geometry problem solving student
TRANSCRIPT
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Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such materials be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with the McGraw-Hill Mathematics program. Any other reproduction, for sale or other use, is expressly prohibited.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 978-0-07-890523-0MHID: 0-07-890523-0
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 10 009 12 11 10 09 08
Illustrators: The Artifact Group, Greg Lawhun, Wayno, Scott Rolfs, Pat Lewis, Jim Callahan, Mark Ricketts
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TABLE of CONTENTS
Letter to the TeacherLetter to the Teacher ......................................................... ......................................................... iviv
Teaching Strategies and AnswersTeaching Strategies and Answers ................................... ................................... v
Reasoning and Proof 1 Series: What’s Shakin’? ........................................................................ 1
2 Reasoning: Money Mystery .................................................................. 4
3 Proof: King of the Learning Lab ........................................................... 5
Practice On Your Own .............................................................................. 6
Triangles and Quadrilaterals 1 Pythagorean Theorem: The Long Walk Home .................................... 7
2 Perpendicular Bisector: The Scavenger Hunt .................................... 10
3 Quadrilaterals: Sunshi Makes a Kite .................................................. 11
Practice On Your Own ............................................................................ 12
Similarity 1 Scale Factors: The Scale of Justice ................................................... 13
2 Ratios: Photo Paper Problem ............................................................. 16
3 Proportions: Radio Riddle .................................................................. 17
Practice On Your Own ............................................................................ 18
Transformations 1 Rotations: Fun By Design .................................................................. 19
2 Reflections: Bank On It ...................................................................... 22
3 Vectors: It’s Your Move ....................................................................... 23
Practice On Your Own ............................................................................ 24
Circles 1 Chords: The Mission .......................................................................... 25
2 Inscribed Angles: Circle Slicing .......................................................... 28
3 Semicircles: Fast Track ...................................................................... 29
Practice On Your Own ............................................................................ 30
Area, Surface Area, and Volume 1 Area: Julia Does Up the Gym ............................................................. 31
2 Surface Area: Problems in Pyramid Painting .................................... 34
3 Volume: What’s Your Volume? ........................................................... 35
Practice On Your Own ............................................................................ 36
iii
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LETTER to the TEACHER
iv
Graphic novels represent a significant segment of the literary market for
adolescents and young adults. They are amazingly diverse, both in terms
of their content and usefulness. Graphic novels are exactly what teens are
looking for—they are motivating, engaging, challenging, and interesting.
They allow teachers to enter the youth culture and students to bring their
“out of school” experiences into the classroom.
Graphic novels have also been used effectively with students with
disabilities, struggling readers, and English learners. One of the theories
behind the use of graphic novels for struggling adolescents focuses on the
fact that the graphic novel presents complex ideas that are interesting and
engaging for adolescents, while reducing the text or reading demands.
However, graphic novels are motivating and engaging for all students.
They allow us to differentiate our instruction and provide universal
access to the curriculum. We hope you’ll find the graphic novels in this
book useful as you engage your students in the study of mathematics
and problem solving.
Sincerely,
Douglas Fisher & Nancy Frey
Douglas Fisher, Ph.D. Nancy Frey, Ph.D.
Professor Associate Professor
San Diego State University San Diego State University
USING GRAPHIC NOVELS:USING GRAPHIC NOVELS:Popular Culture and Mathematics InteractPopular Culture and Mathematics InteractPopular Culture and Mathematics Interact
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TEACHING STRATEGIES and ANSWERS
Graphic Novels in the ClassroomGraphic Novels in the ClassroomAs we have noted, graphic novels are an excellent adjunct text. While they
cannot and should not replace reading or the core, standards-based textbook,
they can be effectively used to build students’ background knowledge,
to motivate students, to provide a different access route to the content, and to
allow students to check and review their work.
Mathematical problem solving is presented in graphic novel format. The
novels contain real-world problems for each of the following mathematical
content strands: Reasoning and Proof, Triangles and Quadrilaterals, Similarity,
Transformations, Circles, and Area, Surface Area, and Volume.
• The first graphic novel that appears in each content strand describes a
real-world problem that is solved in graphic novel format.
• The second and third graphic novels that appear in each content strand
are left to the reader to formulate the solution.
• Finally, there are additional problems for students to practice on their own.
Teaching StrategiesTeaching Strategies
1. Previewing Content You can use a graphic novel as a lesson preview
to activate background and prior knowledge. For example, you may
display a graphic novel on the overhead projector and discuss it with the
class. By doing so, you may provide students with advance information
that they will read later in the book. Alternatively, you may display the
graphic novel and invite students, in pairs or groups, to share their
thinking with one another. Regardless of the approach, the goal is to
activate students’ interest and background knowledge in advance of the
reading.
