work sample final

PACIFIC UNIVERSITY

Perimeter, Area, and Volume 8th Grade Pre-algebra

Jaclyn Fitzgerald

February 2011

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Contents

A. Critical Question and Rationale ........................................................................................................... 3 B. Oregon State Standards……………………………………………………………………………………………………………………….5 C. Learning Goals ................................................................................................................................... 6 D. Key Points .......................................................................................................................................... 6 E. Content Relationships ......................................................................................................................... 7 F1. Assessment Plan .............................................................................................................................. 10

F2. Pre/Post-Assessments and Scoring Guide ..................................................................................... 12 F3. Authentic Performance Task and Scoring Guide .......................................................................... 17

G. Unit Sequence .................................................................................................................................. 24 H. Lesson Plans ..................................................................................................................................... 28 I. Accommodating Individual Differences ............................................................................................. 33 J. Promoting Cultural Competence......................................................................................................... 36 K. Cross-curricular Integration .............................................................................................................. 37 L. Applications of Technology and Multimedia ..................................................................................... 37 M. Communication and Feedback.......................................................................................................... 37 Q. Resources ......................................................................................................................................... 38



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A. Critical Question and Rationale

Geometry comes from a Greek word meaning “to measure the earth”. As one of the

oldest math sciences, Geometry allowed ancient philosophers, astronomers, and mathematicians

to learn about our world far before there were satellites, Google Earth, and many of the other

luxuries we now enjoy. We can credit these great minds and hard workers with a great deal of

the knowledge that is still shared and learned today. Although our world is now only a computer

click away, learning about geometry can help students to take in and process their lives by

expanding their spatial understanding and abstract visualization.

As students progress through a perimeter, area, and volume geometry unit they will

quickly move from the two-dimensional objects that they are very familiar with to examining

three-dimensional objects and their properties. Along the way they will consider and extend their

understandings of perimeter, area, circumference, surface area, and volume. Students will also

begin to inspect and realize perfect squares and square roots. Aside from studying geometry,

students will be responsible for evaluating their effort in mathematics daily, so as to hopefully

encourage more on-task behavior toward their achievement in mathematics.

Instruction of this unit will take place in an eighth grade classroom at Ogden Middle

School, located in Oregon City, Oregon. While Oregon City is quite a large town Ogden is

located on the outskirts and is made up of four, generally rural, feeder elementary schools. Most

students at Ogden are Caucasian and approximately 37% of them receive free or reduced lunch.

For the past few years Ogden has successfully held high marks among national standards in

every subject and for every population except for Special Education. This middle school looks

eerily the same since I was in attendance a little over eight years ago; with the same lockers,

many of the same teachers, and even the same math books and curriculum. Although dated, the



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present textbooks thoroughly cover geometry and will serve as a great resource throughout this

unit.

Mathematics has commonly been referred to by many as a subject that is difficult and

daunting. This loathing and anxiety for math happens for a variety of reasons and to a variety of

people, astonishingly even many students, teachers, and parents. This attitude about math is

distressing when students are at a time in their lives to make leaps and bounds in their learning

and toward their future success. This is a sentiment that many Ogden mathematic students hold

and show in the little amount of effort that they put forth in class and on their homework

assignments. Throughout this geometry unit goal-setting, progress charting, and reflection will

expectantly serve to end these poor math habits and set students on a stronger path to success and

math proficiency.

At the conclusion of this unit students will complete two assessment pieces- an authentic

performance task and a final exam. While the final exam will only provide a limited sketch of the

students’ understanding and recall of geometry concepts the authentic performance task will

offer a much more in depth and collective learning experience and evaluation. The authentic

performance task gives students the opportunity to teach others what they know, strengthen their

understandings, and reflect on their learning and effort in their mathematics class. With the

completion of the unit and these two assessment components students will have satisfied Oregon

and National Standards in regards to eighth grade geometry and be prepared for their high school

mathematics courses.



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B. Oregon State Standards Geometry and Measurement: Analyze two- and three-dimensional spaces and figures by using distance and angle. 5.3.2 Find and justify relationships among the formulas for the areas of triangles and parallelograms. 5.3.3 Describe three-dimensional shapes (triangular and- rectangular prisms, cube, triangular- and square-based pyramids, cylinder, cone, and sphere) by the number of edges, faces, and/or vertices as well as types of faces. 5.3.8 Decompose three-dimensional shapes and find surface areas and volumes of triangular and rectangular prisms. 7.3.1 Use models to explain the reasonableness of formulas for the circumference and area of circles. 7.3.3 Solve problems involving areas and circumferences of circles. 7.3.4 Use models to explain the reasonableness of formulas for the surface area of pyramids and cylinders, and volume of pyramids, cylinders, and cones. 7.3.5 Find and justify relationships among the formulas for the areas of different polygons when determining surface area. 7.3.6 Solve problems involving surface areas of pyramids and cylinders and volumes of pyramids, cylinders, and cones. 7.3.7 Estimate and compute the area and volume of complex or irregular shapes by dividing them into basic shapes. 8.3.3 Use models and logical arguments to show that the sum of the angles of any quadrilateral is 360 degrees, and apply this fact to find unknown angles. 8.3.4 Use models to explore the validity of the Pythagorean Theorem, and use it to find missing lengths. 8.3.5 Apply the Pythagorean Theorem to find distances in a variety of 2- and 3-dimensional contexts, including distances on coordinate graphs. 8.3.6 Use models and referents to explore and estimate square roots. EL.08.WR.01 Use a variety of strategies to prepare for writing, such as brainstorming, making lists, mapping, outlining, grouping related ideas, using graphic organizers, and taking notes. EL.08.WR.31 Use effective note-taking techniques to ensure appropriate documentation of quoted as well as paraphrased material. EL.08.SL.04 Use feedback, including both verbal and non-verbal cues to reconsider and modify the organizational structure and to rearrange words and sentences to clarify the meaning. EL.08.SL.05 Use precise language, action verbs, sensory details, appropriate and colorful modifiers, and the active rather than the passive voice in ways that enliven oral presentations.



