Area Among Friends Grade Level or Special Area: 5 th Grade Written by: Patricia Johnson, Sue Platt, Diadra Williams, E Lisa Young, Hardy Oak Elementary, San Antonio Length of Unit: 6 lessons I. ABSTRACT A. The purpose of this unit, Area Among Friends, is to integrate the Core Knowledge math sequence with hands-on activities. This is a unit on area concepts with a variety of activities, which include problem-solving projects. Students will be engaged in computing the area of rectangles, triangles, parallelograms, and irregular figures. Assessments will be based on students ability on computing oral and written formats. Rubrics and activities will be used to assess students progress. II. III. OVERVIEW A. Concept Objectives 1. The students will develop the concept of area pertaining to geometric figures. 2. The students will apply and demonstrate the concept of area in practical settings. B. Content from the Core Knowledge Sequence 1. Review the formula for the area of a rectangle, page 125 2. Find the area of triangles, using the formula A= ½ (b x h), page 125 3. Find the area of a parallelogram using the formula A = b x h, page 125 4. Find the area of an irregular figure by dividing into regular figures for which you know how to find the area, page 125 C. Skill Objectives 1. Students will review the formula for finding the area of a rectangle. 2. Students will use the formula A = l x w to compute the area of rectangle. 3. Students will apply the formula A = ½ (b x h) to find the area of triangles. 4. Students will use the formula for area of a parallelogram, A= b x h, to solve problems. 5. Students will be able to break irregular figures into known shapes to find the area. BACKGROUND KNOWLEDGE A. For Teachers 1. Rectanus, Cheryl. Math By All Means: Area and Perimeter. Math Solutions Publications, 1997 0-941-355-18-7 2. Hirsch, Jr. E.D. What Your Fifth Grader Needs to Know. Core Publications, Inc. 1992 0-385-31260-1 B. For Students 1. Addition 2. Multiplication 3. Knowledge of Geometric Shapes 4. Knowledge of Formula for Area of Rectangles Fourth Grade 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 1
IV. RESOURCES A. Manipulatives for each lesson color tiles, geometric pattern blocks B. Spaghetti and Meatballs for All! A Mathematical Story written by Marilyn Burns C. The Greedy Triangle written by Marilyn Burns D. Overhead E. Chart paper F. Construction Paper G. Inch graph paper H. Food items bread, peanut butter V. LESSONS VI. Lesson One: Review finding the area of a rectangle A. Daily Objectives 1. Concept Objective(s) a. The students will develop the concept of area pertaining to geometric figures. b. The students will apply and demonstrate the concept of area in practical settings. 2. Lesson Content a. Students will review the formula for finding the area of a rectangle. 3. Skill Objective(s) a. Students will review the formula for finding the area of a rectangle A= l x w B. Materials 1. Color Tiles 2. One inch graph paper 3. Construction paper cut to 8 ½ x 10 size 4. Chart paper 5. Appendix A C. Key Vocabulary 1. Area The number of square units needed to cover the surface of a figure. 2. Rectangle A polygon with 4 sides and 4 right angles. 3. Length The measured distance of an object from end to end. 4. Width The measured distance of an object from side to side. D. Procedures/Activities 1. Teacher will pose the following problem to students. My kitchen floor is hideous and I want to put some new tile down. I need to tell the contractor how much tile to purchase, how do I find this out? Lead the class into discussion on strategies to solve this dilemma. 2. Teacher will introduce/review vocabulary. 3. Teacher will place students into groups to solve the leading problem. 4. Teacher will give each group a bucket of color tiles and large construction paper, representing the floor. 5. Teacher will have students estimate the number of color tiles that will be needed to cover the sheet of construction paper (floor). Chart responses. 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 2
