Area and Perimeter Man


 Norah Wright
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1 Area and Perimeter Man MA.C and.2; MA.B LESSON FOCUS Using counting procedures to determine perimeter and area of rectangles, squares, and other figures. COMPANION ANCHORS LESSONS Perimeter; Patterns with Perimeter; Area; Patterns with Area MATERIALS Excursions student pages square tiles per student Rulers or other straight edges Crayons or markers Colored construction paper and glue sticks Onecentimeter graph paper Oneinch graph paper area estimate perimeter rectangle LANGUAGE DEVELOPMENT LESSON OVERVIEW square square inches units Students begin by using square units to make a picture. They discover how they can count the sides of a square figure to determine perimeter and the number of square units within the figure to determine area. Next, they find and compare the perimeters and areas of various rectangles and squares. They then practice estimating the perimeter and area of different figures. Finally, they use their skills to draw a robot and measure its area and perimeter. least one other square. Also explain that the squares should be placed so that the sides match up evenly and that the squares cannot overlap. You might model the following example (a trailer truck), using tiles on the overhead projector. As students work on their shapes, circulate to ensure that they are following the guidelines (no overlapping, all squares touching another on at least one side) and to assist as needed. When students have designed their pictures, have them glue the squares onto the construction paper and title their pictures. Next, have students trace the outline of their picture. Tell them to draw a short tick mark each time they start to trace a different side. Model this on the picture of the truck you made. Truck SETTING THE STAGE Create pictures with squares. Have students turn to My Picture Squares, page 99, in their Excursions books. Help students cut out the fortyeight squares. Then distribute a sheet of colored construction paper to each student. Explain to students that they are going to use the 1inch squares to create a picture. (They will use their pictures later in this excursion.) Tell students to arrange the squares on the colored construction paper so that each square touches at Tell which pictures are larger. Have students share and compare their pictures. Ask them which figures are larger than others. Ask, How could you tell which pictures are larger? (Students might say that some use more squares; but at this point, accept any reasonable answers.) Then explain to students that they are going to find out about two ways to measure the size of objects. Finally, display students pictures. 72
2 BUILDING CONCEPTUAL KNOWLEDGE Find the perimeter. Distribute four color tiles and a sheet of white paper to each student, and have students place the tiles on the paper. Tell students to use the four small squares (tiles) to make a larger square. Work along with students on the overhead projector. Then have students draw short tick marks on the white paper at each new border of the four tiles. (They should be familiar with this from the activity in Setting the Stage.) Write the word perimeter on the chalkboard, and explain to students that the perimeter of a figure is the distance around it. Point out to students that they are going to find the perimeter of the square they just made. Explain to students that each side of their tiles, or the length between two tick marks, can be referred to as one unit. Then have them count with you the number of units around the squares they made. Explain that the perimeter of the square is 8 units. Find the area. Next, write the word area on the board, and explain that the area of a figure is the number of square units inside the figure. Tell students that each tile represents 1 square unit. Then have them find the area of the square they made. (4 square units) Have students next use the four tiles to form a rectangle and find the perimeter and area of the rectangle. (Students may continue adding the tick marks if they find them useful for counting the sides.) Ask, What is the perimeter of your rectangle? (10 units) What is the area of your rectangle? (4 square units) Point out to students that the areas of the rectangle and the square are the same, but that the perimeter of the rectangle is greater than the perimeter of the square. Ask, Why do you think the Name Area and Perimeter Man Name MEASURE US MY PICTURE SQUARES Figure A 8 inches 3 square inches Figure B 10 inches 6 square inches 10 inches Figure D 4 square inches Figure C 12 inches 9 square inches Page 99 Page
