AUSD Grade 7 Benchmark 3 Study Guide - West Contra ... The plane shown is parallel to the base....
Transcript of AUSD Grade 7 Benchmark 3 Study Guide - West Contra ... The plane shown is parallel to the base....
AUSD Grade 7 Benchmark 3 Study Guide
Page 1 of 21 MCC@WCCUSD 05/13/15
1 What is the measure of angle x?
7.G.5
1´ Which of the following statements are true
about the figure below?
(Note: Not drawn to scale)
7.G.5
A) The 45º, 50º, b angles are
complementary angles.
B) The 45º, 50º, and b angles add up
to 180 º.
C) The 50º and b angles are adjacent.
D) The measure of b is 45º.
E) The measure of b is 85º.
F) The equation b + 45 + 50 = 180
could be used to find the measure
of b.
G) The sum of the measures of
angles a and b is 95º.
H) The measure of a is 20º.
What is the sum of the angle measures in a triangle? 180º
What are the measures of the known angles?
40º and 90º
What equation can be used to find the measure of
the unknown angle in the triangle?
a+ 40 + 90 =180
a+130 =180
a+130 = 50 +130
a = 50
Solution:
The measure of angle x is supplementary to 50º.
Subtract 50º from 180º to get a measure of 130º for x.
AUSD Grade 7 Benchmark 3 Study Guide
Page 2 of 21 MCC@WCCUSD 05/13/15
2 A scale drawing of a letter L sculpture is
shown below where 1 centimeter represents 2
feet of the actual sculpture. The drawing of
the L is divided into two separate rectangles.
What is the area of the real life sculpture?
7.G.1
2´ Ezra made a large E statue for a recent school
project. Each 1 inch on the scale drawing
below represents 4 ft of the statue. He
divided the E into 4 rectangles and labeled
them. Which of the following statements is
true about the drawing below?
7.G.1
How would you find the real life length of the 6 cm side?
Use the proportion 1 cm
2ft=
6 cm
x
Real life length of the 6 cm side is 12 feet.
How would you find the real life length of the 2 cm side?
Use the proportion 1 cm
2ft=
2 cm
x
Real life length of the 2 cm side is 4 feet.
How would you find the real life length of the 8 cm side?
Use the proportion 1 cm
2ft=
8 cm
x
Real life length of the 8 cm side is 16 feet.
A) The length of the longest side of
R4 in real life is 11 ft.
B) The area of R4 in real life
is 336 ft2.
C) The length of the shortest side of
R2 in real life is 12 ft.
D) The area of R2 in real life is 18 ft2.
E) The length of the longest side of
R1 in real life is 16 ft.
F) The areas of R1 and R4 are equal.
G) The sum of the areas of R2 and
R3 in the scale drawing is 22 in2.
H) The combined area of R2 and R3
is smaller than the area of R4.
What is the scale? 1 cm = 2 ft
AUSD Grade 7 Benchmark 3 Study Guide
Page 3 of 21 MCC@WCCUSD 05/13/15
3 Use two different methods to find the area of
the trapezoid below.
Method 1: Break into smaller figures
Method 2: Area of a Trapezoid Formula
7.G.6
3´ Use two different methods to find the area of
the trapezoid below.
7.G.6
AUSD Grade 7 Benchmark 3 Study Guide
Page 4 of 21 MCC@WCCUSD 05/13/15
4 A hotel building with two identical towers and a reception building in the middle is shown below.
7.G.6
The hotel needs a new heating and cooling ventilation system. What is the total
volume of the hotel? Include the two towers and the building in the middle.
3
33
33
towerreception
000,321
000,291000,30
500,1452000,30
2
ftV
ftftV
ftftV
VVV
total
total
total
total
The two tower buildings need a fresh coat of paint. The reception building does not need to be
painted. The roof section and the windows do not need to be painted. There are a total of thirty
four windows, and they are all the same size. How many square feet of paint is needed to paint the
tower buildings?
