Lesson 3 Pre-Visit Perimeter and Area Objective: Students will be able to: Distinguish between area and perimeter. Calculate the perimeter of a polygon whose side lengths are given or can be determined. Calculate the area of a polygon whose side lengths are given or can be determined. Time Required: 1 class period Materials Needed: - Copies of the Shape & Angle Review worksheet (included) 1 for each student - Copies of the World s Biggest Fan worksheet (included) 1 for each student - Students Geometry Dictionaries started in Lesson 1 - Rulers - Protractors - Graph Paper - Pencils Vocabulary: Area - The surface inside a figure or shape Length - The measured distance from one end to the other of the longer side of an object Line Segment A part of a straight line included between two points Perimeter - The distance around the outside of a polygon Polygon A closed figure made up of line segments Width - The measured distance from one end to the other of the shorter side of an object 23
Applicable Common Core State Standards: CCSS.Math.Content.3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. CCSS.Math.Content.3.MD.C.5a A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area. CCSS.Math.Content.3.MD.C.5b A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. CCSS.Math.Content.3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). CCSS.Math.Content.3.MD.C.7 Relate area to the operations of multiplication and addition. CCSS.Math.Content.3.MD.C.7b Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. CCSS.Math.Content.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. CCSS.Math.Content.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. 24
Lesson & Activity 1. Begin the lesson by providing students with copies of the Shape & Angle Review worksheet (included). 2. Have students identify different shapes and angles evident on a baseball field as a warm-up for this lesson. 3. Explain that today you will be discussing different ways to measure shapes. Review the following definitions: - Length - The measured distance from one end to the other of the longer side of an object - Width - The measured distance from one end to the other of the shorter side of an object 4. Have students add length and width (and all following vocabulary words) to their Geometry Dictionaries. 5. Explain that perimeter is the measure of the distance around the outside of a polygon. It is found by adding the lengths of all sides of a figure. Sometimes the lengths of each side are given; sometimes the lengths will need to be measured. 6. On the board, draw a rectangle labeled with a length of 4 feet and width of 3 feet. Then draw a right triangle with a base of 4 feet, height of 3 feet, and a hypotenuse of 5 feet. Demonstrate that to measure the perimeter of any polygon, the lengths of each side are added. 7. Provide students with the formula to find the perimeter of a rectangle: Perimeter = 2 x (length + width) 8. Remind students that rectangles have two pairs of matching sides. Opposite sides are equal. Squares have four equal sides, so if the length of one side is known, the lengths of all other sides are known as well. 25
9. Draw a diagram of a baseball field as shown below. Discuss that the infield is commonly known as the baseball diamond. Home plate, first, second, and third bases make up the four points of the diamond. 10. Ask students to identify what other shape could be used to describe the baseball diamond. 11. The baseball diamond is a square. Review that a square is a quadrilateral with all sides of equal length and all angles measuring 90 degrees. Point out that each side of the baseball diamond measures 90 feet. Have students determine the perimeter of the baseball diamond. 90 ft. 90 ft. 90 ft. 90 ft. 12. Review that 90 + 90 + 90 + 90 = 360. 13. Explain that the area of a figure measures the amount of space inside it. Area is measured using square units. For example, if inches are used to measure length, then the area will be measured in square inches. 14. Show students that square units are indicated with a superscript 2 following the units of measure. For example, 90 ². 15. Provide students with the formula to find an object s area: Area = length x width 26
16. Have students determine the area of the infield drawn previously. 17. Review that 90 x 90 = 8100 ² 18. Provide each student with a copy of the World s Biggest Fan worksheet (included) and have students work independently to find the area and perimeter of each shape. Conclusion: To conclude this lesson and check for understanding, review each worksheet answer as a class. Then have each student answer the following questions independently on their own paper. What is the difference in length between the longest and shortest perimeters on the worksheet? What is the difference in area between the smallest and largest rectangles on the worksheet? Explain the processes you used to get both answers. 27
Shape & Angle Review Defining Shapes & Angles Using the baseball field below, locate the following shapes and angles: 1. Square 2. Rectangle 3. Circle 4. Diamond 5. Triangle 6. Right Angle 28
World s Biggest Fan Name: Date: Instructions: You want your bedroom at home to show that you re a HUGE baseball fan. Figure out the perimeter and area of each of the following posters. Show your work alongside each problem, or on a separate sheet of paper. 1. 20 10 20 2. 6 10 10 3.5 3.5 29
3. 9.5 9.5 Area: 4. Area: 30
5. 8 32 32 8 Area: 6. 5 4 4 5 Area: 31
World s Biggest Fan Answer Key 1. Perimeter: 50 2. Perimeter: 33 3. Perimeter: 43, Area: 114 2 4. Perimeter: 48, Area: 144 2 5. Perimeter: 80, Area: 256 2 6. Perimeter: 18, Area: 20 2 32