2. Narrative Writing Use the second and third graphic novels from each
content strand and ask students to solve the posed problem in graphic
novel format. Students should be encouraged to create character
dialogue and complete the story line detailing their solution. Another
alternative is to provide students with the first two pages of the first
graphic novel and ask students to complete the story line with the
solution to the problem posed. Not only does this engage students in
thinking about the content, but it also provides you with some assessment
information. Based on the dialogue that the students create of their
solution, you’ll understand what they already know, what they
misunderstand, and what they do not yet know.
v
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3. Reviewing Content In addition to narrative summaries, graphic novels
can also be used for content review. While there are many reasons to
review content—such as preparing for a test—graphic novels are
especially useful for providing students with a review of past chapters.
You can use a graphic novel from a previous chapter to review its major
concepts.
4. Analysis In the analysis approach, students read the graphic novel to try
to understand the main point the author is making. This approach is
particularly useful after students have covered the content in their
textbook. Encouraging students to pose questions about the text will help
to uncover the main points. For example:
• Why did the author choose this real-world situation to present this
concept we have studied? What are some other real-world situations
that can be used to present this concept?
• What does the graphic novel tell me about concepts we have studied?
Have students write a few sentences answering these questions. Then, have
them summarize what they believe is the main point of the graphic novel.
5. Visualizing Have your students skim over the exercises in the chapter
you are working on or the Practice On Your Own pages. The student
should then pick one exercise and create their own graphic representation
about it. Another option would be to use other forms of multimedia for
their topic. Students could take pictures, make a computer slide-show
presentation, make a video, or create a song.
These are just some of the many uses of graphic novels. As you introduce
them into your class, you may discover more ways to use them to engage
your students in a new method of learning while exercising the multiple
literacies that your students already possess. We welcome you to the world
of learning through graphic novels!
Cary, S. (2004). Going graphic: Comics at work in the multilingual classroom. Portsmouth, NH: Heinemann.
Fisher, D., & Frey, N. (2004). Improving adolescent literacy: Strategies at work. Upper Saddle River, NJ: Merrill
Education.
Frey, N., & Fisher, D. (2004). Using graphic novels, anime, and the Internet in an urban high school. English
Journal, 93(3), 19–25.
Gorman, M. (2002). What teens want: Thirty graphic novels you can’t live without. School Library Journal,
48(8), 42–47.
Schwarz, G. (2002a). Graphic novels for diverse needs: Engaging reluctant and curious readers. ALAN
Review, 30(1), 54–57.
Schwarz, G. (2002b). Graphic novels for multiple literacies. Journal of Adolescent & Adult Literacy, 46,
262–265.
Schwarz, G. (2004). Graphic novels: Multiple cultures and multiple literacies. Thinking Classroom, 5(4), 17–24.
ReferencesReferencesReferences
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ANSWERSANSWERS
vii
Reasoning and ProofReasoning and ProofReasoning: Money Mystery, page 4
Set up a grid that contains the information Toshiro received. Use each piece
of information to eliminate as many boxes as possible. When the grid is
completed, you will know who put the money box in the wrong place.
long
hair
short
hair
curly
hair
black
hair
straight
hairjeans shorts skirt khakis
black
pants
Tina × × × × × × × ×George × × × × × × × ×Alexa × × × × × × × ×José × × × × × × × ×Paul × × × × × × × ×jeans × × × ×shorts × × × ×skirt × × × ×khakis × × × ×black
pants× × × ×
Alexa has curly hair and put the money box in the wrong place.
Proof: King of the Learning Lab, page 5To find the fallacy, justify each step with a property of real numbers.
1. a > 0, b > 0 Given
2. a = b Given
3. ab = b 2 Multiply each side by b.
4. ab - a 2 = b 2 - a 2 Subtract a 2 from each side.
5. a(b - a) = (b + a)(b - a) Factor each side.
6. a = b + a Divide each side by (b - a).
7. 0 = b Subtract a from each side.
8. b = 2b Add b to each side.
9. 1 = 2 Divide each side by b.
It appears that each step has a justification. However, in Step 6, each side of
the equation was divided by the quantity b - a. This can only be done if
b - a ≠ 0. However, it is given in Step 2 that a = b. By substituting b for a,
you find the quantity b - a = b - b = 0.
The fallacy happens in Step 6 because you cannot divide by zero.
Practice On Your Own, page 6
1. C 2. G 3. D 4. J 5. D 6. F
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viii
Triangles and QuadrilateralsTriangles and Quadrilaterals
Perpendicular Bisector: The Scavenger Hunt, page 10The point that is equidistant from the vertices of a triangle is the point
where the perpendicular bisectors of each side intersect.
