math - berea city school district · menu activity 1 -students match single and double cuisenaire...

Title: Exploring Perimeter and Area Subject: Mathematics

Standard: Measurement

Grade: 5 Date: November. 2001

Geoboards rubber bands color tiles Unifix cubes pencils rulers Cuisenaire rods Geodot paper squared paper crayons chart paper or drawing paper Tyler's Squares handouts

Materials and Resources

Math: Use with Unit 9 Lesson 10 in Evervdav Math Series

Unit Suggestions

Science Applications: Use with Scientific Inquiry controlling variables

Notes: I

Berea City School District

Steps of the Lesson Allocated Time

1. Opening discussion (whole class)

5 - 10 min.

LESSON STUDY PLANNING CHART

Title of Study Lesson: Ex~lor ina Perimeter and Area

Tell me about the measure we call area. How is it determined? What units are used to measure the area of a figure?

Learning Activities Anticipated Response

from Students Opening discussion questions on perimeter and area.

Students may use translations to demonstrate a new figure. Encourage them to find figures that have different dimensions.

Do figures with equivalent perimeters have the same areas?

Key Points and Specific Questions

Assess prior knowledge about the measures of perimeter and area:

*Al and Mary use rabbit fencing around their garden. Next year they want to plant a bigger garden. Will they need more fencing? Explain.

Tell me about the measure we call perimeter. How is it determined? What units are used to measure the perimeter of a figure?

Do figures with equivalent areas have the same perimeters?

*Adapted from: Rectanus, C. (1997). Math by all means: Area and perimeter. Sausalito, CA: Math Solutions Publication.

Assessment Strategies

I n general, students will be more successful if they understand that perimeter is a linear measure and area is measured in square units.

Perimeter units might be inches, fee, yards, miles, cm, m, km, etc.

Area, the amount of surface taken up by a figure, might be measured in square inches, square feet, square centimeters, etc.

Allocated Time

(whole class) 5 min.

Learning charts

3. Drawing squares and determining perimeters and areas.

(whole class) 10 min.

4. Using geoboards to represent Terms 1-4.

(small groups) 5 min.

Geoboards Rubber Bands


Title of Study Lesson: Exolorinq Perimeter and Area

from Students Note taking on learning chart using both the I Review etymology of the words perimeter and

Learning Activities Anticioated Resoonse

notes and drawing sections I area.


Perimeter: from the Greek peri (around) and meter (measure).

Area: Latin for open field; related to arena (sandy field)

Students draw 1 x 1; 2 x 2; 3 x 3; and 4 x 4 grids on their learning charts. Use the word term to label each drawing: Term 1; Term 2, Term 3, Term 4.


Discussion of units of measure for perimeter (linear) and area (square units).

What is a unit? What is a square unit? Can these units vary in size?

Have students repeat Step 3 on geoboards.

Extension: Are there any other squares on the geoboard?

What does the word periscope mean? What is the Gund Arena?

Geoboards help us to keep the units and square units a consistent size.

Extension: Create a new table for the four terms:

Have students do a table of perimeters and areas for all four terms. Look for patterns.

Look for patterns.


Title o f Study Lesson: Ex~lorinQ Perimeter and Area

5. Menu Activities 1-3

(small groups) 15 min.

Centimeter-squared paper

Rules Crayons Pencils Cuisenaire rods


from Students I *Menu Activity 1:

Learning Activities Key Points and Specific Questions Anticipated Response

I Same Perimeter

*Menu Activity 2: Double the Perimeter

*Menu Activity 3: Perimeter with Cuisenaire Rods

activities. Groups report back to the large group summarizing their activity and findings.

Menu Activity 1 -Students match single and double cuisenaire rods with matching perimeters.

Menu Activity 2 - Students create a table to record perimeters and areas after pairing single and double cuisenaire rods. The double rods must double both the length and width of the matching rod.

Menu Activity 3 - Using one red rod, two light green rods, and one purple rod to create various fiaures, students discover the shaoes with the

Strategies

for evidence that students understand the effects of changing shapes or dimensions on measures of perimeter and area.


6. Tyler's Squares (small groups)

20 min. Handouts p. 1 and

p. 2. Crayons

Page 4 LESSON STUDY PLANNING CHART

Title of Study Lesson: Ex~lor ino Perimeter and Area

---


from Students Application activity using perimeter and area skills.

Students use p. 1 to draw floor models and p. 2 to record in table form their findings.

I f students color the border tiles one color and the interior tiles a different color, it will be easier to see the patterns.

Call on students to explain how the patterns in the table can help to determine the number of tiles needed in a floor of size n units by n units and the length of the metal border strip.

I Can students write


Tyler has been hired to install a ceramic tile floor in the center of a large carpeted banquet mom. Special border tile will be used to accent the interior tiles and a metal strip must be installed to create a seam between the tile and the carpet. The tile floor is to be square in shape.

What information does Tyler need to complete the project? (e.g. What size will the square tile floor be? Unknown . . . How big are the tiles? 1 foot x 1 foot.)

Prepare drawings and a table to show various size floors, the number of border and interior tiles needed, and the length of the metal strip.


Although students should explore floors with various dimensions: 3 x 3 ;4x4 ;6x6 ;8x 8; 10 x 10; etc., the goal is to construct a formula for any size floor (n x n).

Explore patterns in the table.

Can students determine a pattern for each successive or recursive term?


Title o f Study Lesson: E x D ~ o ~ ~ ~ Q Perimeter and Area

8. Reflection (individual) Learning charts Cravons


7. Assessment 1 (individual) 10 min. Geodot paper Pencils Rulers

10 min.

I n the reflection box on the learning chart, students write about key points, understandings, questions, and applications of today's lesson.


from Students The first assessment requires students to draw specific rectangles to given measures of perimeter and area.

This is a two-part assessment. Students should draw figures with perimeters of 16 units, then draw a new set of figures with areas of 24 square units.

1) How do the perimeters and areas of different shapes relate?


On Geodot Paper draw label as many rectangles as possible with:

1) a perimeter of 16 units ... ... then:

2) an area of 24 square units.

Label the perimeter and area of each rectangle for both activities.

/ 2) What did you learn today?

3) When do people use perimeter and area in real life applications?

1 4) What don't you understand about perimeter and area?

Assessment I Strategies

attribute of this assessment is the student's ability to keep one measure constant while changing the other measure by varying the dimensions of the figure.

Would Al and Mary need more fencing?

Is this true in all cases?

Names:

TYLER'S SQUARES

Complete this table as your grow attaches each square to your project paper.

TYLER'S SQUARES

Geoboard Dot Paper

Name

j / i .:. ::: :::

, i i j j ::: . . . iji j / j ::: :,: :j:

. . . . . / i /

TEACHER'S MASTERS Blank Geoboards

Geoboard Dot Paper

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . a . a * . a .

. . . . . . . . .

. . . . . . . . . . TEACHER'S MASTERS

. e . . . ~ . . . . i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . * * . a . . . . . . . . . . .

a . . . . . . . . . .

. . . a o o r o a • a

58 ~ e o d o t Paper

Centimeter-Squared Paper 195

196 Inch-Squared Pa per

math - berea city school district · menu activity 1 -students match single and double cuisenaire...

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