students these measuring experiences, as well as experience using similarity, to solve a problem. Be prepared to assist students in their measuring. | Student Activities Make Up Work! | Class Work: SS Problem 5.1 Homework: SS ACE 5.1#1,2,6-9 Pg. 84 | Assessment/Evaluation | Summary: Discuss the variations and possible sources of error. • What is a typical unit of measure to use to tell the height of the building (or other object you choose) based on the class data? Why? • Who can describe to the class exactly how he or she used similar triangles in the work that he or she did measuring the building? • Can you always use this method to estimate the height of an object? Why or why not? | Academic Vocabulary | KIM: none | Additional Resources | CMP Book, notebook, calculators | Class Name | Friday/October 30, 2009 | Objective (Student will…) | • Apply knowledge of similar triangles • Develop a technique for indirect measurement | Teacher Activities & Strategies | SS Problem 5.2:Using Mirrors to Find Heights Launch: Explain the mirror method to students. Demonstrate the set-up in the classroom. Place the mirror on the floor of the room so that there is an unobstructed space between the mirror and the board. Have a student look into the mirror, then move either forward or backward until the top of the board is reflected in the center of the mirror. Explore: Have groups of four estimate the height of the object chosen for the problem. Each group may want to try the method more than once having a different person sight each time. This will give more than one estimate of the height of the object since different people will have different eye heights and different sighting distances. Be prepared to help students with making careful measurements. | Student Activities Make Up Work! | Class Work: SS Problem 5.2 Homework: None J | Assessment/Evaluation | Summary: Ask what would be a typical measurement for the class using the mirror method. Discuss possible sources of error. Ask what they think the best estimate of the height of the object is given the data from the two methods. You are just trying to get the students to think about factors that affect the estimates and to see that measurements are approximate and errors can be compounded through calculation with imprecise measurements. | Academic Vocabulary | KIM: | Additional Resources | CMP Book, notebook, calculators, mirrors, meter sticks |
Mrs. S. Lopez’s Lesson Plans 7th Grade CMP Math Week of October 19-23, 2009 | Monday/October 19, 2009 | Objective (Student will…) | - Use scale factors to make similar shapes.
- Find missing measures in similar figures using scale factor.
| Teacher Activities & Strategies | SS Problem 3.3: Scale Factors and Similar Shapes Launch: Display rectangle A and triangle B on the overhead. Challenge the class to make similar figures given the scale factor, area, or perimeter of the new figure. I will be sure that the students have quarter-inch grid paper. The class will work in pairs. Explore: If students are having a hard time getting started, you might ask: - If the scale factor is 2.5, what will the new side length look alike? How will it compare to the side length of the original figure?
Check to see if students are using the correct scale factor in the parts that give information about area. Look for interesting ways that students solve the problem. Be sure to call on these students during the summary. | Student Activities Make Up Work! | Classwork: SS Problem 3.3 Homework: SS ACE 3.3 #8, 15-18 Pg. 47 | Assessment/Evaluation | Summary: Be sure students explain their reasoning and methods. To find the missing lengths in Question C, students might find the scale factor using two of the known corresponding lengths. They will then use the scale factor to multiply the given length to get the unknown length. Hand out copies of Labsheet 3.3B for students to extend their understanding of similarity to other polygons. - In each set, decide which polygons are similar. Explain.
