Unit 1

Triangle Similarity

Unit 1: Triangle SimilarityDay (60 min period)

CPM Section

CPM Classwork Problems

Vocabulary of the day Instructional Tool

1 2.1.1 2-1 through 2-4 CongruentSSSSASASAAASHL

Vocabulary Visionary

2 2.1.2 2-12 through 2-15 FlowchartReflexive PropertyTransitive Property

Reading RegulatorVocabulary Visionary

3 2.1.3 2-23 through 2-25 Conditional StatementHypothesisConclusionConverseCounterexampleExterior AngleRemote Interior Angles

Dictation Dictator Vocabulary Visionary

4 2.2.1 2-46 through 2-48 DilationSimilarPoint/Center of Dilation

Reading Regulator Vocabulary Visionary

5 2.2.2 2-57 through 2-59 Scale FactorProportion

Word Problem WarriorVocabulary Visionary

6 2.3.1 2-68 through 2-74 AA~SAS~SSS~

Dictation DictatorVocabulary Visionary

7 2.3.2 2-90 through 2-93 Reading Regulator

8 2.3.3 2-100 through 2-102 Word Problem Warrior

9 2.3.4 2-109 through 2-112 Side Splitter Theorem Vocabulary Visionary

10 End of Unit 1 Three-Part Formative Assessment

Unit 1 Day 1CPM Section: 2.1.1

CCSS Math Standard:G-SRT. 5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

ELD Standard:Collaborative ELD Standard 1, Exchanging information and ideas – Bridging Level: Contribute to class, group, and partner discussion by listening attentively, and asking as well as answering questions.

Objective:Students will be able to collaborate with peers in order to use congruence and similarity properties to solve problems as well as prove geometric properties.

Math Practice Standard:CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Materials:-Core Connections Integrated II CPM textbook-See CPM Teacher Notes-6 Vocabulary Visionary per student (refer to template)

Vocabulary Words:Congruent, SSS, SSS, SAS, ASA, AAS, HL

Length:One 60 minute class

Steps: Minutes:

Before class, teacher will write the day’s objective on the board.At the start of class, teacher will choose one student to read the objective from the board.Teacher will choose a second student to read the lesson intro (from CPM text).

2 minutes

Students will work with their table group to complete the following problems from the textbook in their composition books:2-1 through 2-4While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

40 minutes

Teacher will instruct two students from every table to rotate to a different table. The pairs will share their results for problem 2-4 with each other, justifying their steps, and clarifying any misconceptions.

10 minutes

When students complete the above activity, they should begin working on the Vocabulary Visionary graphic organizers in order to solidify their understanding of new vocabulary. All unfinished Vocabulary Visionary graphic organizers will be completed as homework.

8 minutes

Unit 1 Day 2CPM Section: 2.1.2

CCSS Math Standard:G-SRT. 5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

ELD Standard:Interpretive ELD Standard 6a, Reading closely - Bridging Level: Explain ideas, and relationships within texts based on close reading of a variety of grade-level texts using a detailed and accurate diagram of the scenario including precise labels as well as units.

Objective:Students will be able to read a math word problem and explain their ideas through an accurate diagram in order to solve problems as well as prove geometric properties.

Math Practice Standard:CCSS.MATH.PRACTICE.MP6 Attend to precision.

Materials:-Core Connections Integrated II CPM textbook-See CPM Teacher Notes-1 Reading Regulator per student-3 Vocabulary Visionary per student (refer to template)

Vocabulary Words:FlowchartReflexive PropertyTransitive Property

Length:One 60 minute class

Steps: Minutes:

Before class, teacher will write the day’s objective on the board.At the start of class, teacher will choose one student to read the objective from the board.Teacher will choose a second student to read the lesson intro (from CPM text).

2 minutes

Students will work with their table group to complete the following problems from the textbook in their composition books:2-12 through 2-15While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

40 minutes

Teacher will pass out the Reading Regulator.Students will complete independently and turn in when complete.

10 minutes

When students complete the above activity, they should begin working on the Vocabulary Visionary graphic organizers in order to solidify their understanding of new vocabulary. All unfinished Vocabulary Visionary graphic organizers will be completed as homework.

8 minutes

Reading Regulator Name: ______________________________________Read the word problem below and respond to the prompts. You DO NOT need to solve.Unit 1 Day 2 Section 2.1 (2.1.2)Last Saturday Michelle, Anahi, and Eli were on the field playing soccer at 11:30am. The three of them were in non-collinear positions. The distance between Michelle and Eli is 12 meters. The distance between Anahi and both her friends is 7 meters. What is the angle between Michelle and Anahi from where Eli is standing? Provide a detailed sketch of the scenario.Be sure to label important information. Is there unnecessary information? How do you know?

