Lesson Plan - Wikispacesdavidrichardsarl.wikispaces.com/file/view/Unit+Plan+&+Project+Part... · Lesson Plan Name David Richards ... Concept and Skill Development-Testing (46 min)

Lesson PlanName David Richards Subject Geometry Date: 3/19

Unit 11 Practice TestObjective:8.2 The student will solve problems using perimeters and areas of geometricfigures.Standard:3.12.5,4.12.2,4.12.6

Introduction -1. Quietly have a seat and when you are ready I will pass out the test. The

sooner you are ready the more time you will have for the test.2. When you are finished with the test hand it to me and read a book.

Procedures:1. Stand for the Pledged of Allegiance.

(1 min)

Concept and Skill Development-Testing

(46 min)

Assessment Statement-There will be a test on Friday the March 23rd that covers pages 669-694.

What is the purpose of this assessment?I will use this practice test to determine what I need to review with you before thesemester exam coming up.

(1 min)

Closure -Collect all of the tests and make sure I get every one of them back.

Procedures:Pack up and quiet rows will leave first.

(2 min)

7

Unit Practice Test Specification SheetPolygons

Definitions

Radius of the polygonApothem of the polygonCentral angle of a regular polygonArea of similar polygonsArc lengthArea of a sector

Identification

Area of similar polygons

Important Topics

Area of an equilateral triangleCenter of the polygonRadius of the polygonApothem of the polygonArea of a regular polygonCentral angle of a regular polygonArea of similar polygonsArc lengthArea of a sector

Word problem

Unit Practice Test BlueprintPolygons

Combine problem types into each problem.

Use 46 minutes of problems.

Definitions


Identification


Important Topics


Word problems 4

Open ended concept 18

Long term memory 2

Multiple choice 3

Unit 11 Practice Test

Define the following:

1. Radius of the polygon

2. Apothem of the polygon

3. Central angle of a regular polygon

4. Area of similar polygons

5. Arc length

6. Area of a sector

1. Find the area of a regular dodecagon with side 10 em.

2. Find the area of an equilateral triangle with side 6.

3. Each circle is tangent to the other two. If the diameter of the large circle is 12, the area ofthe shaded region is __ .

[A] 9Jr sq. units [B] 18Jr sq. units [C] 24Jr sq. units [D] 36Jr sq. units

4. The figures are similar. Find the missing values.

p=?s12

30A=720

5. Explain why the apothem of a regular polygon is always less than the radius of thecircumscribed circle.

6. Find the area of the shaded region.

[A] 102.63 cnr' [B] 25.66 em" [C] 38.48 em" [D] 153.94 em?

7. The area of an equilateral triangle that has a side length of 4 is __ .

[A] 6+2../3 sq. units [B] 12 sq. units [C] 4../3 sq. units [D] 8 sq. units

8. Find the area of a regular l l-gon with radius 9 em.

9. Find the length of a 40° arc in a circle with a radius of 4.

[A] 81l [B] 81l9

[C] 161l9

[D] 91l8

10. Find the area of a regular dodecagon with radius 8 em. Round to the nearest tenth.

[A] 332.6 cnr' [B] 192.0 em' [C] 384.0 em' [D] 173.4 cnr'

11. The circumference of a circle is 841l cm. Find the diameter. the radius. and the length of anarc of 100°.

12. For a circle of radius 8 feet, find the arc length of a central angle of 60 0 • Leave your answerin terms of rt .

13. For a circle of radius 9 feet, find the arc length s subtended by a central angle of 120•

[A] s = 1081t feet9

[B] s = -1t feet5

3[C] s = -1t feet

56

[D] s = -1t feet5

14. A square is inscribed in a circle of radius 3Ji .Find the area of the square.

15. The distance around the equator of Saturn is about 378,675 km. To the nearest kilometer,what is the equatorial diameter of Saturn? Use 1! == 3.14.

16. Maria needs to make a poster that is 1 m by 3 m for the big game. The cost of the paper is$2.25. Later she needs another poster with dimensions 0.5 m by 1.5 m. What is the paper forthis poster likely to cost?

17. The area of a regular octagon is 55 em". What is the area of a regular octagon with sidesthree times as large as the sides of the first octagon?

