Circumference and Area formulas Do Now 3/16: If I were to divide a pizza evenly into enough pieces for the whole class to have one, how many degrees would the crust of each slice be? Circumference and Area formulas Agenda 1. Do Now 2. Pi and Circumference Review 3. Circumference and Area Derivation 4. Debrief

Derivation of Pi ITEM CIRCUMFERENCE (C) DIAMETER (d) RATIO (C/d)

Circumference Formula Review: From Pi Day - where does the ratio “𝜋” come from? π≈ 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 Solving for C, the circumference is: 𝐶≈ 𝜋 𝑑 𝑜𝑟 𝐶≈2(𝜋)𝑟

Derive Area formula for a Circle http://tube.geogebra.org/student/m279 What is the area formula for the shape that results from this investigation? What measurements can be used to describe the dimensions for this shape? How can we rewrite the area formula using these measurements?

Area and Circumference **MUST BE IN NOTES!**

Going Between Area, Circumference, Radius and Diameter

The Annulus or “Doughnut” To find the shaded area you must find the area of both circles and subtract the smaller from the larger to find the remaining area.

Debrief How are the area and circumference formulas for a circle related?

Arc Length and Sector Area Do Now 3/17: Joe is putting in a circular pool, and wants to have a 2 ft deck around the outside. Find the area of the deck. Arc Length and Sector Area Agenda 1. Do Now 2. Embedded Assessment (Peer Correct) 3. Area/Circumference HW Review 4. Arc Length/Sector Area (Records) 5. Debrief

Area and Circumference: HW REVIEW

Arc Length and Sector Area To find the arc length or sector area, you need to determine how much of the whole circle you are looking for by using (degrees/360) Arc Length: Sector Area B C D 𝑨𝒓𝒄 𝑨𝑩= 𝒎 𝑨𝑩 𝟑𝟔𝟎° 𝟐𝝅𝒓 A 𝑺𝒆𝒄𝒕𝒐𝒓𝑪𝑫= 𝒎 𝑪𝑫 𝟑𝟔𝟎° 𝝅 𝒓 𝟐

Independent Practice Arc Length Sector Area

Oops, I Dropped the single! B Draw a tangent to the arc. Draw a line perpendicular to that tangent at the point of tangency! Repeat steps 1-2. Measure the arc in degrees. Use the radius and the degrees of the arc to find the arc lengths and sector area of your record piece. A

Debrief Use sector area and arc length to determine the dimensions for Lance’s garden (Pg. 326-327) 𝐴𝑟𝑐 𝐴𝐵= 𝑚 𝐴𝐵 360° 2𝜋𝑟

Arc Length and Sector Area Do Now 3/18: Agenda 1. Do Now 2. HW Review 3. Record Piece Project 4. Guided Practice Pg. 327-328 4. Debrief/Exit Ticket

HW REView (#7 Pg. 328)

Guided Practice (Pg. 327-328) For the “garden” layout to the right, determine the answers to questions #7, 9 and 11. #7b - Find the sector area #9 - Find the arc length

Guided Practice (Honors)

Guided Practice (Honors)

Exit Ticket

EXIT Ticket (HONORS)

Arc LENGTH and Sector AREA Do Now 3/19: Find the sector area of the unshaded region ADC. Agenda 1. Do Now 2. HW Review 3. Arc Length and Sector Area Quiz 4. Record Projects/Debrief D

HW Review

Record Projects/Debrief On a blank piece of paper, trace one of the pieces of record. Use string, rulers, protractors and MATH! to figure out the arc length and sector area of the piece of record you have. Draw and decorate the rest of your record! A B