What are you trying to find, include units? (In your own words.)

On a scale of 1 to 5, how confident do you feel about your comprehension of this word problem? (Circle one).1 2 3 4 5 Not at all Somewhat confident Very confidentYou will be graded on the following rubric. Self-assess your work by circling one of the descriptions.Category 4 3 2 16a Reading closely

Students read mathematical scenario and provide an accurate diagram representation with precise labels and units.

Students read mathematical scenario and provide an accurate diagram representation with incomplete labels and units.

Students read mathematical scenario and provide a slightly inaccurate (1-2 errors) diagram representation with incomplete labels and units.

Students read mathematical scenario and provide an inaccurate (more than 2 errors) diagram representation with incomplete labels and units.

ELD Standard:Interpretive ELD Standard 6a Reading closely - Bridging Level: Explain ideas, and relationships within texts based on close reading of a variety of grade-level texts using a detailed and accurate diagram of the scenario including precise labels as well as units.

Unit 1 Day 3CPM Section: 2.1.3

CCSS Math Standard:G-CO. 9 - Prove theorems about lines and angles.

ELD Standard:Productive ELD Standard 12a, Selecting language resources: Use a variety of grade-appropriate general and domain-specific academic words and phrases, accurately and appropriately when producing complex written and spoken texts.

Objective:Students will be able to select appropriate mathematical vocabulary in order to describe proportions of similar figures as well as communicate about mathematics theorems and properties effectively.

Math Practice Standard:CCSS.MATH.PRACTICE.MP6 Attend to precision.

Materials:-Core Connections Integrated II CPM textbook-See CPM Teacher Notes-Dictation problems sheet, print one sheet per four students and cut apart-1 Dictation Dictator per student (refer to template)-7 Vocabulary Visionary per student (refer to template)

Vocabulary Words:Conditional Statement, Hypothesis, Conclusion, Converse, Counterexample, Exterior Angle, Remote Interior Angles

Length:One 60 minute class

Steps: Minutes:

Before class, teacher will write the day’s objective on the board.At the start of class, teacher will choose one student to read the objective from the board.Teacher will choose a second student to read the lesson intro (from CPM text).

2 minutes

Students will work with their table group to complete the following problems from the textbook in their composition books:2-23 through 2-25While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

35 minutes

Teacher will pass out the Dictation Dictator.Students will work in pairs to complete the activity.

15 minutes

When students complete the above activity, they should begin working on the Vocabulary Visionary graphic organizers in order to solidify their understanding of new vocabulary. All unfinished Vocabulary Visionary graphic organizers will be completed as homework.

8 minutes

Unit 1 Day 3 - Section 2.1.1-2.1.3

Dictation #1 Dictation #2 Dictation #3

Student A

Dictation #1 Dictation #2 Dictation #3

Student B

Dictation #1 Dictation #2 Dictation #3

Student C

Dictation #1 Dictation #2 Dictation #3

Student D

Unit 1 Day 4CPM Section: 2.2.1

CCSS Math Standard:G-SRT.1a - A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.G-SRT. 1b - The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

ELD Standard:Interpretive ELD Standard 6a, Reading closely - Bridging Level: Explain ideas, and relationships within texts based on close reading of a variety of grade-level texts using a detailed and accurate diagram of the scenario including precise labels as well as units.

Objective:Students will be able to read a math word problem and explain their ideas through an accurate diagram in order to solve problems as well as prove geometric properties.

Math Practice Standard:CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

Materials:-Core Connections Integrated II CPM textbook-See CPM Teacher Notes-1 Reading Regulator per student-3 Vocabulary Visionary per student (refer to template)

Vocabulary Words:DilationSimilarPoint/Center of Dilation

Length:One 60 minute class

Steps: Minutes:

Before class, teacher will write the day’s objective on the board.At the start of class, teacher will choose one student to read the objective from the board.Teacher will choose a second student to read the lesson intro (from CPM text).

2 minutes

Students will work with their table group to complete the following problems from the textbook in their composition books:2-46 through 2-48While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

40 minutes

Teacher will pass out the Reading Regulator.Students will complete independently and turn in when complete.