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C. Learning Goals After this unit, students will be able to:

1. Develop and use formulas to determine the perimeter and area of parallelograms, triangles, and trapezoids and develop strategies to find the area of more complex shapes.

2. Analyze and use the Pythagorean Theorem and its converse to solve problems. 3. Diagram and identify parts of three dimensional figures. 4. Develop and use formulas to determine the circumference and area of circles. 5. Determine the surface area and volume of prisms, cylinders, pyramids, cones and

spheres. 6. Explore and estimate square roots. 7. Self-evaluate effort and attitude in math to take a role in increasing them by way of

improved on-task behavior and valuing mathematics in their daily lives. D. Key Points

1. Find perimeter of rectangles, parallelograms, triangles, and trapezoids 2. Find area of rectangles, parallelograms, triangles, and trapezoids 3. Find the circumferences of a circle 4. Find the area of a circle 5. Graph polygons and circles on a coordinate plane 6. Use the Pythagorean Theorem 7. Classify three-dimensional figures 8. Construct three-dimensional figures 9. Develop formulas to determine the area of complex shapes 10. Use formulas to find the area of complex shapes 11. Take notes on a graphic organizer 12. Do daily homework math practice 13. Use graphic organizer to arrange and study math concepts 14. Teach a 7th grade student 15. Set a goal to increase effort in math and improve on-task behavior 16. Track effort on homework and in class 17. Reflect on progress toward goals



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E. Content Relationships

Learning Goals Supporting Benchmarks Supporting Lesson Objectives

Supporting Activities

Develop and use formulas to determine the perimeter and area of parallelograms, triangles, and trapezoids and develop strategies to find the area of more complex shapes

5.3.2 Find and justify relationships among the formulas for the areas of triangles and parallelograms. 7.3.5 Find and justify relationships among the formulas for the areas of different polygons when determining surface area. 7.3.7 Estimate and compute the area and volume of complex irregular shapes by dividing them into basic shapes.

-Students will demonstrate prior knowledge of perimeter and area. -Students will be able to calculate the perimeter and area of rectangles and parallelograms by drawing them on graph paper and discovering the number of units the figures occupy. -Students will be able to calculate the perimeter and area of triangles and trapezoids by comparing them to rectangles and parallelograms and then drawing them onto graph paper and discovering the number of units the figures occupy.

-Exploring rectangles (L1) -Exploring parallelograms (L1) -Ticket out the door (L1) -Exploring triangles (L2) -Exploring trapezoids (L2) -Ticket out the door (L2)

Analyze and use the Pythagorean Theorem and its converse to solve problems.

8.3.4 Use models to explore the validity of the Pythagorean Theorem, and use it to find missing lengths. 8.3.5 Apply the Pythagorean Theorem to find distances in a variety of 2- and 3-dimensional contexts, including distances on coordinate graphs.

-Students will be able to demonstrated their understanding of the Pythagorean Theorem by diagramming the relationship of the sides of a triangle and the equation: ܽଶ + ܾଶ = ܿଶ (L3)

Diagram and identify parts of three dimensional figures.

5.3.3 Describe three-dimensional shapes (triangular and- rectangular prisms, cube, triangular- and square-based pyramids, cylinder, cone, and sphere)



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by the number of edges, faces, and/or vertices as well as types of faces.

Develop and use formulas to determine the circumference and area of circles and develop strategies to find the area of more complex shapes.

7.3.1 Use models to explain the reasonableness of formulas for the circumference and area of circles. 7.3.3 Solve problems involving areas and circumferences of circles. 7.3.7 Estimate and compute the area and volume of complex or irregular shapes by dividing them into basic shapes.

Determine the surface area and volume of prisms, cylinders, pyramids, cones and spheres.

5.3.8 Decompose three-dimensional shapes and find surface areas and volumes of triangular and rectangular prisms. 7.3.4 Use models to explain the reasonableness of formulas for the surface area of pyramids and cylinders, and volume of pyramids, cylinders, and cones. 7.3.5 Find and justify relationships among the formulas for the areas of different polygons when determining surface area. 7.3.6 Solve problems involving surface areas of pyramids and cylinders and volumes of pyramids, cylinders, and cones.

Explore and estimate square roots.

8.3.6 Use models and referents to explore and estimate square roots.

-Exploring Squares (L1)

Self-evaluate effort and attitude in math to take a role in increasing them by way of improved on-

EL.08.WR.01 Use a variety of strategies to prepare for writing, such as brainstorming, making lists, mapping, outlining,



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task behavior and valuing mathematics in their daily lives.

grouping related ideas, using graphic organizers, and taking notes. EL.08.WR.31 Use effective note-taking techniques to ensure appropriate documentation of quoted as well as paraphrased material. EL.08.SL.04 Use feedback, including both verbal and non-verbal cues to reconsider and modify the organizational structure and to rearrange words and sentences to clarify the meaning. EL.08.SL.05 Use precise language, action verbs, sensory details, appropriate and colorful modifiers, and the active rather than the passive voice in ways that enliven oral presentations.