By the end of this investigation, students should have a firm understanding of the two criteria for identifying similar figures and the role of the scale factor and its relationship to length, perimeter, and area. | Academic Vocabulary | KIM: None | Additional Resources | CMP Book, Notebook, Labsheet 3.3A & B | | Tuesday/October 20, 2009 | Objective (Student will…) | • Demonstrate mastery level of concepts learned in SS 3 | Teacher Activities & Strategies | SS Check Up 2 Launch: Pass out the Check-Up and give the directions for completing the quiz. Answer any questions that the students may have. Explore: Monitor the students as they complete the Check-Up. | Student Activities Make Up Work! | Class Work: SS Check-Up 2 Homework: None J | Assessment/Evaluation | Summary: Will grade the Check-Up | Academic Vocabulary | KIM: None | Additional Resources | CMP Book, Notebook | | Wednesday/October 21, 2009 | Objective (Student will…) | • Summarize what makes two polygons similar • Explain how to find scale factor and what the perimeter and area relationships are. | Teacher Activities & Strategies | SS Mathematical Reflections 3 Pg. 57 Launch: Have the students write a rough draft to organize their thoughts. 15 minutes. Have a group discussion at their tables to share what they have learned. 5-8 minutes. Open the discussion to the whole class, allowing students to share with other groups. 5-8 minutes Explore: The students will write a final draft of the Mathematical Reflection (page 57) | Student Activities Make Up Work! | Class Work: SS Mathematical Reflections 3 Pg. 57 Homework: None J | Assessment/Evaluation | Summary: Will grade the mathematical reflection using the NM Rubric for Open-Ended Questions | Academic Vocabulary | KIM: None | Additional Resources | CMP Book, Notebook | | Thursday/October 22, 2009 | Objective (Student will…) | • Use ratios of corresponding sides within a figure to determine whether two figures are similar | Teacher Activities & Strategies | SS Problem 4.1: Ratios Within Similar Parallelograms Launch: Open flipchart of a girl and its images. Let the class create the images were found on page 59. • If we think of these girls as we did the Wumps, which ones would be in the same family? How do you know? • Are these similar figures? • These figures don’t have straight sides to measure like the Wumps did. What can we measure? After you have discussed these questions, put up a chart with the measurements for the original figure and the three images. • What patterns do you notice about these measures? Fill in the last column with the ratio written in fraction form. Tell the class that, just as we talk about equivalent fractions, we can talk about equivalent ratios. Have students solve a couple of simple ratio problems to get started. • A new figure is created that is similar to the original girl. The height of the girl in this figure is 15 cm. What is her width? • How could you use ratios to find the width of the girl in the figure? Let students work in pairs. Explore: As you move around check to make sure that students are writing correct ratios and provide any necessary help in keeping track of the place of corresponding measures in the ratios. | Student Activities Make Up Work! | Class Work: SS Problem 4.1: Homework: SS ACE 4.1: #3, 4 Pg. 67 | Assessment/Evaluation | Summary: Discuss the answers. Discuss the relationship between these internal ratios and the scale factor. Be sure that students compare the ratios of corresponding side lengths in similar figures. Review or assess their understanding of equivalent fractions. If your class is ready, you might ask about the ratios of the height of the original to the height of the similar figure and the width of the original to the width of the similar figure. These ratios give the scale factor from the smaller figure to the larger figure. Use this summary to lead into the next problem, which is identical to this problem except it uses triangles. You might want to assign this as homework and discuss it in class the next day. Use the Check for Understanding. | Academic Vocabulary | KIM: ratios, equivalent ratios | Additional Resources | CMP Book, Notebook | | Friday/October 23, 2009 | Objective (Student will…) | • Use ratios to identify similar triangles | Teacher Activities & Strategies | SS Problem 4.2: Ratios Within Similar Triangles Launch: Tell the class that this problem is similar to the last problem. They are to identify which triangles are similar and then use the ratios of corresponding lengths to find missing side lengths. Remind students that they also need to check that corresponding angles are congruent. Explore: Look for ways that students are forming the ratios. Continue to ask students questions that force them to be clear about what is being compared in each ratio. You might challenge students to find the ratios of corresponding lengths across two similar figures and ask, • What information does this ratio give for two similar figures? | Student Activities Make Up Work! | Class Work: SS Problem 4.2 Homework: SS ACE 4: #2 Pg. 66 | Assessment/Evaluation | Summary: Discuss answers. Help students to understand that the order they choose to compare (e.g. height : width vs width : height) doesn’t matter, as long as the comparisons are consistent. • Does it make a difference if we write instead of ? Pick a pair of similar triangles and ask students to sketch two more triangles that are similar to them, including side lengths. Have them check the ratios of the side lengths. Use the Check for Understanding. | Academic Vocabulary | KIM: None | Additional Resources | CMP Book, Notebook |
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