10 minutes

When students complete the above activity, they should begin working on the Vocabulary Visionary graphic organizers in order to solidify their understanding of new vocabulary. All unfinished Vocabulary Visionary graphic organizers will be completed as homework.

8 minutes

Reading Regulator Name: ______________________________________Read the word problem below and respond to the prompts. You DO NOT need to solve.Unit 1 Day 4 Section 2.2 (2.2.1)Sarah is a talented artist. Her fans call her art “modern” because she loves to use lines, angles, and geometric shapes in her art. She is currently sketching a picture of a brick house. The base of the roof and the ground are parallel. She wants a diagonal line to connect from the top-left corner of the house to the bottom-right corner of the house. It takes Sarah 30 minutes to complete each square inch of her sketch. If the angle of depression from the roof to the diagonal is 46 degrees, what will be the angle between the diagonal and the ground?Provide a detailed sketch of the scenario.Be sure to label important information. Is there unnecessary information? How do you know?

What are you trying to find, include units? (In your own words.)

On a scale of 1 to 5, how confident do you feel about your comprehension of this word problem? (Circle one).1 2 3 4 5 Not at all Somewhat confident Very confidentYou will be graded on the following rubric. Self-assess your work by circling one of the descriptions.Category 4 3 2 16a Reading closely

Students read mathematical scenario and provide an accurate diagram representation with precise labels and units.

Students read mathematical scenario and provide an accurate diagram representation with incomplete labels and units.

Students read mathematical scenario and provide a slightly inaccurate (1-2 errors) diagram representation with incomplete labels and units.

Students read mathematical scenario and provide an inaccurate (more than 2 errors) diagram representation with incomplete labels and units.ELD Standard:

Interpretive ELD Standard 6a Reading closely - Bridging Level: Explain ideas, and relationships within texts based on close reading of a variety of grade-level texts using a detailed and accurate diagram of the scenario including precise labels as well as units.

Unit 1 Day 5CPM Section: 2.2.2

CCSS Math Standard:G-SRT.1a - A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.G-SRT. 1b - The dilation of a line segment is longer or shorter in the ratio given by the scale factor.G-SRT. 2 - Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

ELD Standard:Productive ELD Standard 10b, Writing- Bridging Level: Write clear and coherent summaries of text and experiences by using complete and concise sentences and keywords.

Objective:Students will be able to write a clear and coherent summary using complete and concise sentences utilizing mathematical vocabulary in order to prove geometric properties and solve geometric problems.

Math Practice Standard:CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

Materials:-Core Connections Integrated II CPM textbook-See CPM Teacher Notes-1 pre-made Word Problem Warrior per student (attached)-2 Vocabulary Visionary per student (refer to template)

Vocabulary Words:Scale factorProportion

Length:One 60 minute class

Steps: Minutes:

Before class, teacher will write the day’s objective on the board.At the start of class, teacher will choose one student to read the objective from the board.Teacher will choose a second student to read the lesson intro (from CPM text).

2 minutes

Students will work with their table group to complete the following problems from the textbook in their composition books:2-57 through 2-59While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

35 minutes

This is the first day students will see the Word Problem Warrior.Teacher will model the use of the Word Problem Warrior graphic organizer (using the attached template) while students follow along and complete the Word Problem Warrior.

15 minutes

When students complete the above activity, they should begin working on the Vocabulary Visionary graphic organizers in order to solidify their understanding of new vocabulary. All unfinished Vocabulary Visionary graphic organizers will be completed as homework.

8 minutes

Word Problem Warrior Name:

____________________________________

Check each box after you have completed the step.

❏ I read the problem once to get the big picture.

❏ I read the problem again for understanding.

❏ I identified words I do not know / words that confuse me, and I have looked them up and defined them below.

❏ I identified what I know about this scenario in complete sentences.

❏ I identified what I want to know about this scenario in complete sentences.

❏ I read the problem again. Have I left anything out?

❏ I have created a detailed, labeled sketch of the scenario.

Taty, Lily and Aly are playing catch and their positions in the grass form a triangle. Taty is 17 ft from Lily and 6 ft from Aly. Lily is 13 ft from Aly. They are enjoying playing catch, but decide to make it more challenging so they spread out more. They each backed away slowly and their new positions created a similar triangle to the original. The new distance from Taty and Lily is 25 ft. What is the dilation factor? What is the new distance between Aly and Taty? What is the new distance between Aly and Lily?

❏ The following mathematical formulas/functions/equations may be useful:

❏ I can translate the word problem into the following equation(s):

❏ I have solved the problem mathematically.