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F1. Assessment Plan Goal 1: Develop and use formulas to determine the perimeter and area of parallelograms, triangles, and trapezoids and develop strategies to find the area of more complex shapes Formative:

Pre-assessment Rectangle Drawing (L1) Parallelogram Drawing (L1) Triangle Graphing (L2) Trapezoid Graphing (L2) Group Discussions (ALL) Ticket out the door (ALL) Daily homework (ALL)

Summative: Authentic Performance Task Post-assessment

Goal 2: Analyze and use the Pythagorean Theorem and its converse to solve problems. Formative:

Pre-assessment Group Discussions (ALL) Ticket out the door (ALL) Daily homework (ALL)


Goal 3: Diagram and identify parts of three dimensional figures. Formative:



Goal 4: Develop and use formulas to determine the circumference and area of circles and develop strategies to find the area of more complex shapes. Formative:



Goal 5: Determine the service area and volume of prisms, cylinders, pyramids, cones, and spheres. Formative:



Goal 6: Explore and estimate square roots. Formative:

Pre-assessment Rectangle Drawing (L1) Group Discussions (ALL) Ticket out the door (ALL)




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Daily homework (ALL) Goal 7: Self-evaluate effort and attitude in math to take a role in increasing them by way of improved on-task behavior and valuing mathematics in their daily lives. Formative:

Effort charts On-task records Group Discussion (L1)

Summative: Authentic Performance Task



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F2. Pre/Post-Assessments and Scoring Guide Directions: Please complete the following problems using all that you know or have learned. Show as much of your work as possible so that I can at least give you partial credit on problems that you have given the incorrect answer, but also know that if you do not show any work then you cannot receive full credit. BREATHE! You are going to do great =)

(1) Find the perimeter and area of the following figures: (Goal 1 and 4)

Perimeter: _______________

Area: ____________________

Perimeter: _______________

Area: ____________________

Perimeter: _______________

Area: ____________________

Perimeter: _______________

Area: ____________________

5 cm

10 cm

7 in

9 in

8 in

8 cm

7 cm

5 cm

9 cm

8 ft

9 ft 9 ft

7 ft

Circumference: ______________

Area: ____________________

10 mm



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(2) Find the perimeter/circumference and area of the following figures: (Goal 1 and 4)

12

10

12 12

13



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(3) Use the Pythagorean Theorem to find the missing side lengths in the figures below: (Goal 2)

(4) Explain the Pythagorean Theorem using the figure below and drawing in whatever else you need: (Goal 2)

(5) Label an edge, face, and vertex on the figure below: (Goal 3)

5 13

8

15



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(6) Find the perimeter and area of the figure below: (Goal 1)

(7)Find the surface area and volume of the figures below: (Goal 5)

(8) Draw a diagram below to help you answer- what is the square root of 36? (Goal 7)

10 cm

5 cm 8 cm

4 cm

3 cm 4 cm

17 m

10 m

4 cm

6 cm 3 cm

5 cm



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Pre-/Post Assessment Scoring Guide:

Descriptors 5 4 3 2.5 1 (1) Find the perimeter and area of the following figures.

The correct answer with all necessary work shown.

The correct answer with work I cannot follow.

The correct answer with no work.

The incorrect answer with all work shown

The incorrect answer with insufficient or no work shown.

(2) Find the perimeter/circumference and area of the following figures.






(3) Use the Pythagorean Theorem to find the missing side lengths in the figures below.






(4) Explain the Pythagorean Theorem using the figure below and drawing in whatever else you need.






(5) Label an edge, face, and vertex on the figure below.






(6) Find the perimeter and area of the figure below.






(7) Find the surface area and volume of the figures below.






(8) Draw a diagram to help you answer- what is the square root of 36?








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F3. Authentic Performance Task and Scoring Guide Name: Jaclyn Fitzgerald Grade Level: 8 Work Sample Title: Perimeter, Area, and Volume Benchmarks:

5.3.2 Find and justify relationships among the formulas for the areas of triangles and parallelograms. 5.3.3 Describe three-dimensional shapes (triangular and- rectangular prisms, cube, triangular- and square-based pyramids, cylinder, cone, and sphere) by the number of edges, faces, and/or vertices as well as types of faces. 5.3.8 Decompose three-dimensional shapes and find surface areas and volumes of triangular and rectangular prisms. 7.3.1 Use models to explain the reasonableness of formulas for the circumference and area of circles. 7.3.3 Solve problems involving areas and circumferences of circles. 7.3.4 Use models to explain the reasonableness of formulas for the surface area of pyramids and cylinders, and volume of pyramids, cylinders, and cones. 7.3.5 Find and justify relationships among the formulas for the areas of different polygons when determining surface area. 7.3.6 Solve problems involving surface areas of pyramids and cylinders and volumes of pyramids, cylinders, and cones. 7.3.7 Estimate and compute the area and volume of complex or irregular shapes by dividing them into basic shapes. 8.3.3 Use models and logical arguments to show that the sum of the angles of any quadrilateral is 360 degrees, and apply this fact to find unknown angles. 8.3.4 Use models to explore the validity of the Pythagorean Theorem, and use it to find missing lengths. 8.3.5 Apply the Pythagorean Theorem to find distances in a variety of 2- and 3-dimensional contexts, including distances on coordinate graphs. 8.3.6 Use models and referents to explore and estimate square roots. EL.08.WR.01 Use a variety of strategies to prepare for writing, such as brainstorming, making lists, mapping, outlining, grouping related ideas, using graphic organizers, and taking notes. EL.08.WR.31 Use effective note-taking techniques to ensure appropriate documentation of quoted as well as paraphrased material. EL.08.SL.04 Use feedback, including both verbal and non-verbal cues to reconsider and modify the organizational structure and to rearrange words and sentences to clarify the meaning. EL.08.SL.05 Use precise language, action verbs, sensory details, appropriate and colorful modifiers, and the active rather than the passive voice in ways that enliven oral presentations.



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Unit Goals: After this unit, students will be able to:

1. Develop and use formulas to determine the perimeter and area of parallelograms, triangles, and trapezoids and develop strategies to find the area of more complex shapes.

