bridging sequence - web view03.02.2013 · the student will solve word problems...

Theresa Goodwin MATH 1533.02 11/25/2013

Title: Perimeter with Polygons

Grade level: Third

Objectives:

The student will use rubber bands on geo boards to create the appropriate polygon with a given perimeter.

The student will draw appropriate geometric shapes on dot paper with a given perimeter.

The student will solve word problems involving perimeter of polygons and determine missing length when given

perimeter and remaining side lengths.

Prerequisite knowledge/skills: Students should have prior knowledge of the characteristics and

properties of two-dimensional geometric shapes. Students should have prior experience measuring with non-standard

and standard units. Students should have well-developed addition skills and at least

beginning multiplication skills.

TEKS: Chapter 111. Texas Essential Knowledge and Skills for Mathematics§111.5. Grade 3

(6) Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties. The student is expected to:

(B) use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

(7) Geometry and measurement. The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving customary and metric measurement. The student is expected to:

(B) determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems

Vocabulary: Perimeter: The distance around a two-dimensional shape


Polygon: Plane figures made up of three or more closed line segments

Instructional resources/materials: GeoBoards/Rubber Bands Geo Board Paper/Pencils Document Camera or other visualizer Dot Paper

Time frame: Three forty-five minute lessons

Group size: Whole-group, Pairs, and Individual

Concrete Level

Materials/Resources: Masking Tape Four Tape Measures Four new, unsharpened pencils One geo board for each pair of students Rubber bands for each student One overhead geo board Math Journals/Pencils Document Camera or other visualizer

Instructional Plan:1. (Teacher Preparation) Use masking tape to make a large square on

the carpet. 2. (Pre-Assessment) “How could we measure the distance around the

shape on the floor?”3. Have students examine the shape on the floor. Ask questions to elicit

responses; for example, “What tools could we use?” Invite students to share their thoughts and ideas.

4. (Teacher Facilitation) Explain to students that we have just explored ways to find the perimeter of an object. Write the word perimeter on the board and provide students with the definition. (See “Vocabulary” above) Have students record the word and definition in their math journals.

5. Hold a brief discussion to remind students of standard and non-standard units of measurement. (Standard: ruler, yardstick, etc. Non-standard: paperclip, footstep, etc.)

6. Invite four volunteers to measure the perimeter of the shape on the floor using a non-standard unit of measurement (pencil). Each student will measure one side of the square using the pencil to determine how


many units and then record their measurement on the board. A fifth volunteer will come to the board and add up the number of units on each side and record the perimeter as number of units total.

7. Invite four different volunteers to measure the perimeter of the shape on the floor using a standard unit of measurement (inch). Each student will measure one side of the square using a tape measure to determine how many inches and then record their measurement on the board. A fifth volunteer will come to the board and add up the number of inches on each side and record the perimeter as number of inches total.

8. Discuss the difference between the two methods used to measure the square and why standard units are beneficial.

9. Using the document camera (or other visualizer) display a geoboard and using a rubber band, create a 3x3 square. Tell students, “There are three ways that you can find the perimeter of this square.” Ask students to name ways they think it can be done. After hearing all responses, explain to students that you will now model each of the three ways for them.

10. Model counting each unit around the square. Remind students not to count the pegs, but rather, the space between the pegs. (12 units)

11. Model counting the units on each side of the square and then adding them up. (3+3+3+3 = 12 units)

12. Model using the formula 2L+2W. (2x3)+(2x3) = 6+6=12 units 13. Create another shape and invite students to help you to determine the

perimeter. Discuss. 14. Now ask students, “How could I make a shape that has a perimeter of

ten?” Model creating different shapes with a perimeter of ten and adding the distance around the figure.

15. (Student Application) Assign partners and provide each pair of students a geoboard and eight rubber bands of two different colors (4 of each color).

16. Students will work with their partner, taking turns, to create polygons with a perimeter of 8, 10, 12, 14, etc. Students should take turns creating as many polygons as they can with each perimeter and placing one rubber band on top of the other. When they can no longer create any new shapes with that perimeter, rubber bands are

removed and the process begins again for the next perimeter. 17. (Assessment) Walk around the room to observe students’ geo board

creations and check for accuracy. Assist any students who may be struggling with the concept.

