# Lesson 9 2 devoloping formulas for circles

The states of New York, Tennessee, Louisiana and California have recently caught fire in sales because in those areas teachers are searching for meaningful materials that will prepare their students for the high stakes common core curriculum exams. Lots of really good problems to engage students in thinking about geometry. Which in each pair has the greater perimeter? Amy has 36 feet of fencing to make a dog run. She can make a 6 x 6 enclosure or a 4 x 9 enclosure. Which would be best for the dog run? Why do you think so? What information is needed to find circumference of a circle?

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As you come to shapes for each table, have the students sketch and label an example on the Math Journal page, Sir Cumference and the First Round Table Vocabulary. Especially focus on the words pertaining to the circle: Circumference Guess Helping Students Visualize Circumference To help your students visualize the relationship between the diameter and the circumference, select four cylindrical objects such as a glass, a film canister, a toilet paper roll, etc.

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A tennis ball canister with the three balls inside should be one of these objects. Have students number their paper and write the name of each item.

Tell them you will be having them decide which is greater, the circumference of the object or the height of the object. When they have written their guess for each object, show the length of the circumference by wrapping a measuring tape around the object. Then hold that length along the height so the students can compare the two lengths.

They will be surprised when the circumference proves to be longer than the height of the object, because circumference is difficult to visualize.

Tell them estimating distance around is very difficult to do. The way you guess is to estimate the distance across the center the diameter and try to visualize a little more than three of those distances. That will be the distance around or the circumference. Ss you visually estimate the height of the object as compared to the circumference, you try to estimate about three diameters and compare that to the height.

Tell them this relationship between the diameter and the circumference of a circle is called Pi. In any true circle the circumference will always be a little more than three diameters.

Using the tennis ball canister is especially effective since it contains three round balls. The height should be very close to the circumference for this object.

In order to find circumference, then, we need the measure of the diameter, or of the radius. If we only know the measure of the radius, how could we know the measure of the diameter? Use team formations where student groups stand and demonstrate circumference, diameter and radius.

Work with students to complete the Diameter, Radius, and Circumference sections of the Frayer Model for vocabulary. How can I find the circumference?

Have students look at the Math 7 Class Reference Sheet and find the formula for circumference of a circle. Ask several students to read the formula saying the word indicated by the variable. Do Pairs Coach to have them practice finding circumference for the following using their calculators for computations.

In Pairs Coach students work in pairs where one person is the coach explaining how to do the problem and the other is the scribe writing what the coach is saying to do. Students should take turns being coach and scribe for these four problems. What information is needed for finding area of a circle?

Remind students that area is always measured in squares. Review the Perimeter, Area, Volume Song and review area being represented in square units. Did anyone find a way to do this without having to literally count every little square?

Which would have a greater number of squares, the circle inscribed in the square, or the whole box on the worksheet? Ask students to predict the number of squares in the circle and write that down.

Discuss how they decided.

Discuss how they found the number of square units. Lead them to see they could have found the area of one of the 4 sections and then multiplied by four. The length of one of the four squares is Midpoint Formula Slope Formula Slope of Lines in Coordinate Plane Distance Formula circle o A square inscribed in a circle o A regular hexagon inscribed in a Virginia Department of Education © Geometry Vocabulary Cards Page 2 o A tangent line from a point outside a given circle to the circle Triangles Classifying Triangles by Sides.

We will simply state the formula for the circumference C of a circle in terms of the radius (r) or the diameter (d): C = 2 πr = πd Note that with the formula for the circumference, we introduce the number π. II-C__Balancing Equations Student schwenkreis.com Learning Targets: Students will understand that equations must be balanced to obey the law of the conservation of mass.

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## Area of Circles

LESSON Practice B Developing Formulas for Circles and Regular Polygons Find each measurement. Give your answers in terms of.

1. 25 m 6 2. 4A in. (the area of V the area of H A m 2 A 4a 2 in2 3. (X Y) yd mi 2 the circumference of M the circumference of R C (2x 2y) yd C mi. Everyday Mathematics, Grade 5 Developing an understanding of and fluency with division of whole numbers Students apply their understanding of models for division, place of circles; choose and use appropriate formulas to calculate the areas of rectangles, parallelograms.

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