2. Analyze and use the Pythagorean Theorem and its converse to solve problems. 3. Diagram and identify parts of three dimensional figures. 4. Develop and use formulas to determine the circumference and area of circles. 5. Determine the surface area and volume of prisms, cylinders, pyramids, cones and

spheres. 6. Explore and estimate square roots. 7. Self-evaluate effort and attitude in math to take a role in increasing them by way of

improved on-task behavior and valuing mathematics in their daily lives. TASK DESCRIPTION: Ogden 7th graders need our help! Another round of OAKS testing is coming up and they need to know more geometry so that they can do well on their tests too. Luckily, over the next two weeks you will become a Geometry master and the perfect person to help them! I know we can all learn a lot and exceed on this test!!! You are going to help a seventh grader in two ways: -Meet with a 7th grader and teach them a geometry topic

-Create a visual of your geometry topic for them to review and hang up in their math class. You are going to help yourself by:

-Reflecting on your teaching of your geometry topic, your learning during this chapter, your likes and dislikes, and your effort goals.

COMPONENT 1: Teaching the 7th Graders

Goals Addressed: 1, 2, 3, 4, 5, and/or 6 COMPONENT DESCRIPTION: All students will teach a 5-10 minute lesson on a geometry topic to a seventh grader. You may do something with them similar to one of our activities in class or you can come up with your own ideas. You are so creative and smart so I am really excited to see how you would teach someone what you know. (Note: a great place to start could be your own math book- look through the example problems!) CRITERIA: -Pick a geometry concept you feel you know a lot about from the available list or have a different one approved by the teacher.



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-Prepare a 5-10 minute lesson to teach to a 7th grade student -Plan a lesson that makes sense, includes an activity, and meets your goal of teaching a 7th grader about your topic. -Provide at least two examples of test questions that they can use your geometry topic to solve/answer. -Learning should be fun! Make your lesson fun for you and your 7th grade student! -Turn-in a short description of your geometry topic, learning goals and related vocabulary you are going to use, your teaching plans (maybe your script or activity ideas?), and a list of needed materials for the teacher to review at least a week before. -Have a classmate review your lesson the class period before. -Fill out a self-assessment after completing your lesson -Collect lesson reviews from two different classmates COMPONENT 2: Geometry Topic Visual

Goals Addressed: 1, 2, 3, 4, 5, and/or 6 COMPONENT DESCRIPTION: To best help our 7th graders we need to give them something that they can take with them. Remember, it takes over 20 times of looking at something before we are really going to be able to remember it and use it for something. By giving them a visual of the geometry topic that you taught them then they can hang it up in their math class and review it whenever they need to. CRITERIA: -Must include the title or name of your geometry topic. -Must include diagrams, pictures, or procedures necessary to understand the topic and answer test questions about the topic -Must include all necessary vocabulary related to your topic -Include at least two different examples of test questions that they may use your geometry topic to answer and show the step-by-step solution process (should have two different solution processes) and answers so anyone can follow them. (Note: again look at your text book! There are a ton of great example questions available!) COMPONENT 3: Reflection

Goals Addressed: 7 COMPONENT DESCRIPTION: You have learned so much these past few weeks and I want to know all about it! First of all I want to know how teaching your geometry topic went. Do you think they understood and could use it on their test? Then I want to tell me about your learning this chapter and your likes and dislikes about how your math class is set up now. Lastly, I want you to tell me all about your effort goals. Write about why it is your goal, what changes you had to make to accomplish it, and if you did actually met your goals. Be completely honest, you will not be graded down; I just



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want to know what you are truly thinking and feeling! You can do this in a paper or individual poster for you to present to me privately. The criteria below are mostly for the paper, but if you choose to do a poster you still must find a way to creatively present these criteria on your poster. CRITERIA: -Typed, double-spaced, 12 pt font, Times New Roman, and 1 inch margins (if you need access to a computer contact me) -At least one page in length -At least one paragraph about your geometry topic teaching, one paragraph about how you are learning in math class, and one paragraph about your effort goal(s). -Attach completed lesson self-assessment -Attach completed effort chart Component 1: Teaching 5 3 1

Pick a geometry concept you feel you know a lot about from the available list or have a different one approved by the teacher.

Picked a geometry topic

from the list or an appropriate geometry

topic that was approved by the teacher.

Picked an appropriate

geometry topic that was not on the list and did not get approval from

the teacher.

Picked a geometry topic that was not on the list and did not get approval from

the teacher. Topic is inappropriate: not in

math text book or other class resources.

Turn-in a short description of your geometry topic, learning goals and related vocabulary you are going to use, your teaching plans (maybe your script or activity ideas?), and list of needed materials for the teacher to review a week before.

Turned in plan on-time with thorough

descriptions showing strong understanding of the geometry topic, 2 or more learning goals, all possible vocabulary that is relevant in teaching and learning this topic, includes well thought out teaching plans and

describes activities, and provides a list of all materials needed.

Turned in plan on-time with minimum

description that limits showing their

understanding of the topic, provides only one learning goal they have for the 7th grade student,

lists most vocabulary that is important to teach the topic, lists teaching plan ideas

Turned in plan on-time but provides

little to no details or information about

their understanding of the topic, the

learning goals they have for their 7th

grade students, the vocabulary the

lesson will include, their teaching plan,

and/or the list of needed materials.

Prepare a 5-10 minute lesson to teach to a 7th grade student Plan a lesson that

Lesson length is

appropriate for teaching the topic in a fun way. Activity includes the student. The learning

Lesson length is over 5 minutes and under 10 minutes but more/less

information could have been used for the lesson to make the most sense.

Lesson length is under 5 minutes or over 10 minutes.

Includes a very short activity that does not involve the 7th grade



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makes sense, includes an activity, and meets your goal of teaching a 7th grader about your topic.

goals match the lesson and topic and are met

after the lesson.

Includes a basic activity. Learning goals seem to connect to the topic but not the lesson

plan.

student. Learning goals do not seem to match the topic or

lesson.

Provide at least two examples of test questions that they can use your geometry topic to solve/answer.