2
painted
22
painted
22
painted
windowtowerpainted
012,23
088,1100,24
3234050,122
34 2
ftSA
ftftSA
ftftSA
ASASA
3000,30
253040
ftV
ftftftV
lwhV
reception
reception
reception
3
33
prism triangulartrianglebasear rectanglul
prism triangularprismr rectangula
500,145
500,25000,120
3034502
1803050
2
1
ftV
ftftV
ftftftftftftV
hbhlwhV
VVV
tower
tower
tower
tower
tower
2
towerone
222
towerone
towerone
face insideface outsidefacesback andfront towerone
050,12
650,1400,2000,8
3055803080502
2
ftSA
ftftftSA
ftftftftftftSA
bhbhbhSA
2
window
32
84
ftA
ftftA
bhA
window
window
window
The hotel needs a new roof. How many
square feet of roofing material is needed?
2
22
22
roofon rectanglesroofreception
roofon rectanglesroofreception
240,6
040,5200,1
260,14200,1
423043040
4
4
ftA
ftftA
ftftA
ftftftftA
bhbhA
AAA
roof
roof
roof
roof
roof
roof
Hotel
Tower 1 Tower 2
[------------------------------- 140 ft ---------------------------------]
30 ft
[------------------------ ---------------------]
80 ft
4 ft
8 ft
[-------- 40 ft --------]
25 ft
42 ft [------- ------]
34 ft
AUSD Grade 7 Benchmark 3 Study Guide
Page 5 of 21 MCC@WCCUSD 05/13/15
4´ A store building is shown below.
The store is infested with termites and needs to be fumigated. The total volume of the building
determines the amount pesticide needed. What is the volume of the store?
The store needs a new roof. How many square feet of roofing material is needed?
The store needs a fresh coat of paint. The windows are all the same size and do not need to be
painted. The door is metal and does not need to be painted. There are no windows on the back
or the side of the store. How many square feet of paint is needed to paint the store?
7.G.6
15 ft
10 ft
[------------------------ 85 ft -------------------------]
[----- ----]
25 ft
32 ft
10 ft
40 ft
6 ft
6 ft
6 ft
store
AUSD Grade 7 Benchmark 3 Study Guide
Page 6 of 21 MCC@WCCUSD 05/13/15
5
Find the circumference of the circle below. Use 3.14
as an approximation for π.
inC
inC
rC
12.25
414.32
2
Is the answer reasonable?
Yes. The diameter goes around any circle about 3
times. The diameter is 8 and 8 times 3 is 24, which is
close to our answer of 25.12 in.
Find the area of the semicircle below (the shaded
region). Use 3.14 as an approximation for π.
Round to the nearest tenth if necessary.
Estimate the answer to check for reasonableness later.
1
2• 3• 6 • 6 = 54
2
2
2
2
52.56
3614.35.0
614.32
1
2
1
cmA
cmA
cmA
rA
Does the answer make sense? Yes. 56.52 ≈ 54
Final answer?
The area of the semicircle is approximately 56.52 cm2.
7.G.4
5´ Tommy helped paint a basketball key on the
neighborhood playground. Which of the
following statements are true about the
figure below?
7.G.4
The area of a circle is equal to the product of π and
the square of its radius.
A = πr2
The circumference of a circle
is equal to the product of the diameter and π, or two
times the radius and π.
C = πd or C = 2πr
Is the radius or diameter given?
Diameter.
What value should be used for r?
6 cm
A) The area of the semicircle
is 18π ft2.
B) The perimeter of the key
(including the semicircle) is
approximately 70 ft.
C) The perimeter of the key
(including the semicircle) is
approximately 60 ft.
D) The area of the rectangular
portion of the key is 31 ft2.
E) The area of the rectangular
portion of the key is 228 ft2.
F) The area of the entire key is
approximately 285 ft2.
AUSD Grade 7 Benchmark 3 Study Guide
Page 7 of 21 MCC@WCCUSD 05/13/15
6 Determine the shape of the cross section.
Or from above
Trapezoid
7.G.3
6´ Determine the shape of the cross section.
Note: The plane shown is parallel to the base.
7.G.3
AUSD Grade 7 Benchmark 3 Study Guide
Page 8 of 21 MCC@WCCUSD 05/13/15
7 The students in Ms. Floe’s class wrote essays
about their spring break. The table below
shows how many students wrote about each
location.
7.SP.2
7 cont’d
7.SP.2
7´ Using the same table in example 7, identify
which of the following statements are true.
7.SP.2
Example 1: What percent of the students wrote about
staying home?
