TEKS Lesson Plan/Unit Plan



Focus Plan

Texarkana Independent School District

|GRADING PERIOD: |1st six weeks |PLAN CODE: |10M6 reflections |

|Teacher: |Dottie Johnson |Course/subject: |Math 10 |

|Grade(s): |10 |Time allotted for instruction: |2 class periods on block |

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|Title: |Reflections in the Coordinate Plane |

|Lesson TOPIC: |Students discover the relationships of the (x, y) coordinates of the pre-image and the (x, y) |

| |coordinates of the image of reflections over the x-axis; y-axis; and line y=x. |

| | |

| | |

|TAKS Objective: |Objective 6: The students will demonstrate an understanding of geometric relationships and |

| |spatial reasoning. |

|FoCUS TEKS and Student Expectation: |8.6(B) Geometry and spatial reasoning. The student uses transformational geometry to develop |

| |spatial sense. The student is expected to graph dilations, reflections, and translations on a |

| |coordinate plane. |

|Supporting TEKS and Student Expectations: |8.6(D) Geometry and spatial reasoning. The student uses geometry to model and describe the |

| |physical world. The student is expected to locate and name points on a coordinate plane using |

| |ordered pairs of rational numbers. |

|aligned TEKS and Student Expectations for | |

|modifications: | |

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|Concepts |Enduring Understandings/Generalizations/Principles |

| |The student will understand that |

|Reflection over the |When an image is reflected over the x-axis in the coordinate plane, the x-values of the points from the|

|x-axis |pre-image to the image stay the same, while the y-values take on opposite values. |

| |Mathematically stated: (x, y) [pic] (x, -y) |

|Reflection over the |When an image is reflected over the y-axis in the coordinate plane, the x-values of the points from the|

|y-axis |pre-image to the image take on opposite values, while the y-values stay the same. |

| |Mathematically stated: (x, y)[pic](-x, y) |

|Reflection over the line y=x |When an image is reflected over the line y=x in the coordinate plane, the x and y values of the |

| |pre-image to the image are reversed. |

| |Mathematically stated: (x, y)[pic](y, x) |

|a) Reflection of a figure |a) A reflection of a figure is the mirror image of the figure across a line. |

|b) Line of reflection |b) The line that an image is reflected across. |

|pre-image |The original image that will be transformed. |

|image |The image after the transformation has taken place. |

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[pic]I. Sequence of Activities (Instructional Strategies)

A. Focus/connections

1. Give each student a small piece of patty paper. (Demonstrate this activity on a large

sheet of patty paper as you move around the room and are asking the students to

follow your directions.) Teacher: Print your name in the middle of the paper. Fold the

paper so that your name appears through the paper on the other side. Make a crease at

this fold. Copy your name on the other side. Open the paper and trace your name again

to create a reflection over the crease. The crease is called the “line of reflection”

label this on your paper. The first time you wrote your name is called the “pre-image”

and the reflection is called the “image”. Write these terms on your paper.

2. Geometry is not only the study of figures; it is also the study of the movement of figures. If you move the points of a figure according to a certain set of rules, then the new figure will look exactly like the original but be in a different location. This concept is extremely important in the world of robotics where a slight movement on a joy stick causes a change in the position of a robotic arm. Since the computer must give an exact location to the robotic arm, the transformations or moves are made on a coordinate system (place coordinate system on overhead). The moves must be figured using a set of rules using the points on the graph (coordinates). Today we will discover the changes in the coordinates needed to reflect a figure over the x-axis, the y-axis, and the line y=x.

B. Instructional activities

(demonstrations, lectures, examples, hands-on experiences, role play, active learning experience, art, music, modeling, discussion, reading, listening, viewing, etc.)

1. Objectives: The student will discover a pattern between the coordinates of the pre-image and the image of a figure reflected in the coordinate system, express this pattern both verbally (written) and mathematical (symbols), and use this pattern to reflect figures in the coordinate system.

2. Procedures: Day 1, The student will

• draw a figure (pre-image) on graph paper given a set of coordinates.

• use patty paper to trace the figure and the line of reflection.

• reflect the image over the line of reflection ( x-axis, y-axis, or y=x).

• use the push pin to make holes through the patty paper to show where the vertices of the image will be located.

• draw the image.