Creates two or more test questions. Uses these

questions to show how to solve a test problem

with their geometry topic.

Creates two test questions, but does not use them to teach the process of using the

geometry topic on a test.

Creates less than two test questions. Does

not use the test questions at all in

teaching the student.

Learning should be fun! Make your lesson fun for you and your 7th grade student!

Lesson appeared very fun! Included hands on

or moving around activities that kept student interested.

Creative and original activity ideas.

Lesson seemed interesting. Student was involved in more than

just listening and watching. May have

used in-class learning stations

Did not seem at all fun. May have only talked to the student about math and did not involve them.

Fill out a self-assessment after completing your lesson

Grades self accurately and provides comments explaining reasoning.

Grades self accurately but provides no

comments or reasoning.

Does not grade self accurately and adds

no comments.

Collect lesson reviews from two different classmates

Attaches 2 or more lesson reviews.

Attaches less than 2 lesson reviews.

Attaches no lesson reviews.

Component 2: Visual 5 3 1 Include Title/Name of Geometry topic.

Visual includes a creative title that makes

viewers aware of the Geometry topic without just stating it. The title is big enough and easy

to read.

Visual includes

Geometry topic as the title. The title is big enough and easy to

read.

Visual includes Geometry topic as the title. The title is small and hard or

impossible to read.

Include diagrams, illustrations, pictures, and solution process to understand and use the Geometry topic. (This can be part of your 2 test questions below)

Included several diagrams/illustrations/

pictures. The process of using the Geometry

topic is shown step-by-step with very clear

labels and explanations.

Included few diagrams/

illustrations/pictures. The process of the Geometry topic is

shown but is unclear or difficult to follow.

Included little or no diagrams/illustration

s/ pictures. The process of using the Geometry topic is

shown but so limited it is not helpful.

Include all necessary

Visual includes vocabulary that is

necessary to understand

Visual includes vocabulary that is

necessary to understand

Visual includes limited or no

vocabulary that is



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and related vocabulary.

the Geometry topic. Related vocabulary is

also included to extend the topic and connect it with other math topics.

the Geometry topic. No other related vocabulary is used to connect with

other math topics.

helpful in understanding the

Geometry topic. No related vocabulary is

included. Include two different test questions.

Visual provides two different test questions. Two different types of solving processes or

steps using the Geometry topic are shown and labeled.

Visual provides two

different test questions but solves them both the

same way.

Visual provides less

than two test questions or two

questions that are too similar.

Component 3: Reflection 5 3 1

Format: Typed, double-spaced, 12 pt font, Times New Roman, 1 inch margins

Paper follows format guidelines exactly.

Paper has some incorrect formatting.

Paper has mostly or all incorrect formatting.

At least one pate in length including at least on paragraph on each prompt: your teaching, your learning in math class, and your effort goal(s).

Paper is one page in length or longer and includes at least one paragraph about each

prompt.

Paper is less than one page in length but still includes a paragraph

covering each prompt.

Paper is less than one page in length and is missing one

or more prompt paragraphs.

Attach completed effort chart and goals

Goals are written in the correct location and

everyday effort honestly evaluated and graphed on the chart.

Goals are written in the correct location and

effort is evaluated and graphed on the chart for

most days.

Goals are written in the correct location

but effort is not evaluated and

graphed on the chart for most days or

student is dishonest about their actual

effort.



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Possible Lesson Topics: -Angles (pg 223) -Transversals (pg 228) -Triangle Sum Theorem (pg 234) -Angle measures of polygons (pg 239) -Finding the slope of a line (pg 244) -Congruence (pg 250) -Transformations (pg 254) -Symmetry (pg 259) -Tessellations (pg 263) -Area and Perimeter of Rectangles and Parallelograms (pg 280) -Area and Perimeter of Triangles and Trapezoids (pg 285) -Pythagorean Theorem (pg 290) -Circles (pg 294) -Volume of prisms and cylinders (pg 307) -Volume of pyramids and cones (pg 312) -Surface Area of prisms and cylinders (pg 317) -Surface Area of pyramids and cones (pg 321) -Spheres (pg 324) Reflection Prompts: Here are some ideas to get you started, but do not feel like you have to answer all of these or just stick to these questions and ideas. I want to hear your honest opinions. Your teaching- -Were you comfortable enough with your topic to teach it? -What did you like? What did you not like? -Did it seem that your student understood your topic? -Could your student complete your test problems? -How much did you include your student? -If there is anything you could change what would it be and why? Your feelings about class and my teaching- -How is math going for you? -What do you like? What do you wish could be different? -Is my teaching help you? Is there anything more I could do to help you? -Do you feel like you are learning just as much as when you are learning from your normal classroom teacher? Your effort chart and goal(s)- -What were your goals and why? -Did you have to make any changes to reach your goals? -Did you reach your goals or make some progress? -Do you feel that goal setting has helped you at all? If so, how?



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G. Unit Sequence

Lesson # Lesson Title Lesson Highlights

Lesson 1 Perimeter and Area of Rectangles and Parallelograms

-Homework Question and Answer -Correct homework -Introduce effort chart and set goals. -Transition Music: record score, turn in, write down assignment, and record effort score. -Mini-lesson: -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door: complex, irregular figure

Lesson 2 Perimeter and Area of Triangles and Trapezoids

-Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write down assignment, and record effort score. -Mini-lesson: -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door: triangles and trapezoids

Lesson 3 Perimeter and Area Review

-Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write down assignment, and record effort score. -Perimeter and area practice problems, review stations -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door

Lesson 4 Circles

-Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write down assignment, and record effort score. -Mini-lesson: -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door

Lesson 5 The Pythagorean Theorem

-Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write down assignment, and record effort score. -Mini-lesson:



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-Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door

