## Below you will find an example of a complete unit plan...

**UNIT AUTHOR:**Janine Renner

**UNIT TOPIC:**Chapter 3: Parallel and Perpendicular Lines

1. UNIT CONTEXT

**Subject/Content Area :**Mathematics

**Course :**Geometry

**Grade Level:**9th -12th

**Length of Unit:**This unit will span 11 days. The schedule at San Pasqual High School varies. Monday and Friday are 57 min periods 1-6. Tuesday and Wednesday are 120 minute block days with periods 1, 3, and 5 on Tuesday and periods 2, 4, and 6 on Wednesday. Thursday is a short day with 47 min periods 1-6. I co-teach periods 1 and 6 Tuesday through Friday, and my Cooperating Teacher teaches on Mondays. Here is an outline of the Unit schedule:

1. Tuesday/Wednesday, October 21/22- 3.1 Lines and Angles

*Period 1/Period 6 - 120 minutes (Me)*

2. Thursday, October 23 – 3.2 Angles Formed by

*Period 1/Period 6 – 47 minutes (Me)*

3. Friday, October 24 – 3.3 Proving Lines Parallel

*Period 1/Period 6 – 57 minutes (Me)*

4. Monday, October 27 – Constructions

*Period 1/Period 6 – 57 minutes (CT)*

*5. Tuesday/Wednesday, October 28/29 – 3.5 Slopes of Lines*

*Period1/Period 6 – 120 minutes (Me)*

6. Thursday, October 30 – More 3.5

*Period 1/Period 6 – 47 minutes*

*7. Friday, October 31 – Chapter 3 Quiz*

*Period1/ Period 6 – 57 minutes (CT/Me)*

8. Monday, November 3 – 3.6 Lines in the Coordinate Plane

*Period 1/Period 6 – 57 minutes (CT)*

9. Tuesday/Wednesday, November 4/5 - Chapter 3 review

*Period1/Period 6 – 120 minutes (Me)*

10. Thursday, November 6 – Chapter 3 Group test

*Period1/Period 6 – 47 minutes (CT/Me)*

11. Friday, November 7 – Chapter 3 individual test

*Period 1/Period 6 – 57 minutes (CT/Me)*

2. FACTS ABOUT THE LEARNERS

**Period 1:**

· Number of students in class: 31

· Demographic Information:

o 18 girls, 13 boys

o Majority are Hispanic students

o 2 EL’s, 7 RFEP

o 1 504 Plan, 1 student with ADD

Developmental Needs: This class completes their work faster than the other periods. There is a lot of participation in class discussion, most of the students stay on task while doing their work and they work well in groups. A lot of the students participate on campus such as on sports teams, ASB or AVID. There is one group in particular of about 4 students that are high performing and need to be given extra work and responsibilities. There are also a couple ELs, one specifically that has only been in the U.S. for 1 year and is a CELDT level 1. One student strikes me as high risk.

Period 6:

· Number of students in class: 37

· Demographic Information:

o 25 girls, 22 boys

o Majority are Hispanic students

o 2 EL’s, 17 RFEP

o 2 SPED

Developmental Needs: This class is a little more reluctant to participate than period 1. They need a little more urging to participate in class discussions. When we do group work, some groups just sit there not talking until I come over and encourage more participation. This class seems more distracted with social issues and not as lively as period 1, which may be because it is the last period of the day. There are a couple students, that are continually drawing Anime or reading during class time and need to be consistently reminded to stay on the geometry task at hand. But overall, they work well in groups and they know how to stay on task during class time.

**2. Unit Rationale: Enduring Understandings & Essential Questions**

Every unit in Mathematics builds on knowledge from the previous units so it is easy to see how this unit fits into the semester. The students are continuing to understand mathematical theorems and use them in proving geometric proofs. Geometric proofs are important because it requires that students give justification for each step of their mathematical thinking. If students can do this, deeper understanding exists. This chapter will focus on parallel lines, transversals and perpendicular lines. This knowledge will aid student understanding in the next chapter that covers triangle congruence.

