# Lesson 3: Area. Selected Content Standards. Translating Content Standards into Instruction

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1 Lesson 3: Area Selected Content Standards Benchmark Assessed: M.3 Estimating, computing, and applying physical measurement using suitable units (e.g., calculate perimeter and area of plane figures, surface area and volume of solids presented in real-world situations) Lesson Focus: This lesson is intended as an introductory lesson to the concept of area. Students should know by the end of this lesson the following information: The conceptual difference between area and perimeter How to use various methods to determine area of plane figures (including using a ruler, grid paper, and calculation) Use of scale in a scale drawing as it applies to area GEE 21 Connection The skills that will be addressed in this lesson include the following: Understand the concept of area Understand what a square unit is and how it is different from a linear measure Find the area of plane figures using grids Calculate the area of plane figures shown in diagrams or described in real-world terms Understand the connection between area of rectangles and triangles Understand numerical relationships among units within each system (customary and metric) Compare approximate relationships between systems in terms of intuitive reference points Translating Content Standards into Instruction A. The first goal of this lesson is to help students to understand what area is and how it is different from perimeter. 1. The first thing to do is to get students to understand what a SURFACE is something that we can cover or paint (such as floors, tabletops, covering of a ball, etc.) 2. We want students to associate the word SURFACE with the word AREA. Explain to students that The amount of surface that an object has is called its AREA. 3. Emphasize the difference between a length (show students a string and explain that length has no width to it it is one-dimensional) and an area (show students a rectangular book and explain that the surface has both length and width it is two-dimensional). 4. Point out that perimeter (which is a length) and area have two completely different types of units. This will be emphasized throughout the lesson. 20

4 the amount of carpeting required for a room, etc.). Converting within units and from system to system may also be tested. Sources of Evidence about Student Learning A. Have students make measurements of rooms or halls around the school in order to calculate the areas. B. Have students do student worksheets in groups provided with the lesson and have students explain their work for the class. GEE 21 Connection See attachment at the end of the Lessons for sample questions related to the GEE 21. Attributes of Student Work at the Got-It level A. When students are making their measurements for the items that are in the room or around the school, make sure that all students are within an acceptable range in their measurements. Any student or group that is outside the acceptable range should be required to re-measure the item to make sure that the error being made is corrected. B. When going over student work on the provided worksheets, allow students to work alone first, then provide time to allow for students to compare their answers in groups. Let the students talk about how they got their answers and if there were any discrepancies between group members, have the members explain what they did to clear up any differences. Make sure that all students are within an acceptable range when writing down a measurement, but all students must understand that measurement is not an exact science. It is an approximation within a certain degree of accuracy, depending on the measurement tool being used. 23

5 Lesson 3: Area Student Worksheet #1 Directions: Use the figures below to do this activity. First, make estimates of how many sticky tabs it would take to cover each figure. After you make your estimates, actually take sticky tabs and try to cover the figure to see how close your estimate is. The sticky tabs cannot overlap. Figure 1: Estimate Actual: Figure 2: Estimate: Actual: Figure 3: Estimate: Actual: 24

6 Lesson 3: Area Student Worksheet #2 1. Which of the figures below would you say has the most area associated with it? Why? 2. If you were trying to cover the floor in the classroom, which figure below do you think it would be easier to use to cover the entire space without any gaps? Explain why? 3. Area is commonly found using square units. Why do you think that is? 4. How many square units,,does it take to cover the entire figure shown? 5. Use the figure below to answer the following questions. (a) What is the area of the figure? (b) What is the perimeter of the figure? (c) What is the length of the figure? width? (d) What multiplication fact does the figure model? x (e) If you multiply the length and width of the figure, what do you notice in connection with the area? 25

7 6. Use the grid at the right to draw a figure that has an area of 4 square units with a perimeter of 10 units. 7. Mr. Connor is laying out square tiles on his kitchen floor. So far he has laid out the squares shown. Determine how many squares it would take to cover the entire floor. If it took him 14 minutes to lay the tiles shown here, how long would it take to do the rest of the floor? Explain how you got your answer. 8. Shown below are two squares. Answer the following questions. Square #1 Square #2 (a) Measure the sides of square #1 with a centimeter ruler. What is the length of each side of the square? (b) Measure the sides of square #2 with an inch ruler. What is the length of each side of the square? (c) One of the squares shown is called a square centimeter and one of the square is called a square inch. Which name goes with which square? Explain why you chose your answer. (d) Using the figure shown, determine how many square centimeters it would take to cover the figure. 26

8 (e) Using the figure shown, determine how many square inches it would take to cover the below. (f) Look at the figure shown to the right do you think it would take more square centimeters or square inches to cover it? Explain why. 9. Using large sheets of bulletin board paper that you will get from your teacher, make a square foot and a square yard. Using the models you make, determine the following: (a) How many square feet does it take to make a square yard? (b) How many square inches does it take to make a square foot? (c) How many square inches will it take to cover a square yard? Show how you got your answer to this. 10. Explain in your own words what is different about perimeter and area. 27