Lesson 6 More Pythagorean Practice Problems

-Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write down assignment, and record effort score. -Students complete further practice problems and visit review stations to gain a better understanding of Pythagorean Theorem. -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door

Lesson 7 Coordinate Pythagorean


Lesson 8 Mid-chapter quiz and review day

-Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write down assignment, and record effort score. -Take the mid-chapter quiz -If time allows, visit review stations. -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door

Lesson 9 Volume of prisms and cylinders


Lesson 10 Volume of pyramids and cones -Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write



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down assignment, and record effort score. -Mini-lesson: -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door

Lesson 11 More volume practice

-Homework Question and Answer -Correct homework -Introduce effort chart and set goals. -Transition Music: record score, turn in, write down assignment, and record effort score. -Volume practice problems and review stations -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door

Lesson 12 Surface area of prisms and cylinders


Lesson 13 Surface area of pyramids and cones


Lesson 14 Review surface area

-Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write down assignment, and record effort score. -Surface area practice problems, review stations -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door

Lesson 15 Spheres -Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write



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down assignment, and record effort score. -Mini-lesson: -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door

Lesson 16 Review Day and Authentic Performance Task practice and work

-Homework Question and Answer -Correct homework -Transition Music: record score, turn in, write down assignment, and record effort score. -Students visit review stations to prepare for post-assessment -Practice their 5-10 min teaching with a classmate. -Students score their in-class effort and plot their in-class and homework scores on their chart. -Ticket out the door: Classmate lesson review

Lesson 17 Authentic Performance Task

- Discuss rules for the day -Gather all materials -Teach 7th grade students -Return to class and discuss -Computer lab: Authentic Performance Task reflection work.

Lesson 18 Post-assessment

-Turn in Authentic Performance Task Reflection with effort charts. -Take post-assessment test -Start on homework for the following night.



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H. Lesson Plans Name: Jaclyn Fitzgerald Date: February 2011 Lesson 1 Title: Perimeter and Area of Rectangles and Parallelograms Grade Level/Subject: 8th/Mathematics Benchmark(s): 7.3.5 Find and justify relationships among the formulas for the areas of different polygons when determining surface area. 7.3.7 Estimate and compute the area and volume of complex irregular shapes by dividing them into basic shapes. Objectives(s): - Students will demonstrate prior knowledge of perimeter and area. -Students will be able to calculate the perimeter and area of rectangles and parallelograms by drawing them on graph paper and discovering the number of units the figures occupy. Lesson Assessment: Ticket out the door-complex, irregular figure. Materials: Graph paper, document camera, pencils, effort charts Length of Lesson: 50 min Pacing Procedures/Activities

(Teacher & Student) Teacher

Actions/Notes 8 min

5 min

4 min

2 min

26 min

Homework Questions? Correct Homework Further Questions? Introducing effort charts- Each student explores effort chart and sets goals for mathematics. If you are trying to improve your effort on homework what are some things you could do? Students list changes they need to make. What would putting more effort in to class look like? Transition music- Students record their HW scores, their new assignment, and effort chart data. Set: So today we are going to be talking about area and perimeter and learn how to calculate them for rectangles and parallelograms. Information/Input: So I am going to give everyone a piece of graph paper and I

Check understanding from previous lesson Introduce my critical question and effort chart Motivation-degree of concern Group Discussion Theme: Disco Estimated homework length- 40 min Stating Objective Hand out graph paper



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want you to first draw as many different rectangles as possible in the next 30 seconds. How many were you able to make?! Exploring Rectangles: Okay, so for example if I made a rectangle on my graph paper that was 6 units on the base and 2 units for the height my perimeter would be a sum of all the side lengths so 6+6+2+2=16 and what would my area be and how do you know? I want you to talk with your table partner and decide how calculating the perimeter could be done with multiplication.

Remind of in-class effort goals. What did you come up with? What if I made a rectangle that was 4 units for the base and 4 units for the height? It is a square of course because all of the sides are the same length! Is a square a rectangle? YES, so go ahead and draw this onto your graph paper and now we must add together all the sides for the perimeter which would be: 4+4+4+4=16 units. Pencil in the air if you know how could this be represented as a multiplication problem? Okay, so go ahead and finish this problem by finding the area and take the next two minutes to make as many more rectangles (and squares) as you can, but you must calculate the perimeter and area for each before drawing your next rectangle.

Remind of in-class effort goals. Exploring Squares: Okay now try and make as many different rectangles as possible that have an area of 24 units squared. Exploring Parallelograms: What about the perimeter of parallelograms? Well the perimeter is calculated the same as we have been doing using the side lengths, but area is a little different. Well this is where graph paper can really come in handy because the height of a parallelogram is the height from the bottom base to the top base; it is NOT the side length. So by using a parallelogram on a coordinate graph then we can count the height between the bottom base and the top base. So I am going to provide you with a couple of coordinates and we are going to practice finding the perimeter and area of parallelograms. Parallelogram practice

Model TPS Guided Practice Check for understanding Independent Practice Parallelogram practice coordinates and problems.



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5 min

Closure: Ticket out the door- Okay so I want you to practice with one last figure on a new half-sheet of graph paper. By yourself or with your table partner I want you to copy down the figure here and show you work in figuring out the perimeter. This may require you moving or seperating things a little bit. This finished problem is you ticket out the door today. When you are finished I would like you to complete your effort chart for in-class today and then it should be time to pack up your things.

Pre-drawn figure, TPS Check for understanding

Extensions: Provide more of the “Ticket out the door” complex, irregular figure problems as soon as it is clear that they have mastered area during the lesson. Ask them to take daily notes on my lesson to distribute to other students that need more assistance. Accommodations: Post advanced organizer on the board. Classmate made notes to take home with them.

