Transcript Measurement, Dilations, Proportions, Geometric Problem Solving

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To Play Some . . .
JEOPARDY
JEOPARDY
JEOPARDY
Jeopardy Board
Final Jeopardy
Measurement
Dilations and
Measurements
Proportions
Geometric
Problem Solving
100
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200
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300
300
300
300
400
400
400
400
500
500
500
500
Measurement 100
The net of a cylinder is shown below. Use the
ruler on the Mathematics Chart to measure the
1
dimensions of the cylinder to the nearest inch.
8
Which is closest to the total surface area of
this cylinder?
F 4 in.2
G 11 in.2
H 14 in.2
J
25 in.2
Board
Answer
Measurement 100
The net of a cylinder is shown below. Use the
ruler on the Mathematics Chart to measure the
1
dimensions of the cylinder to the nearest inch.
8
Which is closest to the total surface area of
this cylinder?
F 4 in.2
G 11 in.2
H 14 in.2
J
25 in.2
Board
Length _______
3 in
Measurement 100
The net of a cylinder is shown below. Use the
ruler on the Mathematics Chart to measure the
1
dimensions of the cylinder to the nearest inch.
8
Which is closest to the total surface area of
this cylinder?
Area = 12 in2
Lateral Area Only
F 4 in.2
G 11 in.2
Width _______
4 in
H 14 in.2
J
25 in.2
Board
Length _______
3 in
Measurement 100
The net of a cylinder is shown below. Use the
ruler on the Mathematics Chart to measure the
1
dimensions of the cylinder to the nearest inch.
8
Which is closest to the total surface area of
this cylinder? Circles 5
Area = 12 in2
F 4 in.2
Lateral Area Only
Radius = ______
8
G 11 in.2 As a decimal
Two Circles
Width _______
4 in
Total Surface
2
H 14 in.
Area
J
25 in.2
12.000
πr2
Area of a circle = _______
2
A
=
π(0.625)
Board
A = 1.227
Length _______
3 in
1.227
1.227
14.454
Measurement 200
The net of a cube is shown below. Use the ruler
on the Mathematics Chart to measure the
1
dimensions of the cube to the nearest inch.
4
Find the surface area of the cube
to the nearest square inch.
A 2 in.2
B 9 in.2
C 14 in.2
D 18 in.2
Board
Answer
Measurement 200
The net of a cube is shown below. Use the ruler
on the Mathematics Chart to measure the
1
dimensions of the cube to the nearest inch.
4
Find the surface area of the cube
to the nearest square inch.
A 2 in.2
B 9 in.2
C 14 in.2
D 18 in.2
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1
2
1 in
Measurement 200
The net of a cube is shown below. Use the ruler
on the Mathematics Chart to measure the
1
dimensions of the cube to the nearest inch.
4
Find the surface area of the cube
to the nearest square inch.
A 2 in.2
B 9 in.2
C 14 in.2
D 18 in.2
Board
1
2
1 in
1
2
1 in
Measurement 200
The net of a cube is shown below. Use the ruler
on the Mathematics Chart to measure the
1
dimensions of the cube to the nearest inch.
4
Find the surface area of the cube
to the nearest square inch.
A 2 in.2
B 9 in.2
2.25 in2
2.25 in2
C 14 in.2
D 18 in.2
Board
1
2
1 in
1
1 in
2
2.25 in2
2.25 in2
2.25 in2
2.25 in2
Measurement 300
The net of a cylinder is shown below. Use the
ruler on the Mathematics Chart to measure the
dimensions of the cylinder to the nearest tenth of
a centimeter.
Find the total surface area of this cylinder to the
nearest square centimeter.
F 6 cm2
G 14 cm2
H 19 cm2
J
33 cm2
Board
Answer
Measurement 300
2 cm
The net of a cylinder is shown below. Use the
ruler on the Mathematics Chart to measure the
dimensions of the cylinder to the nearest tenth of
a centimeter.
Find the total surface area of this cylinder to the
nearest square centimeter.
