WCCUSD Grade 7 Math
1
Benchmark 3 Study Guide
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?
1´
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 are
true about the drawing below?
What is the scale? 1 cm = 2 ft
How would you find the real life length of the 6 cm side?
Use the proportion
Mark all correct answers.
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
A) The length of the longest side of
R4 in real life is 11 ft.
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
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.
Real life length of the 8 cm side is 16 feet.
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.
7.G.1
Page 1 of 15
7.G.1
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
2
Benchmark 3 Study Guide
The side length of a triangle is 11 cm. Which
group of line segments could form the other 2
sides of the triangle?
2a´ A triangle has two sides that are 4 in. and
10 in. What could be the length of the third
side of the triangle?
Triangle Inequality Theorem: to form a
triangle, the sum of any two sides must be
greater than the length of the third side.
Select all that apply.
Select all that apply.
A) 4 in.
B) 6 in.
A) 4 cm and 4 cm
C) 8 in.
D) 11 in.
E) 12 in.
B) 5 cm and 5 cm
F) 14 in.
7.G.2
C) 5 cm and 6 cm
2b´ A triangle has two sides that are 8 cm and
13 cm. What could be the length of
triangle’s third side?
Select all that apply.
D) 6 cm and 6 cm
A) 5 cm
E) 7 cm and 8 cm
B) 10 cm
C) 17 cm
D) 20 cm
F) 9 cm and 10 cm
E) 21 cm
F) 24 cm
7.G.2
7.G.2
Page 2 of 15
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
3
Benchmark 3 Study Guide
The area of a circle is equal to the product of π and
the square of its radius.
A = πr2
3´
Tommy helped paint a basketball key on the
neighborhood playground. Which of the
following statements are true about the
figure below?
Find the area of the circle below. Use 3.14 as an
approximation for π.
Estimate the answer to check for reasonableness later.
3 • 4 • 4 = 48
A = πr 2
Area of a circle
2
A ≈ 3.14 • 4
A ≈ 3.14 •16
A ≈ 50.24
Substitution of values
Simplify
Simplify
Select all that apply.
Does the answer make sense?
Yes. 50.24 ≈ 48
Final answer?
The area of the circle is approximately 50.24 in2.
A) The area of the semicircle is 18π ft2.
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.
Is the radius or diameter given?
Diameter.
What value should be used for r?
6
Estimate the answer to check for reasonableness later.
1
• 3 • 6 • 6 = 54
2
1
A = πr 2
Area of a semicircle
2
1
A ≈ • 3.14 • 6 2
Substitution of values
2
A ≈ 0.5 (3.14) • 36
Simplify
A ≈ 56.52
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.
Simplify
Does the answer make sense?
Yes. 56.52 ≈ 54
Final answer?
The area of the semicircle is approximately 56.5 cm2.
7.G.4
7.G.4
Page 3 of 15
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
4
Benchmark 3 Study Guide
What is the measure of angle x?
4´
What is the sum of the angle measures in a triangle?
180º
What are the measures of the known angles?
40º and 90º
Which of the following statements are true
about the figure below?
(Note: Not drawn to scale)
Mark all correct answers.
A) 45º, 50º, and b are complementary angles.
What equation can be used to find the measure of
the unknown angle in the triangle?
B) 45º, 50º, and b are supplementary angles.
C) 50º and b are adjacent angles.
D) The measure of ∠b is 45º.
E) The measure of ∠b is 85º.
Solution:
The measure of angle x is supplementary to 50º.
Subtract 50º from 180º to get a measure of 130º for x.
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.
7.G.5
7.G.5
Page 4 of 15
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
5
Benchmark 3 Study Guide
Use two different methods to find the area of
the trapezoid below.
5´
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
7.G.6
Page 5 of 15
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
6
Benchmark 3 Study Guide
The students in Ms. Floe’s class wrote essays
about their spring break. The table below
shows how many students wrote about each
location.
6 cont’d
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.