Name: Jaclyn Fitzgerald Date: February 2011 Lesson 2 Title: Perimeter and Area of Triangles and Trapezoids Grade Level/Subject: 8th/Mathematics Benchmark(s): 7.3.5 Find and justify relationships among the formulas for the areas of different polygons when determining surface area. 7.3.7 Estimate and compute the area and volume of complex irregular shapes by dividing them into basic shapes. Objectives(s): - Students will demonstrate prior knowledge of perimeter and area. -Students will be able to calculate the perimeter and area of triangles and trapezoids by comparing them to rectangles and parallelograms and then drawing them onto graph paper and discovering the number of units the figures occupy. Lesson Assessment: Ticket out the door-finding the perimeter and area of a triangle and trapezoid on a figure Materials: Graph paper, document camera, pencils Length of Lesson: 50 min

Pacing Procedures/Activities (Teacher & Student)

Teacher Actions/Notes



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10 min

4 min

3 min

25 min

Homework Questions? Correct Homework Further Questions? Transition music- Students record their HW scores, their new assignment, and effort chart data. Set: Show triangles and trapezoids as parts of a parallelogram. How do we find the area of parallelograms? If these triangles and trapezoids make up half of a parallelogram, then what do you think that means for the area of the triangle or trapezoid? Information/Input: So today we are continuing to work with perimeter and area but now we are learning how to calculate these for triangles and trapezoids. Exploring Triangles-

1. On your graph paper create your x- and y-axis and plot these points.

2. We need to use this graph paper to find the height of the triangle.

3. Now as we found out before a triangle is half of the area of a parallelogram and that is important to keep in mind when calculating the area of a triangle.

Okay now try this one on your own (Pg 287 #17). When you are finished hold up the answer with your fingers Exploring Trapezoids- Now a trapezoid is a little different because unlike the parallelogram, it has two different base lengths that we must take into account when calculating its area- show on a trapezoid and compare to a parallelogram. Okay so draw this figure on your graph paper with these coordinates Just like the triangle, a trapezoid is only half of the area of a parallelogram so we must use that when calculating the trapezoid’s area. So what is the height of our trapezoid? When finding the area we must use both bases as I said before, because they are different lengths, so in our calculations we add them together (Note: make sure you show this sum in your

Check understanding from previous lesson This Week’s Theme: Disco Estimated homework length: 40 min Check for understanding Group discussion Motivation: Success Stating Objective Modeling, Guided Practice Independent Practice, Check for understanding Modeling Provide figure coordinates Check for understanding- choral response



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10 min

calculations, don’t just do this in your head!) Model calculation for class. Now how about a trapezoid that looks like this…. What is the height and our two bases? Write down on your paper the equation to calculate the area of this triangle and then share it with your table partner. Closure: Okay, now I know you can be successful on your homework tonight. Remember though that for both the triangle and trapezoid finding the perimeter is just the same as before because it is always the sum of all the side lengths of any figure. Also, that a triangle and trapezoid have half the area of the parallelogram. Ticket out the door- In the time you have left please complete this problem as your ticket out the door:

Okay draw this figure here and answer the questions. When you are finished I would like you to complete your effort chart for in-class today and then it should be time to pack up your things.

Model Provide practice problem, guided practice TPS Pre-drawn figure (pg 288), Check for understanding

Extensions: Worksheet- Lesson 6-2 Practice B. Take notes for other students in class. Ask them to take daily notes on my lesson to distribute to other students that need more assistance. Accommodations: Post advanced organizer on the board. Classmate made notes to take home with them.



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I. Accommodating Individual Differences Individual Differences Attributes Activities

Multiple Intelligences

Logical/Mathematical

-Likes to count. -Likes to be organized -Is very precise. -Good at problem solving. -Recognizes patterns and relationships.

-Finding area (L1,2) -Effort chart (ALL)

Verbal/Linguistic

-Good at remembering written and spoken information. -Enjoys reading and writing. -Good at debating or giving persuasive speeches. -Able to explain things well. -Often uses humor when telling stories.

-Authentic Performance Task -Think Pair Share (ALL)

Spatial

-Able to visualize in their head. -Good depth perception. -Good with directions and maps. -Thinks of the big picture. -May speak fast.

-Graphing to calculate area (L1,2) -Diagramming three-dimensional figures (L9)

Musical

-Likely able to sing, play musical instruments, and compose music. -Appreciates musical expression. -Sensitive to rhythm, pitch, meter, tone, melody, or timbre.

-Transition music (ALL) -Closing music (ALL)

Body/Kinesthetic

-Learns by doing. -Uses the body to solve problems. -Coordinates mind and body to think. -May need to move to think. -Handles objects skillfully.

-Review stations (L 3, 6, 8, 11, 14)

Interpersonal/Social

-Good at communicating verbally. -See situations from different perspectives. -Create positive relationships with others. -Good at resolving conflict in groups. -Enjoys team builders.

-Collecting homework (ALL) - Authentic Performance Task

Intrapersonal/Introspective

-Introverted -Intuitive -Independent -Perfectionist -Self-aware

-Effort goals and chart (ALL)

Naturalist

-Able to discriminate between living things. -Sensitive to features of the natural world. -Good at categorizing information about nature. -Prefers topics related to nature.



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Learning Styles

Sensing/Thinking

-Enjoys activities that include drills and the recalling of facts. -Needs clear expectations with feedback. -Difficulty with change. -Active but business like

-Provide feedback (ALL) -Advanced Organizer (ALL)

Sensing/Feeling

-Focus on personal values and interpersonal relationships. -Know how learning relates to getting along with others. -Needs and wants support and encouragement. -Functions best in verbal interactions. -Learns best with content that has meaning.

-TPS/Partner work (ALL) -Authentic Performance Task

Intuitive/Thinking

-Wants instruction that focuses on meaning and relationships. -Wants to understand the reasoning behind things. -Solves problems through logic and analysis. -Enjoys experimentation

-Finding area and perimeter (L1, 2)

Intuitive/Feeling

-Wants instruction that allows personal exploration of a subject. -Likes new challenges. -Very creative and imaginative. -Can see the beauty in things. -Has difficulty organizing and planning time.

