Measurement Warm-up Stringing Lights Powerpoint Squaring a Circle Guided Practice Independent Practice

Stringing Lights (Warm Up) Which equation can be used to find d, the diameter of a circle that can be outlined with a string of lights that is 12 feet long? d = d = 12π d = 2π(12) π 12

Covering a Circle In previous lessons you developed formulas for the area of triangles and parallelograms by comparing them to rectangles. Now you can find out more about the area of a circle by comparing them to squares.

Covering a Circle What is area? Does this definition apply to the area of a circle? Explain. What is the formula for finding area of a circle? Area is the number of unit squares it takes to cover a figure. Yes. Even though squares cannot fit perfectly into a circle, you can approximate the partial squares or you can find the area using a formula.

Covering a Circle What kind of units did we get when we found the circumference of a circle? What kind of units do we get when we find the area of a circle? Why are these units different? We found one- dimensional units such as cm, in, ft, mi, etc. We find square units such as sq. cm, sq. in, sq. ft, sq. mi, etc. Because circumference is a one-dimensional measurement (length only) and area is a two-dimensional measurement (length and width; base and height; radius and radius)

Squaring a Circle (Guided Practice) A portion of each circle is covered by a square. The length of a side of the shaded square is the same length as the radius of the circle. We call such a square a “radius square”. Circle 1 Circle 3 Circle 2

Squaring a Circle (Guided Practice) How many radius squares does it take to cover each circle? Let’s explore further to answer this question. Circle 1 Circle 3 Circle 2

Squaring a Circle (Guided Practice) Cut out the radius squares, cover the circle and see how many it takes to cover each circle. Circle 1 Circle 3 Circle 2

Squaring a Circle (Guided Practice) Record your data in a table with columns for circle number, radius, area of the radius square, area of the circle, and the number of squares needed. Describe in patterns and relationships you see in your table that will allow you to predict the area of the circle from its radius square. Answers will vary but ideally students will notice that it takes a little more than three radius squares to cover any circle.

Squaring a Circle (Guided Practice) How can you find the area of a circle if you know the radius? How can you find the radius of a circle if you know the area? Multiply the radius squared times pi(π). Divide the area by 3.14 to get the area of the radius square. Then find the square root of the area of the radius square.

Area of Circles (Independent Practice) Find the area of a circle that has a radius of 2.5 cm. Find the area of a circle that has a diameter of 14 cm. A = πr ≈ 3.14 x 2.5 cm x 2.5 cm ≈ 9.625 cm 2 d = 2r A = πr r = 7 ≈ 3.14 x 7 cm x 7 cm ≈ 153.86 cm 2