F 6 cm2 Rect. = 18.8 cm2
1.5 cm
G 14 cm2 Circle = 7.1 cm2
9.4 cm
H 19 cm2 Circle = 7.1 cm2
33.0 cm2
J
33 cm2
Board
Measurement 400
The net of a cylinder is shown below. Use the
ruler on the Math Chart to measure the
dimensions of the cylinder to the nearest tenth of
a centimeter. Which of the following best
represents the total surface
area of this cylinder?
F 142 cm2
G 93 cm2
H 23 cm2
J
14 cm2
Board
Answer
Measurement 400
10.5 cm
The net of a cylinder is shown below. Use the
ruler on the Math Chart to measure the
dimensions of the cylinder to the nearest tenth of
a centimeter. Which of the following best
7 cm
represents the total surface
1.7 cm
area of this cylinder?
F 142 cm2 Rect. = 73.5 cm2
G 93 cm2 Circle = 9.1 cm2
2
2
Circle
=
9.1
cm
H 23 cm
2
2
91.7
cm
J
14 cm
Board
Measurement 500
Use the ruler on the Mathematics Chart to
measure the dimensions of the composite
figure to the nearest tenth of a centimeter.
Which best represents the approximate
area of this composite figure?
A
B
C
D
34.7 cm2
38.8 cm2
44.6 cm2
54.5 cm2
Board
Answer
Measurement 500
34.7 cm2
38.8 cm2
44.6 cm2
54.5 cm2
2.5 cm
10.5 cm
3.4 cm
1
bh
2
triangle = _____
Board
Area of
LW
Area of rectangle = _____
3.4 cm
A
B
C
D
3.3 cm
Use the ruler on the Mathematics Chart to
measure the dimensions of the composite
figure to the nearest tenth of a centimeter.
Which best represents the approximate
area of this composite figure?
Dilations and Measurements 100
The scale of two similar quadrilaterals is 1:2.
The perimeter of the smaller quadrilateral is 80
centimeters. What is the perimeter of the larger
quadrilateral?
A 40 cm
B 80 cm
C 160 cm
D 320 cm
Board
Answer
Dilations and Measurements 100
The scale of two similar quadrilaterals is 1:2.
The perimeter of the smaller quadrilateral is 80
centimeters. What is the perimeter of the larger
quadrilateral?
Pick a rectangle with a perimeter of 80 cm
A 40 cm
30 cm
B 80 cm
Area = 300 cm2 10 cm
C 160 cm
Create a rectangle twice as big
D 320 cm
60 cm
Board
Perimeter = 160 cm
Area = 1200 cm2
The area is 4 times as big
20 cm
Dilations and Measurements 200
The scale factor of two similar polygons is 2:3.
The perimeter of the larger polygon is 150
centimeters. What is the perimeter of the smaller
polygon?
A 100 cm
B 75 cm
C 50 cm
D 150 cm
Board
Answer
Dilations and Measurements 200
The scale factor of two similar polygons is 2:3.
The perimeter of the larger polygon is 150
centimeters. What is the perimeter of the smaller
Pick a rectangle with a perimeter of 150 cm
polygon?
60 cm
A 100 cm
Area = 900 cm2
B 75 cm
15 cm
C 50 cm
D 150 cm Create a rectangle 2/3 as big
Board
40 cm
Perimeter = 100 cm
10 cm
2
Area = 400 cm
4
The area is as big
9
Dilations and Measurements 300
Tony and Edwin each built a rectangular garden.
Tony’s garden is twice as long and twice as wide
as Edwin’s garden. If the area of Edwin’s garden
is 600 square feet, what is the area of Tony’s
garden?
A 1200 ft2
B 2400 ft2
C 3600 ft2
D 4800 ft2
Board
Answer
Dilations and Measurements 300
Tony and Edwin each built a rectangular garden.
Tony’s garden is twice as long and twice as wide
as Edwin’s garden. If the area of Edwin’s garden
is 600 square feet, what is the area of Tony’s
Pick a rectangle with an area of 600 ft2
garden?
30 ft
A 1200 ft2
20 ft
Per. = 100 ft
2
B 2400 ft
Create a rectangle twice as big
C 3600 ft2
60 ft
D 4800 ft2
2
Board
Area = 2400 ft (4 times the area)
Per. = 200 ft
40 ft
The perimeter is twice as big
Dilations and Measurements 400
A rectangular solid has a volume of 24 cubic
decimeters. If the length, width, and height are
1
all changed to 2 their original size, what will be
the new volume of the rectangular solid?