[A] 9075 em' [B] 495 em! [C] 165 cnr' [D] 560 cnr'

18. A regular hexagon has an apothem of2 and a side length of 4J3 . Its area is3

C944f

[A] 4.J3 sq. units [B] 8J3 sq. units [e] 167£ •sq. umts

3[D] 47£ sq. units

19. Sam watched a bug crawl through an arc of 30 0 along the rim of his melon, which was cutin half. If the radius of the melon was 4 inches, how far did the bug crawl?

20. Two similar trapezoids have areas 847 cnr' and 448 em", Find the ratio of similarity.

21. Find the circumference of a circle with radius 6 m. Use 7£ ~ 3.14.

22. The diameter of a water glass is 8.4 em. Find the circumference. Use 1t~ 3.14.

23. Angela needs to make a poster that is 2 m by 3.5 m for the big game. The cost of the paperis $4.50. Later she needs another poster with dimensions 1 m by 1.75 m. What is the paperfor this poster likely to cost?[A] $1.38 [B) $2.25 [C] $2.00 [D] $1.13

24. If a circle has a diameter of 5 inches, what is the circumference rounded to the nearest wholenumber? Use st ~ 3.14.

[A] 32 in. [B] 8 in. [C] 16 in. [D] 20 in.

25. Find the area of a regular heptagon with side 7 cm.

[A] 356.1 em" [B] 178.1 cnr' [C] 161.4 cnr' [D] 197.6 em'

[1] _

[2]

[3]--

[4] _

[5] _

[6J __

[7] __

[8] _

[9] __

[to] --

[11] -----------------

[12] -------------------

[13] __

[14J ------------------

[15] --------------

[16] --------------

[17J __

No•.......•,......,-00•.......•

Reference: [11.2.2.23]

[1] 1119.6 cm2


[2] 9.J3 sq. units


[3] -,,-[B-,,-J_


[4] A = 4500, P = 108

Reference: [11.2.2.27]Explanations will vary. The apothem, the radius, and half the side of the regular polygonform a right triangle in which the apothem, a, is a leg and the radius, r, is the hypotenuse. So

[5] a < r.


[6] -,,-[B-,,-]_


[7] -"-[C-L-] _


[8] 240.9 cm2


[9] =[B~]_


[to] ~[B]~


[11] 84 em; 42 cm; 23.33n em


8[12] 3"1t feet


[13] [C]-=----=--


[14] 36 sq. units


[15] 120.597 Ian


[16] $0.56


[17] ~[B,,------]_


[18] [B]-=----=--


[J 9] 2.09 inches


[20] 11 : 8


[21] 37.68m

Reference: (11.4.2.54]

[22] 26.376 cm

Reference: [11.3 .2.3 8]

[23] -,,----[D-,,----] _


[24] ",---[C--,,-]_


[25] ",,---[B--,,--]_

Lesson PlanName David Richards Subject Geometry Date: 3/23

Unit 11TestObjective:8.2 The student will solve problems using perimeters and areas of geometricfigures.Standard:3.12.5,4.12.2,4.12.6

Introduction -l. Quietly have a seat and when you are ready I will pass out the test. The

sooner you are ready the more time you will have for the test.2. When you are finished with the test hand it to me and read a book.

Procedures:l. Stand for the Pledged of Allegiance.

(1 min)

Concept and Skill Development -Testing

(47 min)

Closure -Collect all of the tests and make sure I get every one of them back.

Procedures:Pack up and quiet rows will leave first.

(2 min)

7

Unit Test Specification SheetPolygon

Definitions


Identification


Important Topics


Word problems

Open ended concept

Semester Test 20,36

Proficiency test 33

Long term memory

Unit Test BlueprintPolygon

Combine problem types into each problem.

Use 46 minutes of problems.

Definitions


Identification


Important Topics


Word problems 2

Open ended concept 11

Semester Test 20,36 Could not fmd

Proficiency test 33 1

Long term memory 2

Multiple choice 9

Unit 11 Test

Define the following:

1. Radius of the polygon

2. Apothem of the polygon

3. Central angle of a regular polygon

4. Area of similar polygons

5. Arc length

6. Area of a sector

1. If a circle has a radius of 8 inches, what is the circumference rounded to the nearest wholenumber? Use ,. ~ 3.14.

[A] 50 in. [B] 201 in. [C] 25 in. [D] 100 in.

2. Find the area of a regular decagon with radius 5 cm. Round to the nearest tenth.

[A] 92.1 em' [B] 146.9 cnr' [C] 73.5 cnr' [D] 118.9 cm2

3. The area of a regular octagon is 35 cnr'. What is the area of a regular octagon with sidesthree times as large as the sides of the first octagon?

