and Perimeter of Compound Figures MATERIALS Excursions student pages 175 178 Geoboards and rubber bands Overhead geoboard LANGUAGE DEVELOPMENT area compound figure diagonal perimeter polygon LESSON OVERVIEW rectangle right triangle scale square Students first come up with their own methods of finding the exposed area of a kitchen floor. They then use geoboards to create their own polygons and find their areas, starting with common ones and then creating compound figures. They also find the perimeter of figures that have diagonals. Students then find the area and perimeter of compound figures shown on a grid, design a layout for a backyard, and redesign a room in their home, using a grid and actual measurements. SETTING THE STAGE Discuss area and square units. Ask the class to think about designing a kitchen. Say that the floor will be tiled. Ask students how they could determine the number of tiles to purchase. Have them turn to Kitchen Layout, page 175 in their Excursions books and figure out the number of tiles needed for the kitchen shown. Depending on whether or not students place tiles beneath the furniture and appliances, answers will vary. Ask volunteers to explain their methods. Some will count; some will count and add; some may multiply. Those who don t place tiles beneath furniture and appliances may also subtract. Direct students attention to the cabinet. Ask students how many tiles it covers. Have volunteers explain how they counted the 3 half-tiles. Now ask MA.B.1.2.1.4.1 and.2; MA.B.1.2.2.4.2 LESSON FOCUS Finding the area and perimeter of compound figures. COMPANION ANCHORS LESSONS ; of a Rectangle; Estimating volunteers to explain how to find the number of tiles covered by the pantry. Point out that the diagonal line also creates half-squares, so students can add (or subtract) the appropriate number of halftiles. BUILDING CONCEPTUAL KNOWLEDGE Create common polygons and find their areas. Distribute the geoboards and rubber bands to students. Have students create common polygons such as squares, rectangles, and right triangles. Tell them to find the area of each figure and to find the perimeter of each figure that is not a triangle. Make sure they understand how to find the area of right triangles. (by finding the area of the associated square or rectangle, and then halving it) Create compound figures and find their areas. Tell the class that a compound figure is made by combining common polygons: for example, a square and a rectangle or a rectangle and a triangle. On the overhead geoboard, show some examples. Ask volunteers how they could find the area of each compound figure. Note that there is more than one way to find the area of each figure. Each method will involve addition and/or subtraction. Some students may also be able to use multiplication. You may need to help some students add halfunits. Tell them to make half-squares on their geoboards. Ask them questions such as, If you combine 2 half-squares, what is the area of the new figure? (1 square unit) Now, if you combine 1 more halfsquare, what is the area of the new figure? (1 1 2 square units) Ask volunteers how they could find the perimeter of the compound figures that don t include diagonals. (If students ask why they can t find the perimeter of figures with diagonals, explain that computing the length of diagonals involves 109
TOPIC 5 and Perimeter of Compound Figures advanced geometry. They will have to wait until seventh grade to find the perimeter of such figures.) BUILDING SKILLS AND STRATEGIES Find the area and perimeter of compound figures. Have students turn to Compound Figures, page 176, in their Excursions books. You may wish to assist them to complete the first two problems (figures 1 and 2). Ask volunteers to describe the figures. Ask questions such as, Which common figures make up each compound figure? How can you find the area? Will you use addition? Subtraction? How can you find the perimeter? PUTTING IT INTO ACTION Design a backyard layout and write questions about it. Have students turn to Backyard Layout, page 177, in their Excursions books. Tell them that they are going to design a backyard. They can put whatever they want in their backyards (for example, a pool, a basketball court, a barbecue pit, and a fort). Remind them to include a scale. Encourage them to use compound figures. After they complete their designs, they should write five questions about perimeter and area of the objects in their backyard. Finally, have students exchange papers with partners and answer the questions. HOME CONNECTION Redesign a room at home. Students will redesign a room at home (or plan a new room) using Redesign a Room, page 178, in their Excursions books. Encourage them to work with their parents. Students should measure the room s dimensions, decide what kind of furniture or appliances to put in it, and then draw an appropriate layout. Have them bring their work to class. Ask volunteers to describe their rooms. Pose questions to them about the area and perimeter of objects in their rooms. Name COMPOUND FIGURES and Perimeter of Compound Figures KITCHEN LAYOUT 1 2 Pantry Perimeter 20 16 Table Cabinets Stove Refrigerator 3 5 4 16 24 1 2 Perimeter 13 1 2 38 29 14 6 TOPIC 5 and Perimeter of Compound Figures 175 176 TOPIC 5 and Perimeter of Compound Figures Page 175 Page 176 110
TOPIC 5 and Perimeter of Compound Figures Name BACKYARD LAYOUT Scale Questions: 1. 2. 3. 4. 5. TOPIC 5 and Perimeter of Compound Figures 177 Page 177 111
Name and Perimeter of Compound Figures KITCHEN LAYOUT Pantry Table Cabinets Stove Refrigerator TOPIC 5 and Perimeter of Compound Figures 175
COMPOUND FIGURES 1 2 Perimeter 3 4 5 6 Perimeter 176 TOPIC 5 and Perimeter of Compound Figures
Name BACKYARD LAYOUT Scale Questions: 1. 2. 3. 4. 5. TOPIC 5 and Perimeter of Compound Figures 177
HOME CONNECTION: REDESIGN A ROOM Dear Parent or Guardian, Your child is studying area and perimeter. For this exercise, he or she should measure the dimensions of a room in your home. Your child will decide what furniture to put in the room, redesign the room on the grid below, and bring the completed design to class. 178 TOPIC 5 and Perimeter of Compound Figures