9 Lesson 3: Area Student Worksheet #3 1. This is a square centimeter. (a) Use your centimeter ruler to find the length of each side of the square centimeter. What is the length of each side? (b) What is the perimeter of the square centimeter? (c) About how many of these square centimeters would fit inside this rectangle? What is the area in square centimeters of the rectangle? 2. This is a square inch. (a) Using your inch ruler, measure the sides of the square inch. What is the length of each side? (b) What is the perimeter of the square inch? (c) About how many of the square inches would fit inside this rectangle. What is the area of the rectangle? Measure each side of the rectangle to the nearest inch. What is the length of the rectangle? What is the width? If you multiply the length by the width, what do you get? 3. What is the area and perimeter of the rectangle shown below: Area = Perimeter = 6.25 ft ft 28

10 4. Using your ruler, measure the length and width of this rectangle. Use whole centimeters as the unit. Put dots along the length and width to mark each centimeter. Width: cm Length: cm (a) Remember this is what a square centimeter looks like. (b) How many of these square centimeters could be lined up in one row across the bottom of the rectangle? (c) How many rows of square centimeters would fit in the rectangle? (d) How many square centimeters all together will fit inside the rectangle? How did you figure this out? (e) What is the area of the rectangle in square centimeters? (f) Do you have to have all of the squares already drawn on a rectangle to figure out the area? Why or why not? 5. Using what you learned in problem 4, calculate the area of the rectangle here in square centimeters. 29

11 6. Working in teams of two or three, find the following: (a) Find the perimeter of the classroom floor in inches, feet, yards, millimeters, centimeters, and meters. The PERIMETER of the room is: inches or feet or yards millimeters or centimeters or meters (b) Find the area of the classroom floor in square centimeters, square meters, square inches, square feet, and square yards. The AREA of the room is: sq. centimeters or sq. meters sq. in. or sq. ft. or sq. yd. 7. Below is a triangle located inside a rectangle. Using what you have learned about finding areas of rectangles, answer the given questions. (a) If the area of the rectangle is 20 square feet, what would you say the area of the triangle is? Explain how you know. (b) Using your centimeter ruler, calculate the area of the rectangle in square centimeters. What do you think the area of the triangle is? Explain what you would do if you had to find the area of any triangle. 30

12 8. Julie wants to build an exercise pen for her pet rabbit. She has 36 feet of fencing and 4 metal posts to build a rectangular enclosure. She wants to carefully plan her project, measuring in units of whole feet. Find all the possible ways that Julie could build her pen and have a perimeter of 36 feet and whole units for length and width. Fill in the table below and find the area of each case. Length (ft.) Width (ft.) Perimeter (ft.) Area (sq. ft.) (a) What dimensions (length and width) for the pen should Julie build for her rabbit if she wants the largest possible area? (b) What would be a benefit of building the pen in one of the other ways (the pen without the most area)? 9. Carlos bought some land. The scale drawing below shows the layout of his land. What is the total area (approximately) in square feet, for the land that he bought? (Scale: 1 cm = 30 feet) 31

13 Lesson 3: Area Student Worksheet #4 Directions: Below is a scale drawing of a basketball court. Use the scale drawing to answer the given questions. Jump Area Free Throw Lane ft 19 ft 6 ft radius Circular Outer Jump Area 2 ft inner radius The Arc What is the total area of the basketball court? 2. What is the area of the free throw lane? 3. What is the area of the Jump Area? 4. What is the area of the Circular Outer Jump Area? 5. What is the area of The Arc? 6. What is the perimeter of the basketball court? 7. How many times would you have to run around the basketball court if you wanted to run a mile? Show or explain how you got your answer. 32

15 Lesson 3: Area Answer Sheet Student Worksheet #3 1. (a) 1 cm (b) 4 cm (c) Since it would take 18 square centimeters to fit inside the figure, this is also the area associated with the figure. 2. (a) 1 in (b) 4 in (c) 9 sq in; 9 sq in; length = 3 in, width = 3 in; 9 sq in 3. Area is about 147 sq ft; Perimeter = 59.5 ft 4. length = 8 cm; width = 6 cm (b) 8 (c) 6 (d) 48 square centimeters (e) 48 sq cm (f) You do not have to have all of the squares drawn because you can just measure each side of the rectangle and multiply the two numbers to find the area sq cm 6. Answers will vary from class to class. 7. (a) The area of the triangle is ½ the area of the rectangle, so area of triangle is 10 square feet. (b) The area of the rectangle is 15 sq cm, so the area of the triangle is ½ this amount, or 7.5 sq cm 8. Length (ft) Width (ft) Perimeter (ft) Area (sq ft) 1 ft 17 ft 36 ft 17 sq ft 2 ft 16 ft 36 ft 32 sq ft 3 ft 15 ft 36 ft 45 sq ft 4 ft 14 ft 36 ft 56 sq ft 5 ft 13 ft 36 ft 65 sq ft 6 ft 12 ft 36 ft 72 sq ft 7 ft 11 f. 36 ft 77 sq ft 8 ft 10 ft 36 ft 80 sq ft 9 ft 9 ft 36 ft 81 sq ft 10 ft 8 ft 36 ft 80 sq ft Starts to repeat (a) The dimensions which result in the largest possible area are 9ft by 9 ft. (b) Maybe you wanted a longer pen for the rabbit to be able to run a longer distance without having to turn around, or maybe the space which the yard has won t permit the length or width associated with one of the other measures. 8. The approximate area is 28,800 sq ft. Student Worksheet # sq ft sq ft 3. About 12 sq ft 4. About 96 sq ft 5. About 54 sq ft ft is about 18 times around the gym floor to make a mile (It s actually a little more than that.) 34

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