• record the coordinates of the image.

• find a pattern from the pre-image to the image for each type of reflection.

• express this pattern verbally (written) and mathematically (symbols).

Day 2, The student will

• review rules discovered on day one activity.

• practice rules by working Practice on Reflections. Only the new rules will be used.

3. Modeling: Day 1 the teacher will

• distribute Discovery Activity on Reflections, 3 sheets of full graph paper, one foam board (about 8” x 8”), one push pin, and 3-4 small squares of patty paper to each student

• complete the first table with the students allowing the students to complete as much as possible on their own

Day 2, the teacher will

• review students over concepts learned from Discovery Activity on Reflections

• work the first activity on the Practice On Reflections with the students. Only the new rules learned will be used. No patty paper or foam board may be used.

C. Guided activity or strategy

Day 1: Students will complete table two and table three on their own. The teacher will walk among the students looking at their work, giving instant feedback, and helping as needed. When students have finished the tables, a group discussion should follow on the patterns found for reflection over the x-axis, y-axis, and line y=x, in both verbal and mathematical form. Emphasize that the patty paper, foam board, and push pin are only used as tools to help discover the rules. In the future, all reflections will be worked using the rules. This should complete day one.

D. Accommodations/modifications

Students needing extra time can complete Discovery Activity on Reflections outside of class.

E. Enrichment

Students can complete enrichment activity.

II. STUDENT PERFORMANCE

A. Description

Day 1

Before class begins the teacher may assign students into pairs. This depends on how

familiar the teacher is with each student. Since this is the beginning of the year, it might be

wise to allow the students to do this first lesson independently. Students finishing quickly

may go on to do the enrichment activity or may be asked to provide one –on – one peer

tutoring for those obviously needing help.

Day 2

Students should do the practice sheets on their own after the review and guided practice.

B. Accommodations/modifications

Day 1

All students should be able to handle this activity given extra time. Working in pairs would

be helpful so students with modifications could have peer tutors. Students finishing quickly

may go on to do the enrichment activity or may be asked to provide one –on – one peer

tutoring for those obviously needing help.

Day 2

Again, students with modifications may need a peer-tutor to help them complete this

activity.

C. Enrichment

Some students will complete the worksheet very quickly. These students should

complete the enrichment page.

iii. Assessment of Activities

A. Description

Students will be assessed informally on worksheet 1, a discovery activity, by the teacher

circulating among the students making sure that each activity is completed correctly.

Students will have each answer on worksheet two checked for accuracy. The student will

be allowed to correct any wrong answers since worksheet 2 is a practice activity.

B. Rubrics/grading criteria

No formal independent assessment on this lesson.

C. Accommodations/modifications

Some students complete only 2, 3, and 5 form worksheet two.

D. Enrichment

Bonus for any students completing enrichment activity correctly.

E. Sample discussion questions

1. What pattern did you discover in the coordinates of the pre-image to the image when

you reflected an image over the x-axis?

2. What pattern did you discover in the coordinates of the pre-image to the image when

you reflected an image over the y-axis?

3 What pattern did you discover in the coordinates of the pre-image to the image when

you reflected an image over the line y=x?

F. Sample TAKS questions (attached)

IV. TAKS Preparation

A. Transition to TAKS context

These will be discussed in detail when the three lesson on transformations

are completed.

B. Sample TAKS questions (attached)

V. Key Vocabulary

Reflection

Line of reflection

Coordinate system

x-axis, y-axis

image

pre-image

VI. Resources

A. Textbook Geometry by Glencoe

Chapter 13 lesson 5

Practice Masters from textbook lesson 13-5

B. Supplementary materials

Discovering Geometry by Michael Serra

Chapter 8

C. Technology

VII. follow up activities

(reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.)

VIII. Teacher Notes

A. For a class of 10th grade Algebra Ii Students, give the sample TAKS questions first. Students not scoring 2/2 should work part or all of the practice on Reflections. The Discovery Activity should not be necessary with these students.

B. When plotting points with students be sure to label and name the four different quadrants on the coordinate system.

C. When drawing the line y=x, students will need help in remembering how to graph lines on the coordinate system without using a graphing calculator. Introduce the term “parent function” in discussing the most basic of all linear functions, y=x. A table of values would then be useful be find points on the line.

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