We will also be making connections of geometry to life outside the classroom by finding real life examples of geometry vocabulary as well as working extensively with real life word problems, graphing their geometric information, and interpreting their slopes with real life descriptions.

**Enduring Understandings (EU)**

**Students will understand the relationship between all the angles formed by parallel lines cut by a transversal, as well as identify if two lines are parallel, perpendicular or neither by analyzing their slopes. They will continue to justify mathematics in more complex geometric proofs.**

**Essential Questions**

Where do we see geometry outside of the classroom?

What is the relationship between two lines if they are parallel and if they are perpendicular? What do their slopes represent in real life?

**3. STANDARDS**Content & Common Core Standards

**You can see these standards addressed on specific days on the Unit Calendar given below.**

Common Core: G-GO. Prove Geometric Theorems 9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent, and corresponding angles are congruent.

CA Standard: 7.0 Students prove and use theorems involving properties of parallel lines cut by transversal, the properties of quadrilaterals, and the properties of circles.

Common Core: G-GPE Use coordinates to prove simple geometric theorems algebraically. 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

CA Standard 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point of the line.

Common Core G-CO Make geometric constructions. 12. Make formal geometric constructions with a variety of tools and methods.

CA Standard: 2.0 Students write geometric proofs, including proofs by contradiction.

**ELD Standards**

ELD Standard: C. Productive 9. Presenting (Expanding) Plan and deliver a variety of oral presentations and reports on grade appropriate topics that present evidence and facts to support ideas using growing understanding of register

ELD Standard: A. Collaborative (Expanding) Contribute to class, group and partner discussions, sustaining conversations on a variety of age and grade appropriate academic topics by following turn-taking rules, asking and answering relevant, on-topic questions, affirming others, providing additional, relevant information and paraphrasing key ideas.

ELD Standard: C Productive 11. Justifying/arguing (Expanding) a) Justify opinions and positions or persuade others by making connections between ideas and articulation relevant textual evidence or background knowledge.

**4. UNIT OBJECTIVES**

1. Language: After finding examples of new geometry vocabulary words on campus, students will be able to define 9 new vocabulary words and restate the definition with a picture in an oral presentation on the Show Me app, ELD Standard: C. Productive 9. Presenting (Expanding).

2. Cognitive: After working with exploration word problems in groups, students will be able to determine the slope criteria for parallel and perpendicular lines and use them to solve geometric problems and then present their mathematical justification with a poster project, Common Core: G-GPE

3. Cognitive: After several days of notes and activities, students will be able to prove theorems about lines and angles including parallel lines cut by transversals and prove geometric proofs by taking a test, Common Core: G-GO. Prove Geometric Theorems 9, CA Standard: 7.0, CA Standard: 2.0

**5. ASSESSMENT PLAN**Have an assessment for every objective and standard in unit. Cross-reference the objective and standard for each assessment. Example: Assessment (Objective/Standard #)

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**Name of Assessment -**Show Me App presentations (Objective 1)

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**Formality:**informal, this will just be used to ensure participation by all students and to assess learning.

·

**Purpose:**formative

·

**Implementation Method:**This is a performance assessment. Students will create a presentation that demonstrates their understanding of 9 new vocabulary words.

·

**Communication of Expectations:**I modeled an example of 1 slide in their presentation and then put the expectations of the presentation on the board.

·

**Evaluation Criteria:**Students are evaluated for participation. This is a tool for the teacher to assess if the students understand the new vocabulary words we will be using for the rest of the chapter.

·

**Feedback Strategies:**Students will be given feedback from their peers.

·

**Student Self-Assessments:**None

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**Name of Assessment –**Ticket out the Door (Objective 2)

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**Formality:**Informal

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**Purpose:**summative for the section.