Use a compass and straightedge to construct the
perpendicular bisectors.
1. Set the compass opening to be slightly larger than
half the length of the line.
2. Draw an arc centered at each endpoint.
3. Draw the perpendicular bisector by connecting the
connecting the points where the two arcs intersect.
Repeat these steps to draw the perpendicular bisector
556 ft
428 ft
382 ft
Happiness Park
for each side of the triangle.
Extend all three perpendicular bisectors until they intersect.
This is the point where Jacob should look for the item.
Quadrilaterals: Sunshi Makes a Kite, page 11 Sketch a diagram of Sunshi’s kite and mark the given information.
Use the Pythagorean Theorem to find the lengths of a 1 and a 2 .
In the smaller triangles in the upper portion of the kite, b = 13
and c = 18.4.
a 2 2 + b 2 = c 2 Pythagorean Theorem
18.4 in.
29 in.
18.4 in.
29 in.
13 in. 13 in.
a 1
a 2
a 2 2 + 13 2 = 18.4 2 Substitute 13 for b and 18.4 for c.
a 2 2 + 169 = 338.56 Evaluate powers.
a 2 2 = 169.56 Subtract 169 from each side.
a 2 ≈ 13.02 Take the square root of each side.
In the larger triangles in the lower portion of the kite, b = 13 and c = 29.
a 1 2 + b 2 = c 2 Pythagorean Theorem
a 1 2 + 13 2 = 29 2 Substitute 13 for b and 29 for c.
a 1 2 + 169 = 841 Evaluate powers.
a 1 2 = 672 Subtract 169 from each side.
a 1 ≈ 25.92 Take the square root of each side.
The longer diagonal should be the length of a 1 + a 2 . a 1 + a 2 ≈ 13 + 26 = 39
Sunshi needs to cut the longer wood piece to be 39 inches.
Practice On Your Own, page 12
1. C 2. H 3. A 4. H 5. A 6. G
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ix
SimilaritySimilarity
Ratios: Photo Paper Problem, page 16 Find the ratio of the areas of the papers.
The formula for the area of a rectangle is A = �w.
Write a ratio of the area of the smaller size paper to the area of the larger
size paper.
4 × 6
_ 8 × 12
= 24 _
96 or 1 _
4
The larger size paper is 4 times larger than the smaller size paper. The larger
paper should cost 4 times the cost of the smaller paper.
$0.25 × 4 = $1
The paper for an 8-inch by 12-inch photo should cost $1.
Proportions: Radio Riddle, page 17 Set up a proportion that equates Rosalyn’s height and the length of her
shadow to the tower’s height and the length of its shadow.
height of Rosalyn
__ length of her shadow
= height of the tower
___ length of the tower’s shadow
5.5
_ 3 = x
_ 273
Substitute.
1501.5 = 3x Cross multiply.
500.5 = x Divide each side by 3.
The tower is approximately 500.5 feet tall.
Practice On Your Own, page 18
1. C 2. G 3. C 4. G 5. C 6. G
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x
TransformationsTransformations
Reflections: Bank On It, page 22 In order to line up the shot, Sandra considers the right side of the pool table
a line of reflection. She visualizes the location of the left side pocket if it were
reflected over that line. If she aims at the imaginary image of the pocket after
it is reflected over the line, the ball will bank off of the bumper on the side of
the table and into the left, side pocket.
This is because the ball will bounce off the right side bumper at the same
angle as it hits. Because a reflection preserves angle measure, the angle
from the ball to the image of the pocket is the same as the angle between
the point where the ball hits the side bumper and the target pocket.
Line of Reflection
Reflected Pocket
Back Angle
Vectors: It’s Your Move, page 23 Find the horizontal movement and the vertical movement of the knight.
The knight moves a horizontal distance from b8 to c8. This is a move of
1 square.
The knight moves a vertical distance from c8 to c6. This is a move of
2 squares.
The vector Kanya sends to Analiese to indicate his move is <1, 2>.
Practice On Your Own, page 24
1. D 2. H 3. B 4. D 5. H 6. B
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xi
CirclesCircles
Inscribed Angles: Circle Slicing, page 28Madison can use properties of inscribed
angles to find the center of the circle.
When a right angle is inscribed in a
circle, the intercepted arc is 180°. Begin
by placing the vertex of a right angle
anywhere on a circle. Mark the points
where the sides of the angle intersect
the circle. Draw a line to connect these
points. This line is a diameter of the circle.
Place the right angle at another point
and draw a second diameter. The point
where the two diameters intersect is
the center of the circle.
The location of the fountain is the point
where the diameters intersect.
Semicircles: Fast Track, page 29Because the width of the rectangle is 160 yards, the radius of each
semicircle is 160 ÷ 2 or 80 yards.