A 3 dm3
B 4 dm3
C 6 dm3
D 12 dm3
Board
Answer
Dilations and Measurements 400
A rectangular solid has a volume of 24 cubic
decimeters. If the length, width, and height are
1
all changed to 2 their original size, what will be
the new volume of the rectangular solid?
A 3 dm3 Pick a rectangular solid with a volume of 24 dm3
B 4 dm3
6 dm
C 6 dm3
D 12 dm3 2 dm 2 dm
Create a rectangle half as big
3 dm
Board
1 dm 1 dm
1
8
Vol = 3 dm3 ( the volume)
Dilations and Measurements 500
If the surface area of a cube is increased by a
factor of 4, what is the change in the length of
the sides of the cube?
F The length is 2 times the original length.
G The length is 4 times the original length.
H The length is 6 times the original length.
J The length is 8 times the original length.
Board
Answer
Dilations and Measurements 500
If the surface area of a cube is increased by a
factor of 4, what is the change in the length of
the sides of the cube?
F The length is 2 times the original length.
4 times bigger
Each length 2 times as big makes the area _____
G The length is 4 times the original length.
16 times bigger
Each length 4 times as big makes the area _____
H The length is 6 times the original length.
36 times bigger
Each length 6 times as big makes the area _____
J The length is 8 times the original length.
64 times bigger
Each length 8 times as big makes the area _____
Board
Proportions 100
Kate has 2 similar triangular pieces of paper, as
shown below.
Using the dimensions given,
find the approximate length
of the side labeled p.
Board
Answer
Proportions 100
Kate has 2 similar triangular pieces of paper, as
shown below.
Using the dimensions given,
find the approximate length
of the side labeled p.
F
G
H
J
2.4 centimeters
7.3 centimeters
16.5 centimeters
19.6 centimeters
Board
left side
bottom
18p = 132
18
18
x = 7.3
18 11

p
12
Proportions 200
If ∆TSR is similar to ∆TNM, what is the length of x?
Board
Answer
Proportions 200
If ∆TSR is similar to ∆TNM, what is the length of x?
A
B
C
D
240 units
140 units
120 units
70 units
outside 70
x

diagonal 120 240
Board
18p = 132
120x = 16800
120
120
x = 140
Proportions 300
A certain parallelogram has the dimensions
shown.
Which set of dimensions would
produce a similar figure?
F 17.6 cm, 88 cm
G 70.4 cm, 176 cm
H 105.6 cm, 132 cm
J 140.8 cm, 220 cm
Board
Answer
Proportions 300
A certain parallelogram has the dimensions
shown.
Which set of dimensions would
produce a similar figure?
F 17.6 cm, 88 cm
G 70.4 cm, 176 cm
H 105.6 cm, 132 cm
J 140.8 cm, 220 cm
70.4, 88
(35.2 cm, 44 cm)  2 = __________
140.8, 176
(35.2 cm, 44 cm)  4 = __________
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105.6, 132
(35.2 cm, 44 cm)  3 = __________
Proportions 400
To estimate the height of her school’s gym, Nicole
sights the top of the gym wall in a mirror that she
has placed on the ground. The mirror is 3.6 meters
from the base of the gym wall. Nicole is standing
0.5 meter from the mirror, and her height is about
1.8 meters. What is the height of the gym wall?
Board
Answer
Proportions 400
To estimate the height of her school’s gym, Nicole
sights the top of the gym wall in a mirror that she
has placed on the ground. The mirror is 3.6 meters
from the base of the gym wall. Nicole is standing
0.5 meter from the mirror, and her height is about
1.8 meters. What is the height of the gym wall?
F
G
H
J
1m
5.9 m
7.2 m
12.96 m
Board
height
bottom
1.8
x

0.5 3.6
0.5x = 6.48
0.5
0.5
x = 12.96
Proportions 500
In El Paso, Texas, the streets named Hercules
Avenue, Hondo Pass Drive, and Trans Mountain
Road are parallel. They all intersect Dyer Street
and U.S. Route 54, as shown on the map below.