[A] 250 cnr' [B] 105 em' [C] 3675 em' [D] 315 em'

4. The floor of a gazebo is a regular 20-gon. If the apothem is 30 feet, find the length of eachside to two decimal places.

Regular2(}.gon

a= 30 ft

5. Find the area of a regular decagon with side 6 cm.

6. The circumference of a circle is 84,. em, Find the diameter, the radius, and the length of anarc of 50°.

7. Explain why the apothem of a regular polygon is always less than the radius of thecircumscribed circle.

8. Quadrilaterals ABCD and A' B'C' D' are similar with AB =~ . If the area of ABCD is 115A' B' 2

square units, what is the area of A' B' C'D' ?

8'

~C'

},-\o·

o

9. Two similar trapezoids have areas 108 cm2 and 48 em". Find the ratio of similarity.

10. The base of a gazebo is a regular 20-gon with 6-foot sides. Find its apothem, a, to thenearest tenth of a foot.

Regular20~on

a

11. The perimeter of an equilateral triangle is 18. Find its area.

12. The distance around the equator of Jupiter is about 449,197 km. To the nearest kilometer,what is the equatorial diameter of Jupiter? Use J[ = 3.14.

13. Neil watched a bug crawl through an arc of 60 ° along the rim of his melon, which was cutin half If the radius of the melon was 7 inches, how far did the bug crawl?

14. Maria needs to make a poster that is 1.5 m by 3 m for the big game. The cost of the paper is$1.75. Later she needs another poster with dimensions 0.75 m by 1.5 m. What is the paperfor this poster likely to cost?

r-.15. Find the arc length of AB to two decimal places.

16. The radius of a circular garden is 2.8 m. Find the circumference. Use 1t~ 3.14.

17. Find the area of a regular nonagon with radius 6 em.

18. Given: @O with OC 1.. AB. If OA = 7 and OC = 2, find the arc length of AB to twodecimal places. Explain your reasoning.

B

19. Find the circumference of a circle with radius 9 em. Use 7r ~ 3.14.

----20. Circle 0 has a radius of 7.39. If m LAOB is 112°, then find the length of AB to onedecimal place.

,A ~~~!120/;.39

~'fIo

21. Find the area of an equilateral triangle with side 12.

22. The tires of an automobile have a diameter of22 inches. If the wheels revolve ten times,how far does the automobile move? (Round the result to the nearest tenth of a foot.)

23. An equilateral triangle has a side length of 2.fj. Find its area.

24. The figures are similar. Find the missing values.

oPr= 144

p=?

6A=?

16 A= 180

25. A vehicle travels 125.7 feet while its wheels revolve 16 times. Find the diameter of thewheels to the nearest inch.

[1]

[2]

[3]-----

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13] ---

[14]

[15]

[16]

[17]


[1] -,,---[A--,,-]_


[2] -"-[C-=-]_


[3] .!O-[D--,,-] _


[4] 9.50 ft


[5] 277.0 cm2


[6] 84 cm; 42 em; 11.67n- em

Reference: [11.2.2.27]Explanations will vary. The apothem, the radius, and half the side of the regular polygonform a right triangle in which the apothem, a, is a leg and the radius, r, is the hypotenuse. So

[7] a <r.


[8] 18.4sq. units


[9] 3: 2


[10] 18.9 ft

Reference: [11.2.1.22][11] 9../3 sq. units


[12] 143,056 km


[13] 7.33 inches


[14] $0.44


[15] 2.62 cm


[16] 17.584 m


[17] 104.1 cm2

Reference: [11.4.1.48]2cosLAOC=-7

mLAOC ~ 73.398°mLAOB =2mLAOC ~ 146.797°,.-...mLAOB =mAB

Arc length of AB = (27r . 7)(146.7970) ~ 17.93[18] 360°


(19] 56.52 cm


[20] 14.4 units


[21] 36J3 sq. units


[22] 57.6 ft


[23] 3.J3 sq. units

Reference: [11.3 .1.31 ]

[24] A = 1280, P = 54

Reference: [11.4.2.52][25] 30 in.-------------------------

Documents

Lesson Plan - Wikispacesdavidrichardsarl.wikispaces.com/file/view/Unit+Plan+&+Project+Part... · Lesson Plan Name David Richards ... Concept and Skill Development-Testing (46 min)