Because the radii of the semicircles are 80 yards, the length of the property
remaining for the straight sections is 300 - 2(80) or 140 yards.
300 yd
80 yd 80 yd
The length of the turns is the circumference of the semicircles. Because the
two semicircles make a whole circle, the total length of the turns is the
circumference of a circle with radius 80 yards.
C = 2πr Formula for circumference of circle
= 2π(80) or about 502 yd Substitute 80 for r.
The lengths of two
straight sectionsplus
the circumference
of the two turnsequals
the length
of track.
2(140) + 502 = 782
The maximum length Nate can make the track is 782 yards.
Practice On Your Own, page 30
1. C 2. G 3. B 4. G 5. A 6. C
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xii
Area, Surface Area, and VolumeArea, Surface Area, and Volume
Surface Area: Problems in Pyramid Painting, page 34 Use the formula for the surface area of a pyramid: S = 1 _
2 P� + B, where
P is the perimeter of the base, � is the slant height, and B is the area of the
base. B = 6 × 6 or 36 ft2, and P = 6 × 4 or 24 ft.
SA = B + 1 _ 2 P� Formula for surface area of pyramid
= 36 + 1 _ 2 (24)(8) Substitute 36 for B and 24 for P.
= 36 + 96 or 132 ft 2 Multiply and add.
Alejandro needs paint to cover 132 square feet on the pyramid.
Volume: What’s Your Volume?, page 35 Find the volume of each of Della’s garbage cans. The formula for the
volume of a cylinder is V = πr 2 h, where r is the radius and h is the height.
r = 1 _ 2 d, where d is the diameter; 1 _
2 (34) or 17, and h = 32.
V = πr 2 h Formula for volume of cylinder
= π(17) 2 (32) Substitute 17 for r and 32 for h.
≈ 29,053.4 in 3 Evaluate the power and multiply.
Della collected 3 garbage cans, so she collected 3(29,053.4) or 87,160.2
cubic inches of aluminum.
Find the volume of each of Juanita’s boxes. The formula for the volume of a
rectangular prism is V = �wh, where � is the length, w is the width, and h is
the height.
For one box, � = 3, w = 4, and h = 5. For the other box, � = 2, w = 4, and h = 6.
V = �wh Formula for volume
of rectangular
prism
V = �wh Formula for volume
of rectangular
prism
= 3 × 4 × 5 or 60 ft3 Substitute. = 2 × 4 × 6 or 48 ft3 Substitute.
Juanita collected 60 + 48 or 108 cubic feet of aluminum.
The volume of the garbage cans is in cubic inches, and the volume of the
boxes is in cubic feet. Convert the volumes to the same units. There are
12 inches in 1 foot. Because volume is a cubic measurement, divide Della’s
volume by 123 to find the volume in cubic feet.
87,160.2
_ 123
≈ 50.44
Della collected about 50 cubic feet of aluminum. 108 cubic feet is more than
50 cubic feet, so Juanita collected more aluminum than Della.
Practice On Your Own, page 36
1. C 2. F 3. D 4. H 5. B 6. G 7. C
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1
Reasoning and Proof 1: Series
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2
Reasoning and Proof 1: Series (continued)
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3
Reasoning and Proof 1: Series (continued)
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4
Reasoning and Proof 2: Reasoning
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5
Reasoning and Proof 3: Proof
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PRACTICEPRACTICE
6
Reasoning and ProofReasoning and ProofRead each question. Then, fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
1. Which of the following is the inverse of
the statement, If it is Saturday, then
Jennifer is at work?
A If Jennifer is at work, then it is Saturday.
B If Jennifer is not at work, then it is not Saturday.
C If it is not Saturday, then Jennifer is not at work.
D If it is Saturday, then Jennifer is not at work.
2. Which of the following can you conclude
given the statement, Tara was not the
first person in line?
F Tara did have a person behind her in line.
G Tara did have a person in front of her in line.
H Tara did not have a person behind her in line.
J Tara did not have a person in front of her in line.
3. In the diagram below, ��� AB is an angle
bisector of ∠DAC.
B
CA
D
Which of the following conclusions does
not have to be true?
A ∠DAC ∠BAC
B A and D are collinear.
C 2(m∠BAC) = m∠DAC
D ∠DAC is a right angle.
4. Which property justifies the following
statement?
If m∠A = m∠B and m∠B = m∠C, then m∠A = m∠C.
F Reflexive Property
G Substitution Property
H Symmetric Property
J Transitive Property
5. Which Venn diagram illustrates that all
reality TV shows are on Channel 10?
A
RealityTV Shows
Channel10
B Reality
TV Shows
Channel10
C
RealityTV Shows
Channel10
D
RealityTV Shows
Channel10
6. What is the hypothesis of the statement,
Any two Labradors are similar?