❏ I read the problem again and I know that I have solved the problem.

❏ What does my answer mean? Does my answer make sense? Justify. Be specific.

Unit 1 Day 6CPM Section: 2.3.1

CCSS Math Standard:G-SRT. 2 - Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.G-SRT. 3 - Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.G-SRT. 5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

ELD Standard:Productive ELD Standard 12a, Selecting language resources: Use a variety of grade-appropriate general and domain-specific academic words and phrases, accurately and appropriately when producing complex written and spoken texts.

Objective:Students will be able to select appropriate mathematical vocabulary in order to describe proportions of similar figures as well as communicate about mathematics theorems and properties effectively.

Math Practice Standard:CCSS.MATH.PRACTICE.MP6 Attend to precision.

Materials:-Core Connections Integrated II CPM textbook-See CPM Teacher Notes-Dictation problems sheet, print one sheet per four students and cut apart-1 Dictation Dictator per student (refer to template)-3 Vocabulary Visionary per student (refer to template)

Vocabulary Words:AA ~SAS ~SSS ~

Length:One 60 minute class

Steps: Minutes:

Before class, teacher will write the day’s objective on the board.At the start of class, teacher will choose one student to read the objective from the board.Teacher will choose a second student to read the lesson intro (from CPM text).

2 minutes

Students will work with their table group to complete the following problems from the textbook in their composition books:2-68 through 2-74While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

40 minutes

Teacher will pass out the Dictation Dictator.Students will work in pairs to complete the activity.

10 minutes

When students complete the above activity, they should begin working on the Vocabulary Visionary graphic organizers in order to solidify their understanding of new vocabulary. All unfinished Vocabulary Visionary

8 minutes

graphic organizers will be completed as homework.

Unit 1 Day 6 - Section 2.2.1-2.3.1

Dictation #1 Dictation #2 Dictation #3

Student A3x3 y−8 xy+5

4 y2AB=3.5 A ' B 'BC=3.5 B 'C 'm<A≅m<A '

“x is ¿9as x+2 is¿36.

Dictation #1 Dictation #2 Dictation #3

Student B15(4 xy−9 y4+ 3

8)

2 XY=X ' Y '2YZ=Y ' Z '

Y ' Z '=4Y ' ' Z ' '“AC is¿XZ as BC is¿YZ .

Dictation #1 Dictation #2 Dictation #3

Student C (4 xy−9+3x )( y2−2 xyz)B' A '=3 B ' ' A ' 'C ' A '=3C ' ' A ' 'm<C ' ≅ m<C ' '

“DOis ¿ LV as4 is¿16.

Dictation #1 Dictation #2 Dictation #3

Student D −4 x ( y z4−19 x )−18 xy2

XY5

=X ' Y '

m<Y ≅m<Y 'm<Z ' ≅m<Z ' '

“18 is¿mas6 is ¿4m.

Unit 1 Day 7CPM Section: 2.3.2

CCSS Math Standard:G-SRT. 5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

ELD Standard:Interpretive ELD Standard 6a, Reading closely - Bridging Level: Explain ideas, and relationships within texts based on close reading of a variety of grade-level texts using a detailed and accurate diagram of the scenario including precise labels as well as units.

Objective:Students will be able to read a math word problem and explain their ideas through an accurate diagram in order to solve problems as well as prove geometric properties.

Math Practice Standard:CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

Materials:-Core Connections Integrated II CPM textbook-See CPM Teacher Notes-1 Reading Regulator per student

Vocabulary Words:none

Length:One 60 minute class

Steps: Minutes:

Before class, teacher will write the day’s objective on the board.At the start of class, teacher will choose one student to read the objective from the board.Teacher will choose a second student to read the lesson intro (from CPM text).

2 minutes

Students will work with their table group to complete the following problems from the textbook in their composition books:2-90 through 2-93While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

40 minutes

Teacher will pass out the Reading Regulator.Students will complete independently and turn in when complete.

10 minutes

Teacher will lead a class discussion based on the “Math Notes” provided in the text. The “Math Notes” further explain triangle similarity conditions.

8 minutes

Reading Regulator Name: ______________________________________Read the word problem below and respond to the prompts. You DO NOT need to solve.Unit 1 Day 7 Section 2.3 (2.3.2)Roberto, a 6-foot tall senior, just spotted a rare lizard sleeping on the ground in his backyard. He wants to take a selfie with it to show his followers. He extends his arms and takes the photo. Unfortunately, when he looks at the photo he notices that the top of his head blocked the exact location of the lizard! He was standing 5 feet from the lizard and held his phone 7 feet above the ground. What is the horizontal distance between Roberto and his phone in inches?Provide a detailed sketch of the scenario.Be sure to label important information. Is there unnecessary information? How do you know?