How many students wrote essays? 40
How many students wrote about staying home? 7
What number should go in the numerator? 7 (it represents a part of the whole)
What number should go in the denominator? 40 (it represents the whole)
Convert 7
40 to a decimal.
7
40= 0.175 =17.5%
Final answer? 17.5% of the students wrote about staying
home during their spring break.
Example 2: There are 320 7th grade students at the school
where Ms. Floe teaches. Predict how many students would
write about staying home.
What ratio do we know?
7
40
number of students who wrote about staying home
total number of students in Ms. Floe's class
What should go in the numerator of the new ratio?
The number of students (school wide) who would write about
staying home for spring break.
Do you know this information? If not, how can you represent it? Don’t know; with a variable.
A) Four times as many students
wrote essays about the movies
than about the beach.
B) 15% of surveyed students wrote
essays about the skate park.
C) In a group of 20 students, it is
expected that 11 of the students
wrote essays about the mall.
D) More students wrote essays
about the skate park and home
than about the mall and beach.
E) In a group of 200 students, it is
expected that 20 of the students
will write essays about going to a
theme park.
What should go in the denominator of the ratio?
The total number of students, 320.
Let x represent the number of students who write about
staying home. Solve for x.
Final answer? Of the 320 students, about 56 of them will
write about staying home.
Note: NOT an exact answer. A prediction is an estimate of
what you might expect.
AUSD Grade 7 Benchmark 3 Study Guide
Page 9 of 21 MCC@WCCUSD 05/13/15
8 Find the minimum, maximum, median, lower
quartile, and upper quartile for the data set
below. Then use the values to make a box
plot.
17, 19, 31, 20, 12, 8, 24, 13, 15
Organize the data from least to greatest.
8, 12, 13, 15, 17, 19, 20, 24, 31
6.SP.4
8´ The following data set below represents the
test scores of 10 students. Find the minimum,
maximum, median, lower quartile, and upper
quartile for the data set. Then use the values
to make a box plot.
81, 90, 65, 77, 70, 100, 65, 75, 95, 82
6.SP.4
Minimum: the lowest value in the data set.
Maximum: the highest value in the data set.
Median: the middle value of a data set.
Lower Quartile: the median of the lower half of
a data set.
Upper Quartile: the median of the upper half of
a data set.
median
maximum minimum
When making a box-and-whisker plot,
sometimes it is helpful to plot the values above
the number line first before drawing the plot.
minimum
(8)
maximum
(31)
median
(17)
upper quartile
(22)
lower quartile
(12.5)
minimum: _______
maximum: _______
median: _______
lower quartile: _______
upper quartile: _______
lower quartile upper quartile
AUSD Grade 7 Benchmark 3 Study Guide
Page 10 of 21 MCC@WCCUSD 05/13/15
9 The double box plot below shows the daily
participants for grade 7 and 8 in the after
school program of a local school.
7.SP.4
9´ The double box plot below shows the speed
of cars recorded on two different roads in
Alameda County.
7.SP.4
What does the double box plot show?
Daily level of participants for two grades.
Is either plot symmetric?
Grade 8 is symmetric, but grade 7 is not.
Which grade had more daily participants?
Grade 7.
Which grade had a greater variation of
participants?
Grade 7. The range for grade 7 is 80 and the range
for grade 8 is 40.
What is the difference between the ranges of the
two data sets?
The difference between the two ranges is 40.
What is the difference between the interquartile
ranges of the two data sets?
The interquartile range for grade 7 is 30 and the
interquartile range for grade 8 is 20, so the difference
between the interquartile ranges is 10.
What are the medians for each set of data?
The median for grade 7 is 170 and the median for
grade 8 is 150.
Describe how the data is skewed or symmetric for
each sample.
The data for grade 7 is skewed right and the data for
grade 8 is symmetric.
Which of the following statements are true?
A) The difference between the
medians of the two data sets
is 10.
B) The median for Frontage Road
is 52.5.
C) The interquartile range for
Highway 80 is 5 and the
interquartile range for
Frontage Road is 10.
D) Highway 80 has less variation
so its speeds are more consistent.
E) Frontage Road has less variation
so its speeds are more consistent.
F) The speed of cars is higher on
Highway 80.
G) The speed of cars is higher on
Frontage Road.