F if two dogs are Labradors
G if two Labradors are dogs
H if Labradors are similar
J if two dogs are similar
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7
Triangles and Quadrilaterals 1: Pythagorean Theorem
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8
Triangles and Quadrilaterals 1: Pythagorean Theorem (continued)
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9
Triangles and Quadrilaterals 1: Pythagorean Theorem (continued)
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10
Triangles and Quadrilaterals 2: Perpendicular Bisector
Are you ready for thescavenger hunt?
Here’s a mapwith all the details.
Read it over andbring back what you find.
Any questions? Yeah, it saysthe item is in
a spot equidistantfrom the swing,
the tree andkoi pond.
That’s what you needto figure out!
Hmmm?
Whereshould Jacob
look forthe item?
What doesthat mean?
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11
Triangles and Quadrilaterals 3: Quadrilaterals
YOUR TURN!YOUR TURN!Help Sunshi makeHelp Sunshi make
her kite.her kite.
The shorterpiece needs to
bisect the longerpiece so that twothirds of the lengthof the longer piece
forms the lowerportion ofthe kite.
SUNSHI MAKES A KITE
Sunshiis making akite for the
spring parade.
Theshorter pieceof wood is 26inches long.
Sunshi uses aquadrilateral-shapedpiece of fabric with
two consecutive sideseach measuring18.4 inches andtwo consecutive
sides eachmeasuring29 inches.
YOUR TURN!Help Sunshi make
her kite.
?hi!
this isgoing to beawesome!
What lengthshould I cut the
longer pieceof woOd?
1 3
42
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PRACTICEPRACTICE
12
Triangles and QuadrilateralsTriangles and QuadrilateralsRead each question. Then, fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
1. When Oscar looks at his roof on the side
of his house, he sees an isosceles
triangle. The legs of the triangle are 16
feet and the base is 10 feet. What is the
measurement of the altitude of the roof?
A 10 feet
B 11.6 feet
C 15.2 feet
D 16 feet
2. Cliff has cut an equilateral triangle out of
a sheet of notebook paper. He then
draws an angle bisector through one of
the angles and cuts along that line. Cliff
now has two triangles. Which word best
describes these two new triangles?
F hypotenuse
G equilateral
H congruent
J acute
3. Desiree is at a swimming pool with
her friends Katie and Michaela. Katie
and Michaela are at one corner of the
31 feet by 20 feet rectangular pool.
Desiree is at the opposite corner of the
pool. Katie swims along the diagonal
of the pool to reach Desiree. Michaela
walks around the sides of the pool to
reach Desiree. Estimate the distance
Katie saves by swimming to Desiree
rather than walking.
A 14 feet
B 23 feet
C 28 feet
D 37 feet
4. In the figure below, n is a whole number.
What is the least possible value for n?
25
n
2n
F 7 G 8 H 9 J 11
5. Delsin is constructing a triangular display
case in the shape of an isosceles
triangle. One of the angles is 40°. Which
of the following could be the measure of
one of the other angles?
A 70°
B 80°
C 110°
D 140°
6. Hallie cuts a hexagon from a piece of
poster board. She uses a protractor to
mark the first interior angle along the
bottom edge of the board as shown
below. What is the m∠1 in the piece of
poster board she cut off?
1
F 120° G 60° H 40° J 30°
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13
Similarity 1: Scale Factors
The Scale of Justice
Thanks for helping mewith my civics project,Alex. I’m having a littletrouble getting started.
How so?
Well, I picked a court roomfor my project. And I have
to build a diorama.
Yeah, I even have thecourtroom plan showing
the actual dimensions. See…
Looks like you havewhat you need.
What’s the problem?
Brianna & Alex in
30 feet
20 fe
et
Plaintiff ‘s TableDefendant ‘s Table
Judge’s Bench
WitnessStand
Court clerk’sTable
CourtReporter
Table
Jury RoomJudge’s Chambers
Jury Box
5 ft × 2 ft
5 ft × 2 ft
7 ft × 5 ft
5 ft × 2 ft
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14
Similarity 1: Scale Factors (continued)
I’m not sure what sizethings should be. My basefoam board is 40” x 60”
I get it, you need a scale factor.That will help you figure out
the size of the diorama comparedto the real courtroom.
Okay, how doI do that?
Here. I’ll show you.First we’ll start with the
courtroom length and widthcompared to the foamboard
length and width and fillin the dimensions.
Yep, now you cantake the dimensionsin feet on your planand turn them into
inches in yourdiorama.
length of courtroomlength of foamboard
width of courtroomwidth of foamboard
=
=
30 ft60 inches
20 ft40 inches
1 ft2 inches
1 ft2 inches
or
So, since the ratio is1 ft./2 inches for both the
width and the height,my scale for both dimensions
is the same. Awesome!
