Focus Plan
Texarkana Independent School District
GRADING PERIOD: / 4th Six Weeks / PLAN CODE:Teacher: / Tipton / Course/subject: / Mathematics
Grade(s): / 8 / Time allotted for instruction: / 1 – 1 ½ hours
Title: / Are They Similar?
Lesson TOPIC: / Proportional relationships
TAKS Objective: / Objective 4: The student will demonstrate an understanding of the concepts and uses of measurement.
FoCUS TEKS and Student Expectation: / (9) Measurement. The student uses indirect measurement to solve problems. The student is expected to:
(B) use proportional relationships in similar shapes to find missing measurements
Supporting TEKS and Student Expectations: / (3) Patterns, relationships, and algebraic thinking. The student identifies proportional relationships in problem situations an solves problems. The student is expected to:
(A) compare and contrast proportional and non-proportional relationships
Concepts / Enduring Understandings/Generalizations/Principles
The student will understand that
Polygon / A polygon is a simple, closed figure in a plane formed by three or more sides.
Similar Polygons / Two polygons are similar if their corresponding angles are congruent and their corresponding sides are in proportion. Similar polygons have the same shape, but may not have the same size.
Proportion / A proportion is a statement of equality of two or more ratios.
I. Sequence of Activities (Instructional Strategies)
A. Focus/connections
After students are seated, place one square pattern block on the overhead. Ask students to describe what they see. Next, use three more of the pattern blocks to show that four squares can be combined to create a new square that is similar to the original square. Ask students to describe what it means when objects are similar. Place student statements on the board.
B. Instructional activities
(demonstrations, lectures, examples, hands-on experiences, role play, active learning experience, art, music, modeling, discussion, reading, listening, viewing, etc.)
Now tell the students that the side of one of the smaller squares has a length of 8 cm. Ask the class to predict what the perimeter of the larger square formed by the four smaller squares would be. Discuss how the perimeter and area of the larger square compares to the perimeter and area of the smaller square. Next place the following words on the board and ask the class help you to define them:
polygon, similar polygon, proportion
Leave the words and definitions on the board for remainder of class. Emphasize that polygons are similar if their corresponding angles are congruent and their corresponding sides are in proportion. Next draw the following similar figures on the board and label:
D H
8 ft
12 ft C
4 ft G
A B 6 ft
E F
21 ft
Ask students how they could find the length of side AB. After students have been given time to brainstorm, place the following proportional equation on the board:
BC FG 4 6
BA = FE Substitute values from the quadrilaterals x = 21
Find the cross product: (4)(21) = 6x
84 = 6x
x = 14
The length of side AB is 14 feet.
Now that you know the length to AB, help students find the length of the remaining sides of polygon EFGH. Make sure students understand the proportional relationship between similar polygons.
C. Guided activity or strategy
Place the following on the board:
Tell the class the triangles you have put on the board are similar. Have students (on scratch paper) set up a proportion to solve for x. Monitor as students are solving. After students have been given time to solve the problem, discuss the correct answer with the class.
D. Accommodations/modifications
Students requiring modifications may be paired with a peer to complete the guided activity.
E. Enrichment
II. STUDENT PERFORMANCE
A. Description
Students will complete the Are They Similar? Worksheet individually.
B. Accommodations/modifications
If students are having trouble with the concepts in this lesson, they may be paired with a peer to complete the Are They Similar? Worksheet. This will allow for peer tutoring.
C. Enrichment
As needed, students requiring enrichment may be used to teach the concepts of this lesson in a small group class setting.
iii. Assessment of Activities
A. Description
Individual student grades may be taken on the Are They Similar? Worksheet.
B. Rubrics/grading criteria
Grades may be taken based on the Are They Similar? Worksheet Answer Key and Grading Rubric.
C. Accommodations/modifications
D. Enrichment
E. Sample discussion questions
· What real world applications would you use what you learned in this lesson today?
· Why is it important to know how to utilize proportions?
· How can you tell if two polygons are similar?
IV. TAKS Preparation
A. Transition to TAKS context
The teacher will lead the students in a discussion of how proportional problems with similar shapes may look in test format by placing the following TAKS questions on the overhead/board.
B. Sample TAKS questions
1. Trapezoid STUV is similar to trapezoid NOPQ.
Q
18 cm N
U V
6 cm
12 cm
O
T S
14 cm
P
What is the length of OP?
F. 4 2/3 centimeters
G. 5 1/7 centimeters
H. 28 centimeters
J. 36 centimeters
2. r EFG is similar to rHJK.
F 21 G
J ? K
10.5
3.5
E H
Find the length of JK.
A. 3 units
B. 7 units
C. 14 units
D. 24.5 units
3. Rectangle I is similar to rectangle II.
Rectangle I Rectangle II
6 cm
18 cm
The area of rectangle II is 216 square centimeters. Find the area of rectangle I.
A. 4 cmˆ
B. 12 cmˆ
C. 24 cmˆ
D. 108 cmˆ
V. Key Vocabulary
Polygon, Similar Polygons, Proportion
VI. Resources
A. Textbook
Glencoe Mathematics ~ Applications and Connections
Chapter 8: Applying Proportional Reasoning
· Similar Polygons, pp. 357 – 360
· Extra Practice, Lesson 8-7, pp. 629
· Extra Practice, Lesson 8-8, pp 629
B. Supplementary materials
· Are They Similar? Worksheet
· Are They Similar? Worksheet Answer Key and Grading Rubric
C. Technology
For reinforcement, students could be taken to the computer lab to utilize objects from the MS Word Drawing toolbar for the following:
· Construct similar figures
· To continue to make decisions about whether figures are similar based upon constant angle measurements and ratios between two sides of the same figure
· To continue to build understanding of angles as measures of rotation
· To create problems involving scaling and its effects on side lengths and area
· To manipulate figures visually to ensure understanding of proportional concepts
Have students create similar figures, label and print. Compile all created and let the class work together to solve.
VII. follow up activities
(reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.)
A lesson introducing indirect measurement would be a good follow-up for this lesson
VIII. Teacher Notes
Students may be a little rusty on the concepts of perimeter and area. Ask questions frequently throughout this lesson to assess understanding.
¨ Division of Curriculum and Instruction ¨ School Improvement Department ¨ Texarkana Independent School District