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**Implementation Method:**written

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**Communication of Expectations:**None

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**Evaluation Criteria:**Rubric Provided

·

**Feedback Strategies :**I will hand back rubric with comments.

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**Student Self-Assessments:**None

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**Name of Assessment –**Homework Problem from 3.5 (Objective 2)

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**Formality:**Informal

·

**Purpose:**Formative

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**Implementation Method**: written

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**Communication of Expectations:**Modeled an example of the problem they are to create in class.

·

**Evaluation Criteria:**Rubric attached.

·

**Feedback Strategies:**Rubric with comments will be passed back to students. Also, peers will do the homework problem (Day 6) in class and give feedback to the creator of problem.

·

**Student Self-Assessments:**If students feel that their homework problem is test worthy, they put two stars at the top before they turn it in.

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**Name of Assessment –**Chapter 3 Quiz (Objective 3)

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**Formality:**formal

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**Purpose:**summative of 3.1-3.5

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**Implementation Method**: Multiple-Choice and short answer

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**Communication of Expectations:**None

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**Evaluation Criteria:**Graded

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**Feedback Strategies:**Review answers in class

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**Student Self-Assessments:**None

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**Name of Assessment –**Chapter 3 Group/Individual Test (Objective 3)

·

**Formality:**formal

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**Purpose:**summative of Chapter 3

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**Implementation Method:**Multiple-choice, short answer and written

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**Communication of Expectations:**None

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**Evaluation Criteria:**Graded

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**Feedback Strategies:**Time to go over questions in class.

·

**Student Self-Assessments:**Test corrections are given as an option.

**ANTICIPATORY SET**

At the beginning of the unit, I planned a lesson to introduce students to the vocabulary that we will be using for the rest of the chapter. This lesson, 3-1, is very engaging because it lets the students work with the ipads, they get to go on campus to take pictures of geometry vocabulary they see outside of the classroom, and then they record their voices and make a presentation to show other groups

**CLOSURE**

The closure activity will be a fun review game on day 9. They will play the game and use the clicker to answer sample multiple-choice questions. They will use the graphic organizer to organize the topics and information that need to be studied for the test. They will also draw pictures to represent the different vocabulary and theorems used in the chapter. This graphic organizer is great to have in their interactive notebooks because each chapter builds on the previous chapter. A lot of what we learned in Ch. 3 will be the building blocks for proving congruency in chapter 4.

**LESSON PLANS (Day 5)**

1. TITLE OF LESSON: Slope of Lines Poster Project – Chapter 3 -5

2. CURRICULUM AREA & GRADE LEVEL: Geometry. This is the third unit of study titled Parallel and Perpendicular Lines, and the fifth lesson in the unit that focuses on the slope of parallel and perpendicular lines. Most of the students are 9th and 10th graders with a few 11th graders. All students have passed Algebra 1.

3. DATE OF LESSON/TIME NEEDED: The lesson will occur in period 1 and 6 of Tuesday/Wednesday, October 28/29, 2014. The total time needed is 1hr 50min

4. RESOURCES:

**Warm up activity**– This is a graph I will put on the document projector of 4 lines graphed on one axis representing 4 different scenarios of bank account balances over time. Students will interact with the graphs by answering the prompts on the graph in order to analyze slope and what the slope means in real life.

**Exploration scenarios**- These are the 3 problems that different groups will be solving and showing on a poster.

**Ticket out the door**– This worksheet is used when students are doing the gallery walk and reflecting at the end of the lesson.

**Homework problem**– This is handed out at the end of class as a homework assignment. It has the directions I gave in class explicitly written.

**Supplies**for poster project - markers, graphed poster paper, rulers or protractors.

5. CA CONTENT STANDARD(S):

Preparation for CA standard 17.0 – Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.

Preparation for Common Core Standard G-CO Congruence 11. Prove theorems about parallelograms.

*Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.*

Preparation for Common Core Standard G-SRT 4. Prove theorems about triangles.

*Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity*

6. CA ELD STANDARD(S):

*Address how this lesson helps develop language*

During the Anticipatory set, students are asked to answer questions independently, then share with their elbow partner. While one partner is sharing the other is listening and then repeating back what they heard. This addresses:

CA ELD Collaborative Standard 1. Exchanging Information/Ideas (Expanding): Contribute to class, group, and partner discussions, sustaining conversations on a variety of age and grade-appropriate academic topics by following turn-taking rules, asking and answering relevant, on-topic questions, affirming others, providing additional, relevant information, and paraphrasing key ideas.

This standard is further developed when the students are working in groups to complete their poster.

*7.*BIG IDEA ADDRESSED/ENDURING UNDERSTANDING:

This material is important to understand because students are acquiring math skills that will help them create geometric proofs as well as help aid their understanding of graphing parallelograms, squares, and other polygons in later chapters.

8. ESSENTIAL QUESTIONS:

What do the slopes of parallel lines represent and what do the slopes of perpendicular lines represent in a general sense?

*9.*OBJECTIVE(S) OR LEARNING GOAL(S): Cognitive.

After working in groups to solve an exploratory word problem involving slopes of parallel and perpendicular lines, students will be able to determine if the lines are parallel, perpendicular, or neither and explain what the slopes represent by completing their ticket out the door at the end of the lesson.

10. ASSESSMENT(S):

Summative – I will assess students understanding of the lesson today by collecting, reading and commenting on their ticket out the door, which addresses the essential question as well as checks their understanding of the slope of parallel and perpendicular lines.

**7. MATERIALS/RESOURCES**

Day 1 -Warm up picture (given)

Day 1 -

**Vocabulary Worksheet (given)**

ipads with Show Me app

**Interactive Notebook**

Day 2 -

Day 2 -

Ruler

Protractor

**Day 3 –**Interative Notebook

Ruler

Protractor

Patty Paper

**Day 4 –**Compass

Protractor

**Day 5 -**Warm up Graph (provided)

**Poster Project Questions (given)**

“Ticket out the Door” (given)

Graphed poster paper

Markers

Rubric (given)

**Day 6 -**Student’s Homework from the previous night (given)

Rubric (given)

**Day 7 -**Ch.3 Quiz – multiple choice (provided)

**Day 8 -**Class run by CT. No materials provided

**Day 9 -**Graphic organizer (given)

Smart board with clickers

Review questions

**Day 10 -**Ch.3 group test

**Day 11 -**Ch. 3 individual test

**8. REFLECTION**

· In what ways have you differentiated instruction to meet the varying needs of your students?

I differentiated instruction by having a variety of modes of instruction. I gave visuals, I had students work with patty paper to see relationships between lines and angles, I used rubrics to assess and give feedback to students, I had peers assess students, I did a lot of group work, and I let students use technology in the classroom.

· What strengths and possible limitations do you see in your plan?

I see weakness in my assessment plan and my objectives. Sometimes I try to make activities fun for the students, but the activities may not precisely meet standards or objectives. The assessments are difficult for me to use to inform instruction because I don’t know if there will be enough turn around time to inform my instruction for the next day when everything is already planned. Also, I don’t like how heavily weighted tests and quizzes are but that is the culture of the geometry department and my Coordinating Teacher so I have to be the culture right now.

· What forms of data/evidence might you collect from this unit to measure its effectiveness?

The test scores from the quiz and chapter test, the results of the interactive multiple choice review and the 3.5 homework problems can be a measure of effectiveness.

· What have you learned about yourself, students, your unit plan topic, and/or planning in general as a result of designing this unit plan? What do you know now that you didn’t know at the start of this unit or program?

I know that although I can keep certain students in mind while planning a unit and individual lessons, every day cannot meet the needs of every student in my class. Each day you can rotate which students you are keeping in mind while planning an activity, but the lesson probably won’t be a home run for every student every day. I have found it difficult to try and find a way to deliver dry information like theorems and definitions to the students without all my EL’s, low level kids, ADD kids and high level kids disengaging. I am still learning innovative ways to get the information to them in a way that they care about it.