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15
Similarity 1: Scale Factors (continued)
So I can plan out mydiorama dimensionsand start building!
Thanks, Alex!
Let’s see… thecourt clerk’s tableis 5 feet x 2 feet.So in my diarama,
that’s 10” x 4”.
Hey sis, how’s thediorama coming?
Just putting onthe finishing touches.What do you think?
I think I’m getting anA on my Civics project!
One week later.
60 in.
40 in
.
Plaintiff ‘s TableDefendant ‘s Table
Judge’s Bench
WitnessStand
Court clerk’sTable
CourtReporter
Table
Jury RoomJudge’s Chambers
Jury Box14 in. × 10 in.
10 in. × 4 in.
10 in. × 4 in.
10 in. × 4 in.
Terra’s Diagram
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16
Similarity 2: Ratios
I thought youhad plenty.
All I have is4” X 6” paper,and I wantedto print these
on 8” X 12”.
I wonder how muchmore that will cost.
How much isa single sheet
of 4” X 6”paper?
Only 25¢.
I wonder if thecost of paper
increasesproportionally.
Probably not,but if it did...
...a sheet of8” × 12”
photo papershould only
cost me...
?
Boy, the printeris getting low on
photo paper!
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17
Similarity 3: Proportions
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PRACTICEPRACTICE
18
1. The Eiffel Tower in Paris, France, stands
324 meters tall. The Paris Hotel in Las
Vegas has a 1 _ 2 scaled replica of the
tower. How tall, to the nearest foot, is the
tower in Las Vegas? Use the conversion
1 meter ≈ 3.3 feet.
A 99 ft
B 162 ft
C 535 ft
D 1063 ft
2. Each time a sheet of plain 8 1 _ 2 -inch
by 11-inch paper is folded in half, a
rectangle similar to the original rectangle
is formed. What are the dimensions of
the rectangle formed after the paper is
folded four times?
F 4 1 _ 4 in. by 5 1 _
2 in.
G 2 1 _ 8 in. by 2
3 _
4 in.
H 2 1 _ 4 in. by 2 1 _
2 in.
J 1 1 _ 16
in. by 1 3 _
8 in.
3. Travis, who is 5 feet 9 inches, measured
his shadow to be 2 feet 6 inches. At the
time, Taina measured the shadow of the
tree in their backyard to be 7 feet 3
inches. What is the estimated height of
the tree?
A 3 ft 2 in.
B 16 ft 6 in.
C 16 ft 8 in.
D 17 ft 10 in.
4. If you set a copy machine at 120%, what
will be the dimensions of the copy of a
6-inch by 8-inch image?
F 5 in. by 6 2 _ 3 in.
G 7.2 in. by 9.6 in.
H 8 in. by 10 in.
J 720 in. by 960 in.
5. Given that trapezoid BCDE is similar to
trapezoid KLMN, find the length of −−− MN .
15 cm 12 cm
10 cm 8 cm
6 cm
A 12 cm
B 8 cm
C 7.5 cm
D 4.8 cm
6. The dimensions of the home plate in a
professional baseball stadium are shown
in the diagram. An architect is creating a
model of a new baseball stadium that is
a 3 _
8 scale of the actual stadium. What is
the perimeter of a home plate he makes
for the model stadium?
F 14 in.
12 in.
8.5 in. 8.5 in.
12 in.
17 in.
G 21.75 in.
H 54.19 in.
J 58 in.
SimilaritySimilarityRead each question. Then, fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
000i_0036_GNG_890523.indd 18000i_0036_GNG_890523.indd 18 6/17/08 9:07:33 AM6/17/08 9:07:33 AM
19
Transformations 1: Rotations
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20
Transformations 1: Rotations (continued)
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21
Transformations 1: Rotations (continued)
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22
Transformations 2: Reflections
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23
Transformations 3: Vectors
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PRACTICEPRACTICE
24
TransformationsTransformationsRead each question. Then, fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
1. A reflection has been applied to the
letter N. Which of the following images
has had the same reflection applied?
A C
B D
2. In a board game, moves are made using
translations. Which translation will allow
the black chip to capture the white chip?
F ⟨6, -3⟩ H ⟨5, -3⟩G ⟨-3, 5⟩ J ⟨-4, 2⟩
3. What is the order of rotation for the yard
ornament shown here?
A 2
B 4
C 8
D 16
4. What are the coordinates of the image
of vertex C after a reflection over the
x-axis?
