TEKS Lesson Plan/Unit Plan



Focus Plan

Texarkana Independent School District

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

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

|Grade(s): |10 |Time allotted for instruction: |3 class periods on block |

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|Title: |Dilations on 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 after a dilation of scale factor k. |

| | |

| | |

|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: | |

[pic]

|Concepts |Enduring Understandings/Generalizations/Principles |

| |The student will understand that |

|dilation |A transformation determined by a center point and a scale factor k. A dilation is a nonridgid |

| |transformation in that the shape will be a different size but similar. |

| |[pic] |

|reduction |A dilation where the image is smaller than the preimage. |

| |[pic] |

|enlargement |A dilation where the image is larger than the preimage. |

| |[pic] |

|congruence |A dilation where the image is equal to the preimage. |

| |[pic] |

|similar figures |Figures that have the same shape but may differ in size. |

|scale factor |The ratio of the lengths of two corresponding sides of two similar polygons. Sometimes referred to as |

| |the magnitude of a dilation. |

[pic]

I. Sequence of Activities (Instructional Strategies)

A. Focus/connections

1. Give each student a ruler, calculator, the worksheet Introduction to Dilations-Enlargements, and the worksheet Introduction to Dilations – Enlargements Worksheet. Teacher says,” Today we will discuss a different type of transformation. With a reflection and a translation the premiage and the image are exactly the same size or congruent. We will now explore a transformation where the size of the image and the preimage are different. You will be able to recognize the image because both will be similar figures . When the size of a figure changes, the figure can become larger which is called an enlargement or the figure can become smaller which is called a reduction. If a dilation occurs and the image is exactly like the preimage then a congruence relationship exists.” At this point the students are ready to begin the introduction. The teacher may choose to work through the activity with the students using overhead transparencies, or allow the students in groups or independently to work through the introduction. In any case the final conclusion must be carefully discussed. The sides will be twice as long. It is easy to fall into the trap of saying that the figure is “twice as big”. This statement is ambiguous. “Big” could be described as perimeter or area. It will be discussed with the students in a later lesson that while the sides grow by a scale factor of 2, the area will grow by a scale factor of 4.

Give each student the worksheet Introduction to Dilations-Reductions, and the worksheet Introduction to Dilations – Reductions Worksheet. At this point the students are ready to begin the second part of the introduction. The teacher may choose to work through the activity with the students using overhead transparencies, or allow the students in groups or independently to work through the introduction. In any case the final conclusion must be carefully discussed. The sides will be one-half as long. It is easy to fall into the trap of saying that the figure is “one half as big”. This statement is ambiguous. “Big” could be described as perimeter or area. It will be discussed with the students in a later lesson that while the sides shrink by a scale factor of one-half, the area will shrink by a scale factor of one fourth.

2. During these introduction activities many new symbols will be shown on the worksheets. Students must become familiar with these. At this time you may wish to discuss such symbols and make a list of them for the students. These include:

Points are always named with capital letters. Point P

Segments are named by their two endpoints written in either order.

segment PD (in mathematical symbols) [pic] or [pic]

measure segment PA ( in mathematical symbols) m[pic]

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 dilated in the coordinate system where the origin is the center of dilation. Using a scale factor, k, the student will express this pattern both verbally (written) and mathematical (symbols), and use this pattern to dilate figures in the coordinate system where the origin is the center of dialtion.

2. Procedures: Day 1, The student will

Complete the introduction lessons on enlargements and reductions.

Day 2, The student will

Discover the relationship of the scale factor, k, when dilations are preformed on the coordinate axis with the origin as the center of dilation.

The student will use this information when independently working Practice on Dilations.

The student will work Sample TAKS Questions on Dilations.

Day 3, The student will

Work Review on Reflections, Translations, and Dilations, and take a test on

Reflections, Translations, and Dilations.

3. Modeling: Day 1 the teacher will

• distribute calculators, rulers, and introductions sheets

• make sure each students completes and understands the two lessons on reductions and enlargements.

Day 2, the teacher will

• review students over concepts learned from day one

• make sure each student completes and understands the activity lesson on reductions and enlargements.

• help each student complete the practice sheet and sample TAKS questions

Day 3, the teacher will

• review the material with the students

• give an independent test

C. Guided activity or strategy

This has already been discussed.

D. Accommodations/modifications

Students needing extra time can complete Introduction activities outside of class.

E. Enrichment

Students can begin enrichment activity. They will need the enrichment worksheets.

II. STUDENT PERFORMANCE

A. Description

Day 1

Before class begins the teacher may assign students into pairs. Whole group may also be

used.

Day 2

Students should do the practice sheets on their own after the activity. The enrichment

activity can be used for any student. Be cautious of “copied” answers.

Day 3

The review and test should be accomplished in one class period.

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 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. Enrichment can be provided on this day.

C. Enrichment

Worksheet attached.

iii. Assessment of Activities

A. Description

Students will be assessed informally on the introduction and discovery activity by the

teacher circulating among the students making sure that each activity is completed

correctly. Students will have each answer on the Practice Activity checked for

accuracy and will be allowed to correct any wrong answers.

A formal assessment will be given in the form of a test where reflections,

translations and dilations are assessed.

B. Rubrics/grading criteria

The review should be carefully worked and discussed before students take

the test.

The test will be 9 multiple choice and one open response. There

are 3 forms of the quiz. The forms are not labeled, but the first listed coordinate on

question 1. is different on each form.. One of the forms may be used for a makeup test.

It is recommended that each multiple choice question be given a point value of 9 points.

The open response question would have a point value of 22. Each correctly graphed

point from the pre-image is given 3 points. Each correctly graphed image point given 3

points. Even if a student misses one of the original points, if the image for their point is

correct 3 points will be awarded. Four additional points are given if the students draw

and label the pre-image and image even if the pre-image and/or image points are

incorrectly graphed.. Total points on the quiz 103/100 allows for 3 built in bonus points.

The questions on the different are not all different. Some questions only have the irder if

the answers changed. The modified test is taken from form A.

C. Accommodations/modifications

TestM is modified with one less multiple choice problem and fewer choices.

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 translated using a scale factor when 0< k < 1?

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

you translated using a scale factor of k > 1?

F. Sample TAKS questions (attached)

IV. TAKS Preparation

A. Transition to TAKS context

The TAKS questions on transformations require the students to have a thorough knowledge of the concept of how figures are moved on the coordinate system. Students need to verbalize frequently when they are working with practice problems. Getting the correct answer is not sufficient. Constantly explain to students that in order to correctly answer TAKS questions they must be able to apply the concepts in new and different ways. Emphasize that they should not simply memorize how to work one type of problem but understand the relationships that are occurring. A true test is whether or not they could explain a problem to someone else. Each student should take turns trying to “teach a problem” to a member of their group.

B. Sample TAKS questions (attached)

V. Key Vocabulary

Dilation

Enlargement

Reduction

Scale Factor

Congruent

Similar

VI. Resources

A. Textbook Geometry by Glencoe

Chapter 13 lesson 8

Practice Masters from textbook lesson 13-8

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 should score at least 4/5 to be considered proficient on this lesson. Students not meeting this criteria should work the practice exercises. The Introduction and Discovery Activity may be necessary for the students.

B. Dilations are hard for students to understand. Do not be surprised by their confusion.

C. Four days may be required to complete this lesson along with the review and quiz.

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