What are you trying to find, include units? (In your own words.)

On a scale of 1 to 5, how confident do you feel about your comprehension of this word problem? (Circle one).1 2 3 4 5 Not at all Somewhat confident Very confidentYou will be graded on the following rubric. Self-assess your work by circling one of the descriptions.Category 4 3 2 16a Reading closely

Students read mathematical scenario and provide an accurate diagram representation with precise labels and units.

Students read mathematical scenario and provide an accurate diagram representation with incomplete labels and units.

Students read mathematical scenario and provide a slightly inaccurate (1-2 errors) diagram representation with incomplete labels and units.

Students read mathematical scenario and provide an inaccurate (more than 2 errors) diagram representation with incomplete labels and units.

ELD Standard:Interpretive ELD Standard 6a Reading closely - Bridging Level: Explain ideas, and relationships within texts based on close reading of a variety of grade-level texts using a detailed and accurate diagram of the scenario including precise labels as well as units.

Unit 1 Day 8CPM Section: 2.3.3

CCSS Math Standard:G-SRT. 5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

ELD Standard:Productive ELD Standard 10b, Writing- Bridging Level: Write clear and coherent summaries of text and experiences by using complete and concise sentences and keywords.

Objective:Students will be able to write a clear and coherent summary using complete and concise sentences utilizing mathematical vocabulary in order to prove geometric properties and solve geometric problems.

Math Practice Standard:CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

Materials:-Core Connections Integrated II CPM textbook-See CPM Teacher Notes-3 Word Problem Warrior per student (refer to template)

Vocabulary Words:none

Length:One 60 minute class

Steps: Minutes:

Before class, teacher will write the day’s objective on the board.At the start of class, teacher will choose one student to read the objective from the board.Teacher will choose a second student to read the lesson intro (from CPM text).

2 minutes

Students will be provided with one Word Problem Warrior to be used to solve problem 2-100.While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

15 minutes

Teacher will model the completion of Word Problem Warrior for 2-100.

8 minutes

Students will be provided with two Word Problem Warriors to be used to solve problem 2-101 and 2-102.While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

35 minutes

Unit 1 Day 9CPM Section: 2.3.4

CCSS Math Standard:G-SRT. 3 - Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.G-SRT. 4 - Prove theorems about triangles.G-SRT. 5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

ELD Standard:Collaborative ELD Standard 1, Exchanging information and ideas – Bridging Level: Contribute to class, group, and partner discussion by listening attentively, and asking as well as answering questions.

Objective:Students will be able to collaborate with peers in order to use congruence and similarity properties to solve problems as well as prove geometric properties.

Math Practice Standard:CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

Materials:-Core Connections Integrated II CPM textbook-See CPM Teacher Notes-1 Vocabulary Visionary per student (refer to template)

Vocabulary Words:Side Splitter Theorem

Length:One 60 minute class

Steps: Minutes:

Before class, teacher will write the day’s objective on the board.At the start of class, teacher will choose one student to read the objective from the board.Teacher will choose a second student to read the lesson intro (from CPM text).

2 minutes

Students will work with their table group to complete the following problems from the textbook in their composition books:2-109 through 2-112While students are working on the problems above, teacher will circulate the class and facilitate. Teacher will informally check for understanding by observing and asking questions while students are working.

40 minutes

Teacher will instruct two students from every table to rotate to a different table. The pairs will share their results for problems 2-109 through 2-112 with each other, justifying their steps, and clarifying any misconceptions.

13 minutes

When students complete the above activity, they should begin working on the Vocabulary Visionary graphic organizers in order to solidify their understanding of new vocabulary. All unfinished Vocabulary Visionary graphic organizers will be completed as homework.

5 minutes

Unit 1 Day 10Formative Assessment

CCSS Math Standard:G-SRT. 5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

ELD Standard:Productive ELD Standard 10b, Writing- Bridging Level: Write clear and coherent summaries of text and experiences by using complete and concise sentences and keywords.

Objective:Students will be able to write a clear and coherent summary using complete and concise sentences utilizing mathematical vocabulary in order to prove geometric properties and solve geometric problems.

Math Practice Standard:CCSS.MATH.PRACTICE.MP4 Model with mathematics.