O
y
x-6 -4-8 -2 2
-3
-1
1
3
5
7
B
A
C
A (-2, -4) C (0, -1)
B (2, 4) D (0, 1)
5. A series of transformations are shown.
What is a single transformation to get
from Step 1 to Step 7?
Step 1
Step 7
F vertical reflection
G 90° counterclockwise rotation
H 90° clockwise rotation
J 180° rotation
6. What angle of rotation does Riley use to
completely surround the circle with his
name?
A 30° C 120°
B 60° D 360°
NN
KK
RR
FF
RileyRile
yR
ileyRileyRileyR
ileyR
iley
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25
Circles 1: Chords
There is a distress beaconburied somewhere in the woods.
It’s my mission to locate it.
Marcos in
THE MIsSION
The pressureis on! |'m upagainst the
clock.
If | want to become apart of my community
rescue team, |’ll have toretrieve the beacon...
...before mytime runs out.
blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip!blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip!blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip!
blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip!blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip!blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip!
blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip!blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip!blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip! blip!
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26
Circles 1: Chords (continued)
At this point, | need to walk at a rightangle, away from the sound, until | canno longer hear the signal--point C.
The beacon emits a signalthat can be heard within a
30-meter radius.
To locate the center of a circle with a 30-meter radius, | must use the properties of chords
and diameters.
| can hear the signal at point A, so | shouldwalk in a straight line until | can no longer
hear the signal--point B.
If a radius of a circle intersects a chordat a right angle, then the diameter bisectsthe chord. | should find the midpoint of thepath AB. That is where the sound should
be the loudest.
A B
A B
C
blip!blip!blip!
blip!blip!blip!
blip!blip!blip!
blip!blip!blip!blip!blip!blip!
blip!blip!blip!
blip!blip!blip!
blip!blip!blip!
blip!blip!blip!
blip!blip!blip!
| haveto hurRy. the
clock isticking!
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27
Circles 1: Chords (continued)
Because it is perpendicular toAB at its midpoint, this path is part of
a radius of the circle that has thebeacon at its center.
thedistresSbeaconis buriedhere!
To find the rest of the radius,| need to turn 180˚ and walkthe opposite direction until| can no longer hear the
signal--point D.
The midpoint of the path, CD, isthe center of the circle.
Okay,this is
the centerof thecircle.
D
A B
C
blip!blip!blip!
blip!blip!blip!
blip!blip!blip!
blip!blip!blip!
blip!blip!blip! blip!blip!blip!
CONGRaTULATIONS,MARCOS.
youmade the
team!
END
almostthere, and I thinkI’m making goOd
time, toO.
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28
Circles 2: Inscribed Angles
What’chadrawing, Sis?
with Madison and her little brother
I need to come upwith a sketch
for my communityservice project.
Is it a horse?
No, silly!I’m drawing acircular water
garden forthe park.
I can use my paper cupto make a circle.
This will be the total area of my garden.
And thehorse will bein the middleof the garden?
No horse!I want to place a fountain
directly in the center,but all I have with me is this
cup and a fewpieces of paper
to use as right anglesand a straightedge.
If I keep talking insteadof drawing, I’m gonna be
a little hoarse!
That wouldmake
you a pony!
What canMadison do
to findthe center
of hercircle?
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29
Circles 3: Semicircles
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PRACTICEPRACTICE
30
1. The diameter of Earth at the equator is
about 7926 miles. An airplane flies at
600 mph about 5.5 miles above Earth in
a path that follows the equator. About
how long will it take for this plane to
travel all the way around Earth?
A 42 days C 42 hours
B 21 days D 21 hours
2. In a circular theater, Laura wants to sit
along the edge of the room, as close to
the center of the theater as possible. In
the diagram below, she is seated at
Point L. What is the minimum angle of
vision that Laura needs to be able to see
the entire stage?
stage
118°110°
L
F 33° H 76°
G 66° J 152°
3. A guest that wants the largest portion
should select a slice from which of the
following pizzas?
A a 10-inch pizza cut into four equal-sized pieces
B a 14-inch pizza cut into six equal-sized pieces
C a 16-inch pizza cut into eight equal-sized pieces
D an 18-inch pizza cut into ten equal-sized pieces
4. Circle C has radius r and ABCD is a
rectangle. Find DB.
F r √ � 3
G r
H r √ � 2 _
2
J r √ � 3 _
2
5. James bakes an apple pie in an
8-inch pie plate. He cuts the pie twice
through the center to make 4 equal
pieces. What is the length of the arc in
each piece that the outermost crust
makes?
A 2π inches
B 3π inches
C 4π inches
D 8π inches
6. In geometry class, Callie was given a
piece of grid paper with the graph of the
circle with equation
(x + 2) 2 + (y + 2) 2 = 25.