3 perimeter of the rectangle you made is greater than the perimeter of the square you made? (more sides exposed) Compare areas and perimeters. Distribute five more tiles to each student. Then have them repeat the above procedure, forming rectangles with six, seven, and eight tiles, and a square and rectangle with nine tiles. Record the perimeters and areas that students find. Point out that students could form two rectangles with six tiles (1 6 and 2 3). Ask, How did the areas of the two rectangles vary? (The areas did not vary.) How did the perimeters of the two rectangles vary? (The perimeter of the narrower rectangle was 4 units greater.) Repeat the questions for the rectangles students made with eight tiles. Ask, What do you notice about the narrower rectangles? (They have greater perimeters.) Finally, distribute the pictures students made in Setting the Stage, and have them find the perimeter and area. Have them compare their results and identify the picture or pictures with the greatest perimeter and area. BUILDING SKILLS AND STRATEGIES Measure perimeter and area in inches. Show students how to use a pencil and ruler to draw a rectangle of 5 units on 1inch graph paper. Then explain that the side of each unit on the graph paper measures 1 inch. Explain to students that when they know the length of a side of each square unit, they can use that measure to label the perimeter. Then find the perimeter of the rectangle you drew (12 inches) and write it on the board. Explain to students that because the unit used for the perimeter is one inch, each square unit is one square inch. Show students how to find the area of the rectangle by counting the number of squares. (5) Ask students how they would label the area. (5 square inches) Have students turn to Measure Us, page 101, of their Excursions books. Point out to them that the side of each square unit is 1 inch. Direct their attention to Figures A D and ask the following questions: DRAW THE MEASURES Students squares and rectangles should reflect the measures you gave them. Name NO SQUARES HERE Figure A 16 inches 7 square inches Figure B 16 inches 9 square inches Figure C 18 inches 9 square inches Page 102 Page
4 Which figure has an area of 9 square inches? (C) Which figure has a perimeter of 8 inches? (A) Then, have students work in pairs to find the area and perimeter of each figure, writing the perimeter above the figure and the area inside it. Remind students to label their measurements. When students have completed Measure Us, ask them to identify the figure with the greatest perimeter. (C) Then ask them to describe what is unusual about Figures B and D. (Though their areas are different, they have the same perimeter.) Draw figures with certain perimeters and areas. Next, have students turn to Draw the Measures, page 102, in their Excursions books. Point out that they are again using a 1inch grid. Then tell students that you are going to give them some perimeters and areas and that they are going to draw rectangles or squares that have these measurements. Have students work in pairs, giving them a few minutes to complete each figure. Tell them to label their figures A, B, C, and D as they draw them. Then say the following: IT S ABOUT THIS SIZE Estimate the perimeter and area of each figure. about 7 inches Figure A about 3 or square inches Figure C about 12 inches 104 about 8 inches Figure B about 8 or 9 square inches about 13 or 14 inches Figure D about or 7 square inches about 4 square inches Draw a rectangle with a perimeter of 6 inches. (A) Draw a square with an area of 4 square inches. (B) Draw a rectangle with a perimeter of 16 inches. (C) Draw a rectangle with an area of 8 square inches and a perimeter of 12 inches. (D) Have students find the areas and perimeters of their figures and compare their work, discussing any problems they had completing the figures. BUILDING MORE SKILLS AND STRATEGIES Find the area and perimeter of different kinds of figures. Have students turn to No Squares Here, page 103, in their Excursions books. Explain that they can find the perimeter and the area of figures that are not squares or rectangles. Work with students to find the perimeter and area of Figure A. Point out that they can use the same method of counting the sides and squares that they used to find the perimeter and area of squares and rectangles. Then have students complete the page, writing the perimeter above the figure and the area inside the figure. Ask, Which figures have the same perimeter? (A and B) What do you notice about figures B and C? (They have different perimeters but the same area.) Estimate perimeter and area. Explain to students that sometimes a figure may contain parts of square units. When this is so, they can estimate to tell about how large the area and perimeter are. Check to be sure that students understand that they are not finding the exact perimeter or area but a measure that is about the actual size. Have students turn to It s About This Size, page 104, in their Excursions books. Point out that all the figures contain units that are not complete squares. Tell students that to estimate the perimeter, they need to look for parts of units, such as half lines, that make a whole unit. Model for students how to estimate the perimeter of Figure A. Explain that when they estimate area, they also look for parts of whole square units, such as halves of squares, that would make up a whole square unit. Then model how to estimate the area of Figure A. Page