-Estimated Homework Length (ALL) -Authentic Performance Task

Special Needs

ADD/ADHD

-Needs large tasks broken down into smaller parts. -Possibly on medication -Needs instant and positive feedback -Needs simple and clear instructions and scheduling. -Possibly has difficulty completing or turning in tasks. -Likes teacher to model tasks.

-Advanced Organizer (ALL) -Authentic Performance Task -Correcting homework (ALL) -Modeling (ALL) -Effort goal setting and analysis (ALL)

IEP/504

-Needs large tasks broken down into smaller parts. -Likes teacher to model tasks. -Needs simple and explicit instructions. -Likes cooperative group work and visual materials.

-Advanced Organizer (ALL) -Authentic Performance Task -Modeling (ALL) -Exploring Rectangles (L1) -Exploring Parallelograms (L1) -Exploring Squares (L1)



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Aspergers Syndrome

-Interest concentrated in particular areas. -Has difficulty interacting with others. -Is physically clumsy. -May have a sophisticated vocabulary but difficulties with figurative language.

-Advanced Organizer (ALL) -Independent Practice (ALL)

Learning Disabilities

-Needs large tasks broken down into smaller parts. -Enjoys cooperative group work and visual materials. -Needs simple and explicit instructions. -Likes teacher to model tasks.

-Advanced Organizer (ALL) -Authentic Performance Task -TPS/Partner work (ALL) -Exploring Rectangles (L1) -Exploring Squares (L1) -Exploring Parallelograms (L1) -Modeling (ALL)

TAG

-Curious but logical thinker. -Focused, passionate, and creative. -Exhibits an understanding and awareness of problems. -Is advanced intellectually. -Demonstrates oral proficiency.

-Authentic Performance Task -Lesson Extensions (ALL)

Low SES

-Needs school to be a safe and friendly place. -Wants to be included in lessons. -Needs teacher’s positive support. -May have limited or no resources at home. -Needs teacher to have open communication lines with home. -Enjoys cooperative group work.

-Safe and friendly classroom (ALL) -TPS/Partner work (ALL)

ELL

-Wants teachers approval -Enjoys hands on activities and cooperative group work. -Needs opportunities to listen, speak, read, and write

-TPS/Partner Work (ALL) -Guided Practice (ALL) -Effort Chart (ALL)



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J. Promoting Cultural Competence Collaborating with parents and families to nurture and support competence in home and school cultures:

Written letter to family introducing myself and the unit of study. Communication with parents about achievement. Involving an interpreter when necessary. Inviting family volunteers and observers into the classroom. Inviting parents to meet with me at conferences.

Communicating high expectations:

Student goal setting. Providing specific and explicit scoring rubric for tasks, assignments, and assessments. Communicating the value of improvement. Providing students with the opportunity to revise so that they may turn in their best work. Consistent and immediate feedback on work.

Including instructional strategies that correspond with the norms and values of culture(s):

Providing students with consistent opportunities to self-regulate and self-reflect. Combining various guided practice, work group sizes, and independent work time. Fostering a welcoming and safe environment. Presenting a variety of different activities to accommodate all learners.

Engaging students in cooperatively developed and community-oriented learning:

Using cooperative learning strategies. Offering group assignments and partner work. Sharing math learning with others. Working with an authentic audience.

Integrating diverse ways of knowing, understanding, and representing knowledge:

Presenting a variety of different activities to accommodate all learners. Allowing for various ways of presenting information (oral, visual, written).

Connecting students’ cultural backgrounds and personal experiences to the acquisition of new knowledge and skills:

Using personal understanding and ideas to teach others.



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K. Cross-curricular Integration

Cross-curricular Integration Activities

Literacy-Writing -Authentic Performance Task Components 1, 2, and 3 -Graphic Organizers

Literacy- Speaking -Authentic Performance Task Component 1 -Class Discussions (ALL)

Literacy- Reading -The History of Pythagoras Social Studies -The History of Pythagoras L. Applications of Technology and Multimedia

Technology and Multimedia Activities -Document Camera -ALL lessons -Computer Lab -Authentic Performance Task Component 3 M. Communication and Feedback Students:

Consistent and immediate feedback on work Providing specific and explicit scoring rubric for tasks, assignments, and assessments. Consistently updating grades and attendance on ESIS.

Families:

Written letter to family introducing myself and the unit of study in all necessary languages.

Inviting family volunteers and observers into the classroom. Responding promptly to emails from family members. Communicating with parents about achievement. Consistently updating grades and attendance on ESIS for family to track. Inviting parents to meet with me at conferences.

Colleagues:

Attending Professional Learning Community weekly meetings and staff meetings. Communicating and collaborating with my mentor teacher and team members. Inviting administrators into the classroom often. Establishing an open line of communication with resource staff members.



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Q. Resources Debra Barrett Ogden Middle School Oregon City, Oregon 503-785-8300 Benntt, J., Burger, E.B. & Chard, D. J. Holt Mathematics: Course 3. Holt McDougal. Benntt, J., Burger, E.B. & Chard, D. J. Holt Mathematics: Teacher Resources. Holt McDougal. Benntt, J., Burger, E.B. & Chard, D. J. Holt Mathematics: Assessment. Holt McDougal. National Council of Teachers of Mathematics: http://www.nctm.org/ Oregon Public Education Network (OPEN)-Practice Scoring: http://www.openc.k12.or.us/scoring/ National Library of Virtual Manipulatives: http://nlvm.usu.edu/ Oregon Department of Education Math Scoring Guide


http://www.nctm.org/

http://www.openc.k12.or.us/scoring/

http://nlvm.usu.edu/


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