AUSD Grade 7 Benchmark 3 Study Guide
Page 11 of 21 MCC@WCCUSD 05/13/15
10 The double dot plot shows the daily number
of smoothies sold to two different grade
levels during a two-week period.
7.SP.4
10´ The double dot plot below shows the daily
high temperatures for two cities in 12 days.
7.SP.4
What does the double dot plot show?
The number of smoothies sold for two grades over a two
week period.
Is either plot symmetric?
No.
Which grade level generally sold more smoothies per
day?
Grade 7.
Which grade had a greater variation of smoothies
sold?
Grade 7. The range for grade 7 is 40 and the range for
grade 8 is 25.
What is the difference between the means of the two
data sets?
The mean for grade 7 is 70.7 and the mean for
grade 8 is 66.1 so the difference between them is
approximately 5.
What is the difference between the medians of the two
data sets?
The median for grade 7 is 70 and median for grade 8 is
65, so the difference between the medians is 5.
Which grade had more consistent numbers sold?
Grade 8 had more consistent numbers sold per day.
Which of the following statements are true?
A) The mean for Richmond is
approximately 75.
B) The median for Richmond is 76.
C) The mean for Oakland is greater
than the mean for Richmond.
D) The difference between the means
of the two cities is approximately 5.
E) The difference between the medians
of the two cities is approximately 8.
F) If you prefer warmer temperatures,
based on the data above, you
probably would choose Oakland.
G) In the 12 days data was collected,
only one of the cities had a high
of 72º.
AUSD Grade 7 Benchmark 3 Study Guide
Page 12 of 21 MCC@WCCUSD 05/13/15
11 The spinner below has 10 equal-sized
wedges, each labeled A-J.
7.SP.5
11´
7.SP.5
Example 1: The spinner is spun one time. Find the
probability or P(E) of landing on the E.
How many E’s are on the spinner? One.
How many outcomes are possible when spinning the
spinner one time? Ten.
P E( ) =number of favorable outcomes
number of possible outcomes
=1
10
The probability of the spinner landing on the E
is 1
10, 10%, or 0.1
Example 2: The spinner is spun one time. Find the
probability of landing on the D or G.
The word or indicates that the number of favorable
outcomes needs to include the letters D and G.
P D or G( ) =number of favorable outcomes
number of possible outcomes
=2
10
=1
5
The probability of the spinner landing on the D or G
is 1
5, 20%, or 0.2
Using the spinner to the left (question 9) and the
graphic above, choose True or False to indicate
whether each statement correctly describes the
probability of the outcome. The spinner is only
spun once for each statement.
A) The probability of landing on
the A is less than .
B) The probability of landing on the
C, D, E, or F is less than 50%.
C) The probability of landing on a
vowel is more than 0.4.
D) It is likely that the spinner will
land on a vowel.
E) It is impossible that the spinner
will land on a Z.
F) If one of your favorite letters is on
the spinner, it is unlikely that the
spinner will land on that letter.
G) The probability of not landing on
the J is less than 80%.
H) The probability of not landing on
the F, G, or H is greater than .
AUSD Grade 7 Benchmark 3 Study Guide
Page 13 of 21 MCC@WCCUSD 05/13/15
12 The tree diagram shows the results of flipping
a coin and spinning a spinner with four
sections numbered 1, 2, 3, and 4.
Flip: H T
Spin: 1 2 3 4 1 2 3 4
What is the probability of flipping a heads
and then spinning an odd number?
There are 8 possible outcomes. 2 of the
possible outcomes have a heads and an odd
number. They are H-1 and H-3.
P(heads and odd)8
2
P(heads and odd)4
1
Describe what happens to the number of
possible outcomes if you spin the spinner a
second time.
If you spin the spinner a second time each of
the 4 previous spins would have another 4
outcomes branched off from them. So, the
number of possible outcomes increases to
from 8 to 32.
7.SP.8
12´ The tree diagram shows the results of
flipping a coin and spinning a spinner with
four sections labeled A, B, C, and D.
Flip: H T
Spin: A B C D A B C D
What is the probability of flipping a tails
and then not spinning a B?
Describe what happens to the number of
possible outcomes if you flip the coin a
second time.
7.SP.8
AUSD Grade 7 Benchmark 3 Study Guide
Page 14 of 21 MCC@WCCUSD 05/13/15
13 Use a ruler and protractor to create and label a
triangle with the given conditions.