5 Then have students work in pairs to estimate the perimeter and area of Figures B, C and D. Have students write the perimeter above the figure and the area inside it. When they have finished, have them compare their work. To extend this activity, you could have students draw squares and rectangles on any size graph paper and estimate the perimeter in units and the area in square units. PUTTING IT INTO ACTION Make Area and Perimeter Man. Distribute a sheet of 1cm graph paper to each student. Tell them that they are going to use squares and rectangles to create pictures of robots. Explain to students that all the lines must be drawn along the grid lines. They should include a head, eyes, nose, mouth, torso, arms, hands, legs, and feet. Calculate the perimeter and area of the robot. When students have completed their robot pictures, have them calculate the perimeter of the figure. Then have them calculate the area of each body part and add them together to find the area of the robot. Point out to students that they may need to estimate the perimeter or area, depending on their picture. (Students can express their measures in units and square units or centimeters and square centimeters.) Have students name their robots and compare the areas and perimeters of their drawings. Finally, display their completed robots in the classroom. LANGUAGE ARTS CONNECTION Write a robot story. Have students write a short story about the adventures of their robot and share their stories with the class. HOME CONNECTION Find perimeter and area. Students use Home Connection: Measure Up!, pages , in their Excursions book to measure the perimeter and area of a table in their home. The page is used as the unit of measure. You might want to model how to flip the page around your desk to measure the perimeter. Show students how they could use sheets of notebook paper to cover the area of the desk. Then have students practice using Home Connection: Measure Up! to find the perimeter and area of surfaces in the classrooom before they try it at home. 76
6 Name MY PICTURE SQUARES Area and Perimeter Man 99
7 100
8 Name MEASURE US Figure A 8 inches Figure B Figure D Figure C 101
9 DRAW THE MEASURES Students squares and rectangles should reflect the measures you gave them. 102
10 Name NO SQUARES HERE Figure A 16 inches Figure B Figure C 103
11 IT S ABOUT THIS SIZE Estimate the perimeter and area of each figure. about 7 inches Figure A Figure B Figure C Figure D 104
12 Name HOME CONNECTION: MEASURE UP! Dear Parent or Guardian: Your child has been learning how to find areas and perimeters. To do so, he or she has been drawing figures on grid paper and finding the area of each figure by counting the squares within it. Here is an example of how your child has been using counting to find area and perimeter: Area is found by counting the squares inside the figure. The area is 17 square units. Perimeter is found by counting the sides. The perimeter of this figure is 20 units. Now, your child is going to find the area and perimeter of a table in your home, using this page as a measuring tool. You can help your child while participating in his or her learning experience. Because your child will be using only this page to measure the perimeter and area, he or she will have to move it around the surface of the table and count the number of pages. You can help your child keep track of the number of "pages" it takes to measure the perimeter and cover the area. If you have extra notebook paper in your home, your child could use it to cover the table and then just count the sheets to find the area. If not intrusive, your child can also use the page to find the perimeter of a room in your home. 105
13 Measure the Perimeter Use this page to measure the perimeter and area of a table in your home. First lay the page lengthwise along the edge at one corner of the table. Place your finger along the edge where the page ends. Then flip the page over your finger. Be careful to keep the page along the edge. When you get to the next corner, turn the page lengthwise and move down the next side. Move around the table this way and count each time you flip the page. When you get back to where you started, the number you have counted will be the perimeter. The perimeter of my table is Measure the Area You can also use the page to find the area. This time, move back and forth across the table from one end to the other. The point is to find out how many pages it takes to cover the table. The area of my table is Use the page to measure the perimeter and area of other surfaces in your home. Use the space below to record the measurements. 106
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