Pictorial Level

Materials/Resources: Dot Paper Geo Board paper Worksheet (Resource 1)


Pencils Document camera or other visualizer

Instructional Plan:1. (Teacher Facilitation) Review the definition of perimeter with

students. Invite students to remind you of the three ways to find perimeter that we learned in the previous lesson. Discuss.

2. Explain to students that the activity we will be doing today is similar to the previous lesson. Remind students of previous lesson. Display overhead dot paper and model how to create a shape with a perimeter of “12” . . . and a perimeter of “8”.

3. (Student Application) Students will work independently to draw shapes with a given perimeter and to calculate perimeter of a given shape using Student Resource 1. (See Teacher Resource 1 for answer sheet.)

4. When all students have finished, ask for volunteers to share a few answers (Maybe #1-4 ) and discuss the many different shapes students were able to create with the same perimeter.

5. (Assessment) Students will turn in completed papers to the teacher at the end of class. Teacher will take note of students who achieved success with the independent activity and students who struggled to solve a variety of the problems and provide additional practice and assistance as needed.

Abstract Level

Materials Needed: Document Camera or other visualizer Grid Paper (Teacher Resource 2) Blank paper Marker Student/Teacher Resource 3

Instructional Plan:

1. (Pre Assessment) “What shape has four sides that are all the same length?” (Square) “What shape has two long sides that are the same length and two short sides that are the same length?” (Rectangle)


2. (Teacher Facilitation) Using the document camera or other visualizer, display “Teacher Resource 2” – only show the first square and first rectangle. Discuss with students the measurements of the square. Each side is three units. Then discuss the rectangle; both of the long sides are six units each and both of the short sides are two units each.

3. Next, show the second square and rectangle. “This square shows that the left side is four units. How can we determine the length of each of the remaining sides?” Discuss. Explain that the rectangle shows that the top is five units and the left side is one unit. “How long is the bottom? And the other short side?” Discuss.

4. On blank paper, draw a square and label one side as eight units. Ask students to provide the measurement of each remaining side. Discuss. Next, draw a rectangle and label one long side as seven units and one short side as three units. Ask students to provide the measurements for the remaining two sides. Discuss how they arrived at their answer.

5. Next, demonstrate a word problem: “If a square has a perimeter of eight inches, how long is each side?” (Two inches) Elicit responses from students and remind them that each side has to be the same length. Draw a square on the board and write “P=8 inches”. Discuss student responses until the correct answer is achieved.

6. (Student Application) Students will work independently to solve word problems involving perimeter. (Student/Teacher Resource 3)

7. (Assessment) Students will turn in completed word problems at the end of class for the teacher to review and determine which students, if any, require additional practice on this concept.


NAME_________________________________________________

PERIMETER WORD PROBLEMS (STUDENT RESOURCE 3)

1.) A rectangular countertop is 9 feet long and 5 feet wide. What is its perimeter?

2.) The perimeter of a square postage stamp is 8 inches. How long is each side of the postage stamp?

3.) A rectangular swimming pool is 10 meters wide and 17 meters long. What is its perimeter?

4.) The perimeter of a rectangular rug is 20 feet. The rug is 3 feet wide. How long is it?

5.) The perimeter of a rectangular roof shingle is 52 inches. It is 10 inches wide. How long is it?

NAME_________________________________________________


PERIMETER WORD PROBLEMS (TEACHER RESOURCE 3)

1.) A rectangular countertop is 9 feet long and 5 feet wide. What is its perimeter?

28 feet

2.) The perimeter of a square postage stamp is 8 inches. How long is each side of the postage stamp?

2 inches

3.) A rectangular swimming pool is 10 meters wide and 17 meters long. What is its perimeter?

54 meters

4.) The perimeter of a rectangular rug is 20 feet. The rug is 3 feet wide. How long is it?

7 feet

5.) The perimeter of a rectangular roof shingle is 52 inches. It is 10 inches wide. How long is it?

16 inches

DOT PAPER

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