Given: The measure of A is 90 degrees.
The length of side AB is 2 cm. The measure
of B is 50 degrees.
Given: The length of side LM is 1 cm. The
length of side MN is 5 cm. The length of
side NL is 2 cm.
This is a trick question. You cannot create a
triangle with the given conditions.
7.G.2
13´ Use a ruler and protractor to create and label
a triangle with the given conditions.
Given: The length of side QR is 3 cm. The
measure of Q is 100 degrees. The length
of side QS is 4 cm.
Given: The measure of X is 20 degrees.
The measure of Y is 45 degrees. The last
angle is Z.
7.G.2
End of Study Guide
2 cm L
L
A 2 cm B
50°
C
M 5 cm N
1 cm
AUSD Grade 7 Benchmark 3 Study Guide
Page 15 of 21 MCC@WCCUSD 05/13/15
You Try Solutions:
1´ Which of the following statements are true
about the figure below?
(Note: Not drawn to scale)
7.G.5
2´ Ezra made a large E statue for a recent school
project. Each 1 inch on the scale drawing
below represents 4 ft of the statue. He
divided the E into 4 rectangles and labeled
them. Which of the following statements is
true about the drawing below?
7.G.1
A) The 45º, 50º, b angles are
complementary angles.
B) The 45º, 50º, and b angles add up
to 180 º.
C) The 50º and b angles are adjacent.
D) The measure of b is 45º.
E) The measure of b is 85º.
F) The equation b + 45 + 50 = 180
could be used to find the measure
of b.
G) The sum of the measures of
angles a and b is 95º.
H) The measure of a is 20º.
A) The length of the longest side of
R4 in real life is 11 ft.
B) The area of R4 in real life
is 336 ft2.
C) The length of the shortest side of
R2 in real life is 12 ft.
D) The area of R2 in real life is 18 ft2.
E) The length of the longest side of
R1 in real life is 16 ft.
F) The areas of R1 and R4 are equal.
G) The sum of the areas of R2 and
R3 in the scale drawing is 22 in2.
H) The combined area of R2 and R3
is smaller than the area of R4.
AUSD Grade 7 Benchmark 3 Study Guide
Page 16 of 21 MCC@WCCUSD 05/13/15
3´ Use two different methods to find the area of
the trapezoid below.
Method 1: Break into smaller figures
Method 2: Area of a Trapezoid Formula
7.G.6
4´
What is the volume of the store?
3
33
prism triangularprismr rectangula
750,17
000,5750,12
1025402
1151085
ftV
ftftV
ftftftftftftV
VVV
total
total
total
total
How many square feet of roofing material is
needed?
2
22
eon triangl rectangles windows threeabove tangle
090,1
640450
103221045
2
2
ftA
ftftA
ftftftftA
bhbhA
AAA
roof
roof
roof
roof
recroof
How many square feet of paint is needed to
paint the store?
7.G.3
15 ft
10 ft
[------------------------ 85 ft -------------------------]
[----- ----]
25 ft
32 ft
10 ft
40 ft
6 ft
6 ft
6 ft
store
2
222
2222
2222
doorwindowsidefront
doorwindowprismr rectangulapainted
646,2
204300550,2
60144150212752
603641510215852
422
4
ftSA
ftftftSA
ftftftftSA
ftftftftSA
AAbhbhSA
AASASA
AUSD Grade 7 Benchmark 3 Study Guide
Page 17 of 21 MCC@WCCUSD 05/13/15
5´ Tommy helped paint a basketball key on the
neighborhood playground. Which of the
following statements are true about the
figure below?
7.G.4
6´ Determine the shape of the cross section.
Note: The plane shown is parallel to
the base.
Or from above
Rectangle
7.G.3
A) The area of the semicircle
is 18π ft2.
B) The perimeter of the key
(including the semicircle) is
approximately 70 ft.
C) The perimeter of the key
(including the semicircle) is
approximately 60 ft.
D) The area of the rectangular
portion of the key is 31 ft2.
E) The area of the rectangular
portion of the key is 228 ft2.
F) The area of the entire key is
approximately 285 ft2.
AUSD Grade 7 Benchmark 3 Study Guide
Page 18 of 21 MCC@WCCUSD 05/13/15
7´ Using the same table in example 5, identify
which of the following statements are true.