Materials:- Unit 1 Formative Assessment Parts 1, 2 and 3- 1 meter stick per pair- Chromebooks

Vocabulary Words:none

Length:One 60 minute class

Steps: Minutes:

Teacher will inform students that their exam will be three parts. The first part will be individual where they will solve a word problem. The second part will be an extension of the first part that they can solve with their elbow partner. The third part will be an application problem where they will have to determine the height of an object with their table group around the campus such as light poles, flagpole, or tall signs. Teacher passes out the first part of the exam.

4 minutes

Students work on the first part of the exam for 16 minutes. When time is up teacher collects exams and passes out the second part of the exam, which is completed within pairs. Teacher gives students 9 minutes to complete the second part.

16 minutes

Students work on the second part of the exam in pairs for 9 minutes. When time is up teacher collects the second part from every student. Teacher passes out the third part of the exam. Students are allowed to go around the main quad to determine the height of an object. Teacher provides students with 21 minutes.

9 minutes

Students walk around the main quad and choose an object they want to find the height of. Students work with their table group to determine the height of the object using similar triangles. Teacher brings students back together and go back to the classroom.

21 minutes

Teacher has students share results of objects they found the height of. Students analyze whether the answers make sense or seem inaccurate. Teacher collects the third part of the exam.

10 minutes

On Your Own Assessment #1

What can I do with similar triangles?Four summers ago, I visited Cancun, Mexico with Mrs. Ayala. We took a photo in front of the famous Mayan ruins named Chichen Itza.We were trying to take a photo in front of the ruins, but the photographer kept taking the photo in such a way that the top of my head exactly blocked the top of the pyramid!Although I was disappointed with the picture, I thought that I might be able to estimate the height of the pyramid using the photo. Since the photographer took the picture while kneeling, the camera was only 2.49 feet above the ground.In addition, the photographer was standing 10 feet away. My horizontal distance to the center of the tower was 270 feet. Lastly, I am 5.9 feet tall.

a) Sketch a diagram to represent the scenario and locate as many triangles as you can. Can you identify any triangles that must be similar? If so, explain how you know they are similar.

b) Use similar triangles to determine the height of Chichen Itza.

c) Research the actual height of Chichen Itza. If your result was close but not exact, why might that be?

d) In at least five sentences, describe how similar triangles can be used to find the height of an object. Be sure to describe what information is necessary for solving.

Your Own Application with a Partner: Assessment #2

Applications of Similar Triangles!With your partner look up any tall, existing structure, like Chichen Itza, and fill in the blanks. Use one chromebook to find the height of the structure. Make sure you include units.

You were standing in front of _________________________________ (any tall, existing

structure), which is ____________ feet tall. Your friend ________________(name) is 5 feet

away from you and you are _______ feet tall (round to the nearest .25 feet). Your friend took a

picture while holding their phone 3 feet from the ground. The top of your head exactly covered

the top of the structure.

With your partner draw a detailed diagram of the scenario and answer the following question:How far away from the building were you standing when the photo was taken?

Real World Application with a Group: Assessment #3

Finding the Height of an Object Around Vista HighHow tall is ___________________________________________________ in the main Quad?

Select a tall object in the main Quad. Choose one person to stand in front of the object (Person X), another to take the photo, and the remaining team members will measure distances.Your team must gather the following information:-Height of Person X-Distance from the object-Distance from the photographer to Person X-The height above the ground that the camera must be in order for Person X’s head to perfectly block the top of the objecta) Draw a diagram to represent the scenario. Label all known lengths and sketch any triangles.

b) Show all calculations needed to find the height of the object.

c) In at least five sentences, respond to the following: How has your knowledge of similar triangles grown/evolved since the beginning of the unit? What insights would you provide to someone just learning about similar triangles?

Unit 1 Word Wall Vocabulary

The following vocabulary words are for the classroom Word Wall. The words are for Unit 1: Triangle Similarity. Refer to each day’s lesson plan to determine which words students learn on specific days. Refer to instructions for implementation.

CongruentSSS ≅

SAS ≅ASA ≅

AAS ≅HL ≅

FlowchartReflexive Property

Transitive Property

Conditional Statement

HypothesisConclusion

ConverseCounterexample

Exterior Angle

Remote Interior Angles

DilationSimilar

Point/Center of DilationScale Factor

ProportionAA ~

SAS ~SSS ~

Side Splitter Theorem

This page intentionally left blank. This concludes Chapter 1 vocabulary.