She must write the equation of
another circle that can be graphed
on the same piece of paper and
completely fit into the circle she was
given. Which equation could be the
one Callie wrote?
A (x + 1) 2 + (y - 1) 2 = 9
B (x - 1) 2 + (y + 1) 2 = 9
C (x + 1) 2 + (y + 1) 2 = 9
D (x - 1) 2 + (y - 1) 2 = 9
CirclesCirclesRead each question. Then, fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
000i_0036_GNG_890523.indd 30000i_0036_GNG_890523.indd 30 6/17/08 9:07:43 AM6/17/08 9:07:43 AM
31
Area, Surface Area, and Volume 1: Area
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32
Area, Surface Area, and Volume 1: Area (continued)
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33
Area, Surface Area, and Volume 1: Area (continued)
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34
Area, Surface Area, and Volume 2: Surface Area
Your minature golf course is gonna be cool
Alejandro and Tyler in...
Yeah... all we needto do is paint this
pyramid!
when we’re done!I want it to look like sandstone
when it’s finished.
That will besweet!
It would be so mucheasier to figure if the sides were
square.
Like you?
How wide is the base,Alejandro?
I come upwith 6 feet
wide.
And what is theslant height?
Looks like8 feet.
What is thesurface area
that Alejandroand his
buddy needto paint?
000i_0036_GNG_890523.indd 34000i_0036_GNG_890523.indd 34 6/17/08 9:07:47 AM6/17/08 9:07:47 AM
35
Area, Surface Area, and Volume 3: Volume
Juanita & Della in
What’s yourVolume?
You FigureIt Out!
Who HasMore
Volume?
Okay. All 3 ofmy trash cans are34 inches high and
have a 32 inchdiameter.
Whatever! Let’s figureout the volume to see
who has more.
How do youfigure? I think I’ve got more!
I think it’sobvious. My boxeshave more volume.
Hi, Juanita! Are youready to see who has the
most aluminum cans?
RECYCLINGRECYCLINGCENTER Hey, Della!
Take a look at my boxes. Ithink I’ve got you beat!
You’re on! Whoever hasless can pay for movie
tickets tonight.
RECYCLINGRREECCYYCCLLIINNGGCENTERSpr ing C leanup C o n t e s t
My first box is 3feet by 4 feet by5 feet. The otherbox is 2 feet by4 feet by 6 feet.
000i_0036_GNG_890523.indd 35000i_0036_GNG_890523.indd 35 6/17/08 9:07:47 AM6/17/08 9:07:47 AM
PRACTICEPRACTICE
36
Area, Surface Area, and VolumeArea, Surface Area, and VolumeRead each question. Then, fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
1. Hinto is wrapping a box that is 14 inches
long, 8 inches wide, and 2 inches tall. At
the very minimum, how much wrapping
paper will he need?
A 224 in 2 C 312 in 2
B 224 in 3 D 312 in 3
2. During the week, Evita drinks 6 glasses
of water each day using the glass shown
below on the left. On Saturday and
Sunday, she drinks 5 glasses of water
using the glass shown below on the
right. How much more water does she
drink each weekday than each day on
the weekend?
6 in.
3 in.
4 in.
2 in.
F about 3 in 3
G about 8 in 3
H about 250 in 3
J about 670 in 3
3. Nestor wants to know the volume of the
Great Pyramid of Giza in Egypt. The
height of the pyramid is 455 feet and the
length of each side of the base is 756
feet. What is the approximate volume of
the Great Pyramid of Giza?
A 38,278,280 ft 3
B 52,170,300 ft 3
C 65,012,220 ft 3
D 86,682,960 ft 3
4. Roberto pulled the pages out of a
catalogue and laid them side by side.
The catalogue had 750 8-inch by 10-inch
pages. What was the total area
covered by the pages?
F 750 in 2
G 6,000 in 2
H 30,000 in 2
J 60,000 in 2
5. Cleveland wants to build a fence around
the circular field where his horses graze.
The diameter of the field is 500 feet.
Approximately how many feet of fencing
does Cleveland need?
A 786 feet C 196,350 feet
B 1570 feet D 785,399 feet
6. Ella finds an artist that will paint an
ornamental garden ball with any design
she wants, but she charges $0.06 per
square inch of surface area. The ball
she wants painted has a diameter of
12 inches. About how much will it
cost her for a design that covers the
entire ball?
F $4.50 H $54.00
G $27.00 J $90.00
7. Bianca has a rectangular fish tank. Its
dimensions are 4 feet by 3 feet by 2 feet.
How much water does she need to fill
the tank if 6 cubic feet are taken up by
coral and sand?
A 144 ft 3 C 18 ft 3
B 24 ft 3 D 3 ft 3
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