VII. 6. Students will work cooperatively to solve the problem. 7. Teacher will lead a discussion that the number of tiles used is the area of the paper (floor). Show the students that length times width will equal the area. 8. Students will record in their math journal what was learned today. (Appendix A) E. Assessment/Evaluation 1. Students will turn in their math journal so teacher can check understanding. Lesson Two: Guests for dinner A. Daily Objectives 1. Concept Objective(s) a. The student will apply and demonstrate the concept of area in a practical setting. 2. Lesson Content a. Find the area of a rectangle. 3. Skill Objective(s) a. Students will use the formula A= l x w to compute the area of a rectangle. B. Materials 1. Spaghetti and Meatballs for All! A Mathematical Story 2. Math By All Means Area and Perimeter Grades 5-6 3. Inch-squared paper 4. Inch-square color tiles 5. Overhead color tiles 6. Overhead 7. Appendix A 8. Appendix B C. Key Vocabulary 1. Area The number of square units needed to cover the surface of a figure 2. Rectangle A 4 sided polygon with 4 right angles 3. Perimeter The distance around a figure 4. Square specific kind of rectangle with four equal sides 5. Congruent Same size and same shape. 6. Length The measured distance of an object from end to end. 7. Width The measured distance of an object from side to side. D. Procedures/Activities 1. Teacher pose a problem to the students, Your teacher is in charge of a setting up tables and chairs for a charity function. Your teacher needs to find out the best possible way to arrange chairs and tables to seat twenty guests. How could I figure out this problem? Lead the class into a discussion about how they could solve this problem. 2. Read aloud Spaghetti and Meatballs for All! A Mathematical Story. 3. Discuss the problems and solutions stated in the book. 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 3
4. Teacher will use overhead color tiles to illustrate the first problem that appears in the book. Discuss the length and width of the table/tiles. Review concept of perimeter. 5. While creating the arrangements stress to the students that the entire side of the color tile must touch. (Not corner to corner) Discuss how to count how many people sit at the table each side represents a chair/person. 6. Have the students use twelve color tiles to create tables/arrangements to sit as many guests possible. Students may only build rectangular tables with the color tiles. 7. Discuss arrangements of tiles. Create a chart of arrangements. Label the length and width of each table. 8. Have the students create table arrangements with two more tiles. How many guests with 14 tiles? 9. Teacher asks students ways of find out how many tiles we may need to accommodate thirty-two guests. Students work with a partner to solve the problem. 10. Students will draw the arrangements of tables sitting thirty-two guests. Teacher walks around observing students work. 11. Lead the class discussion about arrangements seen in the room. E. Assessment/Evaluation 1. Students will answer the following question in their math journals. What were the patterns that you noticed while working on the problem? How many different arrangements were made to accommodate thirty-two guests? Draw and label the length and width of each arrangement. 2. Teacher will check math journal for understanding. 3. Students will complete Appendix B for assessment. VIII. Lesson Three: Triangles A. Daily Objectives 1. Concept Objective(s) a. The students will develop the concept of area pertaining to geometric figures. 2. Lesson Content a. Find the area of triangles, using the formula A= ½ (b x h) 3. Skill Objective(s) a. The students will be able to apply the formula A = ½ (b x h) to find the area of triangles. B. Materials 1. Bread 2. Peanut Butter creamy 3. Rulers 4. Plastic knife 5. Napkins 6. Appendix A C. Key Vocabulary 1. Triangle polygon with three sides D. Procedures/Activities 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 4
IX. 1. Begin with a review discussion about finding the area of a rectangle. 2. Pass out two slices of bread to each student, and put a bowl of peanut butter & a bowl jelly on each table with plastic knives. Have students make a sandwich and leave it on a paper napkin in front of them. 3. Ask students to measure the length and the width of the sandwich and to compute the area of the sandwich. 4. Next have the students cut the sandwich in half diagonally. Ask the students what is the area of one half of the sandwich. 5. Brainstorm with the students how you can show the area of the triangle mathematically. Reminding them as needed that they are finding ½ of the rectangle that they started with. Guide them into A= ½(l x w), then explaining that the length is the base and the width, making it A = ½ (b x h). 