7.SP.2
8´ The following data set below represents the
test scores of 10 students. Find the minimum,
maximum, median, lower quartile, and upper
quartile for the data set. Then use the values
to make a box plot.
81, 90, 65, 77, 70, 100, 65, 75, 95, 82
Put in order from least to greatest:
65, 65, 70, 75, 77, 81, 82, 90, 95, 100
Box-and-Whisker Plot:
6.SP.4
minimum: 65 maximum: 100
median: 79
lower quartile: 70 upper quartile: 90
upper quartile
maximum minimum
lower quartile
79
A) Four times as many students
wrote essays about the movies
than about the beach.
B) 15% of surveyed students wrote
essays about the skate park.
C) In a group of 20 students, it is
expected that 11 of the students
wrote essays about the mall.
D) More students wrote essays
about the skate park and home
than about the mall and beach.
E) In a group of 200 students, it is
expected that 20 of the students
will write essays about going to a
theme park.
AUSD Grade 7 Benchmark 3 Study Guide
Page 19 of 21 MCC@WCCUSD 05/13/15
9´ The double box plot below shows the speed
of cars recorded on two different roads in
Alameda County.
7.SP.4
10´ The double dot plot below shows the daily
high temperatures for two cities in 12 days.
7.SP.4
Which of the following statements are true?
A) The difference between the
medians of the two data sets
is 10.
B) The median for Frontage Road
is 52.5.
C) The interquartile range for
Highway 80 is 5 and the
interquartile range for
Frontage Road is 10.
D) Highway 80 has less variation
so its speeds are more consistent.
E) Frontage Road has less variation
so its speeds are more consistent.
F) The speed of cars is higher on
Highway 80.
G) The speed of cars is higher on
Frontage Road.
Which of the following statements are true?
A) The mean for Richmond is
approximately 75.
B) The median for Richmond is 76.
C) The mean for Oakland is greater
than the mean for Richmond.
D) The difference between the means
of the two cities is approximately 5.
E) The difference between the medians
of the two cities is approximately 8.
F) If you prefer warmer temperatures,
based on the data above, you
probably would choose Oakland.
G) In the 12 days data was collected,
only one of the cities had a high
of 72º.
AUSD Grade 7 Benchmark 3 Study Guide
Page 20 of 21 MCC@WCCUSD 05/13/15
11´ The spinner below has 10 equal-sized
wedges, each labeled A-J.
7.SP.5
11´
Cont’d
7.SP.5
Using the spinner to the left (question 9) and the
graphic above, choose True or False to indicate
whether each statement correctly describes the
probability of the outcome. The spinner is only
spun once for each statement.
A) The probability of landing on
the A is less than .
B) The probability of landing on the
C, D, E, or F is less than 50%.
C) The probability of landing on a
vowel is more than 0.4.
D) It is likely that the spinner will
land on a vowel.
E) It is impossible that the spinner
will land on a Z.
F) If one of your favorite letters is on
the spinner, it is unlikely that the
spinner will land on that letter.
G) The probability of not landing on
the J is less than 80%.
H) The probability of not landing on
the F, G, or H is greater than .
AUSD Grade 7 Benchmark 3 Study Guide
Page 21 of 21 MCC@WCCUSD 05/13/15
12´ The tree diagram shows the results of
flipping a coin and spinning a spinner with
four sections labeled A, B, C, and D.
Flip: H T
Spin: A B C D A B C D
What is the probability of flipping a tails
and then not spinning a B?
There are 8 possible outcomes. 3 of the
possible outcomes have a talis and a letter
that is not B. They are H-A and T-C and T-D.
P(tails and not B)8
3
Describe what happens to the number of
possible outcomes if you flip the coin a
second time.
If you flip the coin a second time that will
double the amount of possible outcomes to
16.
7.SP.8
13´ Use a ruler and protractor to create and label
a triangle with the given conditions.
Given: The length of side QR is 3 cm. The
measure of Q is 100 degrees. The length
of side QS is 4 cm.
Given: The measure of X is 20 degrees.
The measure of Y is 45 degrees. The last
angle is Z.
Possible answer:
7.G.2
100°
4 cm
3 cm Q R
S
X Y
Z
20° 45°