If all of these streets are straight line segments, how
long is Dyer Street between Hercules Avenue and
Trans Mountain Road?
Board
Answer
Proportions 500
In El Paso, Texas, the streets named Hercules
Avenue, Hondo Pass Drive, and Trans Mountain
Road are parallel. They all intersect Dyer Street
and U.S. Route 54, as shown on the map below.
If all of these streets are straight line segments, how
long is Dyer Street between Hercules Avenue and
Trans Mountain Road?
left
5280 10560
A
8,450 ft

right 6600
x
B
9,900 ft
5280x = 69696000
C
13,200 ft
5280
5280
D
19,800 ft
Board
x = 13,200
Geometric Problem Solving 100
The map below shows 2 different routes Ms.
Bentsen can take to drive to the airport from her
house.
How many miles could Ms. Bentsen save by
traveling on Airport Road instead of Mountain
Highway and Oak Road to get to the airport?
Board
Answer
Geometric Problem Solving 100
The map below shows 2 different routes Ms.
Bentsen can take to drive to the airport from her
house.
How many miles could Ms. Bentsen save by
traveling on Airport Road instead of Mountain
Highway and Oak Road to get to the airport?
2 + b2 = c 2
a
A
20 mi
252 + b2 = 652
B
30 mi
625 + b2 = 4225
-625
-625
C
35 mi
b2 = 3600
60 mi
D
60 mi
b = 60
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Distance = _____
85 mi
Distance saved = _____
20 mi
Geometric Problem Solving 200
The total area of trapezoid FGHJ is 52 square inches.
What is the approximate length of FJ?
Board
Answer
Geometric Problem Solving 200
The total area of trapezoid FGHJ is 52 square inches.
What is the approximate length of FJ?
A
B
C
D
8.0 in.
8.5 in.
11.0 in.
11.5 in.
a 2 + b2 = c 2
82 + 32 = c2
64 + 9 = c2
73 = c2
8.5 = c
Board
8 in
3 in
Geometric Problem Solving 300
What is the area of the square in the figure below?
Board
Answer
Geometric Problem Solving 300
What is the area of the square in the figure below?
A
B
C
D
5.2 square units
6.7 square units
27 square units
45 square units
a 2 + b2 = c 2
62 + 32 = c2
36 + 9 = c2
45 = c2
6.7 = c
Board
Area of a square ______
s2
6 in
3 in
Geometric Problem Solving 400
The shaded area in the circle below represents the
section of a park used by the chamber of commerce
for a fund-raising event.
What is the approximate area of the section of the park
used for the fund-raiser?
Board
Answer
Geometric Problem Solving 400
The shaded area in the circle below represents the
section of a park used by the chamber of commerce
for a fund-raising event.
What is the approximate area of the section of the park
used for the fund-raiser?
F
G
H
J
339 square feet
1,357 square feet
4,071 square feet
12,214 square feet
Board
120
 (36) 2
360
Geometric Problem Solving 500
A frozen dinner is divided into 3 sections on a
circular plate with a 12-inch diameter.
What is the approximate length of the arc of the
section containing peas?
Board
Answer
Geometric Problem Solving 500
A frozen dinner is divided into 3 sections on a
circular plate with a 12-inch diameter.
What is the approximate length of the arc of the
section containing peas?
F 3 in.
G 21 in.
H 16 in.
J 5 in.
52
 (12)
360
Board
Final Jeopardy Category
Board
Final Jeopardy Question
In ∆STR, QP and TR are parallel
If SQ = 6 units, QT = 24 units, and the perimeter of
∆SQP is 20 units, what is the perimeter of ∆STR?
Answer
Final Jeopardy Answer
In ∆STR, QP and TR are parallel
24 units, and the perimeter of
If SQ = 6 units, QT = 24
∆SQP is 20 units, what is the perimeter of ∆STR?
A
B
C
D
80 units
100 units
320 units
500 units
30
How long is ST? _______
How many times bigger is the
5
larger triangle? _______
Board
5
The perimeter is how many times larger? _______