6. Give students several more examples on the overhead, working them together. E. Assessment/Evaluation 1. Students will write in their math journal about today s lesson. (Appendix A) 2. Teacher will check math journal for understanding. Lesson Four: Parallelograms A. Daily Objectives 1. Concept Objective(s) a. The students will develop the concept of area pertaining to geometric figures. 2. Lesson Content a. Find the area of a parallelogram 3. Skill Objective a. Students will use the formula for area of a parallelogram to solve problems. A = b x h B. Materials 1. Several rectangular shapes from construction paper 2. Appendix A 3. Appendix C C. Key Vocabulary 1. Parallelograms A 4-sided polygon in which each pair of opposite sides are parallel. D. Procedures/Activities. 1. Teacher will review how to find the area of a rectangle on the overhead. 2. Teacher will discuss the shape of a parallelogram and show several different assortments of parallelograms. 3. Teacher will ask the students how could we figure out the area of parallelograms, and brainstorm (using the overhead) methods that can be used. 4. Lead the discussion so that students will discover that there is a rectangle in the middle of two triangles. 5. Teacher will pass out two different parallelograms per group. 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 5
6. Have students fold the parallelogram showing only the rectangle with two triangles folded back. 7. Students will cut one of the triangles off of the rectangle. Then unfold the other triangle and tape the first triangle on to form a new rectangle. 8. Students will measure and compute the area of the rectangle. 9. Teacher will show the students on the overhead how to draw the line for height without cutting the paper. 10. Teacher will show different problems on the overhead and students will solve problems with a partner. E. Assessment/Evaluation 1. Students will find the area of parallelograms on Appendix C. 2. Students will make notes in math journal about parallelograms. Teacher will check math journal for understanding. X. Lesson Five: Irregular Shapes A. Daily Objectives 1. Concept Objective a. Students will develop the concept of finding area for irregular shapes. 2. Lesson Content a. The students will find the area of irregular shapes. 3. Skill Objective a. Students will be able to break irregular figures into known shapes to find the area. B. Materials 1. Appendix A 2. Appendix D 3. Geometric Shape Pattern blocks 4. Butcher paper 5. Pre-cut trapezoids construction paper C. Key Vocabulary 1. Trapezoid A quadrilateral with two parallel sides D. Procedures/Activities 1. Teacher will hold up a large trapezoid made from butcher paper. 2. Lead the discussion on how to find the area of this shape by using what we know about triangles and rectangles. 3. Pass out pre-cut trapezoid manipulatives. Students will manipulate the trapezoid to form two triangles and a rectangle. Students will measure the length, width, and height of the shapes to calculate the area of the trapezoid. 4. Teacher will discuss with the students the area of their trapezoids. 5. Post all trapezoids on a chart to show the ways the trapezoids were folded to find the area of the triangles and rectangles. 6. Teacher will use the overhead to have the students solve area problems with trapezoids. E. Assessment/Evaluation 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 6
1. Students will complete the worksheet on trapezoids. (Appendix E) 2. Students will reflect in their math Journal. (Appendix A) XI. Lesson Six: Irregular Shapes, Part 2 A. Daily Objectives 1. Concept Objective a. Students will develop the concept of finding area for irregular shapes. 2. Lesson Content a. The students will find the area of irregular shapes. 3. Skill Objective a. Students will be able to break irregular figures into known shapes to find the area. B. Materials 1. Pattern blocks 2. Butcher paper 3. Pre-cut hexagon construction paper 4. Appendix E 5. Appendix F 6. Appendix G C. Key Vocabulary 1. Hexagon A polygon with 6 sides D. Procedures/Activities 1. Teacher will hold up a large hexagon made from butcher paper. 2. Lead the discussion on how to find the area of this shape by using what we know about triangles, rectangles, and trapezoids. 3. Pass out pre-cut hexagon manipulatives. Students will manipulate the hexagon to form two trapezoids. Students will measure the length, width, and height of the shapes to calculate the area of the hexagon. 4. Teacher will discuss with the students the area of their hexagon. 5. Post all hexagons on a chart to show the ways the hexagon were folded to find the area of the trapezoid. 