Title: Exploring Perimeter and Area Materials and Resources 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 Subject: Standard: Mathematics Measurement Grade: 5 Date: November. 2001 Unit Suggestions Math: Use with Unit 9 Lesson 10 in Evervdav Math Series Science Applications: Use with Scientific Inquiry controlling variables Notes: I Berea City School District Page 2
LESSON STUDY PLANNING CHART Title of Study Lesson: Ex~lorina Perimeter and Area Steps of the Lesson Allocated Time 1. Opening discussion (whole class) 5-10 min. 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. 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? Tell me about the measure we call area. How is it determined? What units are used to measure the area of a figure? Assessment Strategies In 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. Do figures with equivalent perimeters have the same areas? Do figures with equivalent areas have the same perimeters? Area, the amount of surface taken up by a figure, might be measured in square inches, square feet, square centimeters, etc. *Adapted from: Rectanus, C. (1997). Math by all means: Area and perimeter. Sausalito, CA: Math Solutions Publication.
LESSON STUDY PLANNING CHART Title of Study Lesson: Exolorinq Perimeter and Area Allocated Time (whole class) 5 min. Learning charts Learning Activities Anticioated Resoonse from Students Note taking on learning chart using both the notes and drawing sections Key Points and Specific Questions Review etymology of the words perimeter and I area. Perimeter: from the Greek peri (around) and meter (measure). Assessment Strategies What does the word periscope mean? What is the Gund Arena? Area: Latin for open field; related to arena (sandy field) 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 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. Have students repeat Step 3 on geoboards. Extension: Are there any other squares on the geoboard? 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? 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.
LESSON STUDY PLANNING CHART Title of Study Lesson: Ex~lorinQ Perimeter and Area Steps of the Lesson Allocated Time 5. Menu Activities 1-3 (small groups) 15 min. Centimeter-squared paper Rules Crayons Pencils Cuisenaire rods Learning Activities Anticipated Response from Students I *Menu Activity 1: Same Perimeter I *Menu Activity 2: Double the Perimeter *Menu Activity 3: Perimeter with Cuisenaire Rods Key Points and Specific Questions 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. Strategies for evidence that students understand the effects of changing shapes or dimensions on measures of perimeter and area. 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
LESSON STUDY PLANNING CHART Page 4 Title of Study Lesson: Ex~lorino Perimeter and Area Steps of the Lesson Allocated Time 6. Tyler's Squares (small groups) 20 min. Handouts p. 1 and p. 2. Crayons --- Learning Activities Anticipated Response 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. If 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. Key Points and Specific Questions 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. Assessment Strategies 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? I Can students write
Steps of the Lesson Allocated Time 7. Assessment 1 (individual) 10 min. Geodot paper Pencils Rulers 8. Reflection (individual) Learning charts Cravons 10 min. Title of Study Lesson: Learning Activities Anticipated Response 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. In the reflection box on the learning chart, students write about key points, understandings, questions, and applications of today's lesson. LESSON STUDY PLANNING CHART ExD~o~~~Q Perimeter and Area Key Points and Specific Questions 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. 1) How do the perimeters and areas of different shapes relate? / 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? I Assessment 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
Geoboard Dot Paper
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Geoboard Dot Paper
.............. a. a *. a........... e... ~.... i........**. a... a............. a o o r o a a TEACHER'S MASTERS 58 ~eodot Paper
Centimeter-Squared Paper 195
196 Inch-Squared Pa per