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Pre-AP Pre-Algebra
Shayne Lopez
HOUSTON JR HIGH
Contact Shayne Lopez

Page Last Updated Nov 01, 2009
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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

SummaryWhen 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

LaunchOpen 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