6. Review the formulas for all shapes discussed in this unit. 7. Students will complete the Flipbook during the review. (Appendix E/F) 8. Students will have time to explore the pattern blocks to make connections between the shapes and area. 9. Students will create a design using only six pattern blocks. Students will be expected to find the area for their design. 10. Teacher will monitor the students work and discuss the strategies used to find the area of their design. 11. Teacher will lead a whole class discussion on the designs that were seen around the room. Discuss the strategies used to find the area of the designs. 12. Allow time in class to complete the assessment activity. E. Assessment/Evaluation 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 7
1. Students will use the cardstock shapes to create a design and calculate the area of their design. (Appendix G) XII. CULMINATING ACTIVITY A. Design a dream home using the rubric 1. Teacher will read The Greedy Triangle to the class to review shapes. 2. Teacher will then explain to students that they are going to design their Dream House. On the overhead place a transparency of the grid (Appendix H) Tell the students that they can design the house any way they would like to, using any number or rooms, but they must use at least 2 rectangle/square room, 2 triangle room, 2 parallelogram room and 2 irregular shaped rooms. 3. After drawing the house students are to calculate the area for each room and then for the whole house 4. Post house plans to share with others. XIII. HANDOUTS/WORKSHEETS A. Appendix A Math journal B. Appendix B - Rectangles C. Appendix C - Parallelograms D. Appendix D - Trapezoids E. Appendix E Flip book rubric F. Appendix F- Flip book G. Appendix G Shapes H. Appendix H Rubric for House Design I. Inch squared paper - Rectanus, Cheryl. Math By All Means: Area and Perimeter. Math Solutions Publications, 1997 0-941-355-18-7, p. 196 XIV. BIBLIOGRAPHY A. Rectanus, Cheryl. Math By All Means: Area and Perimeter. Sausalito, CA: Math Solutions Publications, 1997. 0-941-355-18-7 B. Hirsch, Jr. E.D. What Your Fifth Grader Needs to Know. New York, NY:Core Publications, Inc. 1992 0-385-31260-1 C. Burns, Marilyn. Spaghetti and Meatballs for All! New York, NY: Scholastic Press, 1997. 0-590-94459-2 D. Burns, Marilyn. The Greedy Triangle. New York, NY: Scholastic Press, 1994. 0-590-48991-7 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 8
Appendix A Area Journal Name Rectangle Square 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 9
Appendix A Triangle Parallelogram Trapezoid Hexagon 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 10
Appendix B Use your ruler (centimeters) to find the area for the rectangles below. 1. 2. 2. 4. 5. 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 11
Appendix C Use your ruler (centimeters) to find the area for the parallelograms below. 3. 2. 3. 4. 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 12
Appendix D Use your ruler (centimeters) to find the area for the trapezoids below. 4. 2. 3. 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 13
Appendix E Area Among Friends Name Date: Area Flipbook Rubric You will create a flipbook that will contain the formulas for calculating the area of a rectangle, triangle, parallelogram, and irregular shapes. You will also create a word problem that requires the calculation of area. Area formula was given for: Rectangle Triangle Parallelogram Irregular Shapes Example drawn for each shape Word problem Instructions followed Neatness 10 points 10 points 10 points 10 points 20 points 20 points 10 points 10 points Total 100 points 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 14
Appendix F Rectangle 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 15
Appendix F Triangle 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 16
Appendix F Parallelogram 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 17
Appendix F Irregular Shapes 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 18
Appendix F Word Problem 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 19
Appendix G 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 20
Appendix H My Dream House Rubric Has at least 2 rectangles Has at least 2 triangles Has at least 2 irregular shapes Has at least 2 parallelograms 10 points 10 points 10 points 10 points Has correctly figured the area of each figure 40 points Has figured the total area correctly Neatness and Creativity 10 points 10 points TOTAL 100 points Name: 2005 Core Knowledge National Conference, Area Among Friends, 5 th Grade 21