Example 1: What percent of the students wrote about
staying home?
How many students wrote essays? 40
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.
7.SP.2
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
6´
to a decimal.
Using the same table in example 6, identify
which of the following statements are true.
Mark all correct answers.
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?
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.
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.
D) More students wrote essays about the skate park
and home than about the mall and beach.
Do you know this information? If not, how can you
represent it? Don’t know; with a variable.
E) In a group of 200 students, it is expected that 20
of the students will write essays about going to
a theme park.
7.SP.2
Page 6 of 15
7.SP.2
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
7
Benchmark 3 Study Guide
Find the minimum, maximum, median, lower
quartile, and upper quartile for the data set
below. Then use the values to make a box
plot.
7´
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.
17, 19, 31, 20, 12, 8, 24, 13, 15
81, 90, 65, 77, 70, 100, 65, 75, 95, 82
Minimum: the lowest value in the data set.
Maximum: the highest value in the data set.
minimum: _______
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.
maximum: _______
median: _______
lower quartile: _______
upper quartile: _______
Organize the data from least to greatest.
8, 12, 13, 15, 17, 19, 20, 24, 31
minimum
median
maximum
When making a box-and-whisker plot,
sometimes it is helpful to plot the values above
the number line first before drawing the plot.
lower quartile
(12.5)
minimum
(8)
upper quartile
(22)
median
(17)
maximum
(31)
6.SP.4
Page 7 of 15
6.SP.4
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
8
Benchmark 3 Study Guide
The double box plot below shows the daily
participants for grade 7 and 8 in the after
school program of a local school.
8´
The double box plot below shows the speed
of cars recorded on two different roads in
Alameda County.
What does the double box plot show?
Daily level of participants for two grades.
Which of the following statements are true?
Is either plot symmetric?
Grade 8 is symmetric, but grade 7 is not.
Select all that apply.
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.
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.
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.
7.SP.4
Page 8 of 15
7.SP.4
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
9
Benchmark 3 Study Guide
The double dot plot shows the daily number
of smoothies sold to two different grade
levels during a two-week period.
What does the double dot plot show?
The number of smoothies sold for two grades over a two
week period.
9´
The double dot plot below shows the daily
high temperatures for two cities in 12 days.
Which of the following statements are true?
Select all that apply.
Is either plot symmetric?
No.
Which grade level generally sold more smoothies per
day?
Grade 7.
A) The mean for Richmond is approximately 75.
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.
C) The mean for Oakland is greater than the mean
for Richmond.
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.
B) The median for Richmond is 76.
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.
Which grade had more consistent numbers sold?
Grade 8 had more consistent numbers sold per day.
7.SP.4
Page 9 of 15
7.SP.4
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
Benchmark 3 Study Guide
10 The spinner below has 10 equal-sized
wedges, each labeled A-J.
10´
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.
Using the spinner to the left (question 10) and
the graphic above, indicate whether each
statement correctly describes the probability of
the outcome. The spinner is only spun once for
each statement.
Mark all correct answers.
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%.
The probability of the spinner landing on the E
is
C) The probability of landing on a vowel is more than 0.4.
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.
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
.
The probability of the spinner landing on the D or G
is
7.SP.5
7.SP.5
Page 10 of 15
End of Study Guide
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
Benchmark 3 Study Guide
You Try Solutions:
1´
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 are
true about the drawing below?
2a´ A triangle has two sides that are 4 in. and
10 in. What could be the length of the third
side of the triangle?
Select all that apply.
A) 4 in.
B) 6 in.
C) 8 in.
D) 11 in.
E) 12 in.
F) 14 in.
Mark all correct answers.
7.G.2
2b´ A triangle has two sides that are 8 cm and
13 cm. What could be the length of
triangle’s third side?
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.
Select all that apply.
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.
A) 5 cm
E) The length of the longest side of
R1 in real life is 16 ft.
B) 10 cm
C) 17 cm
F) The areas of R1 and R4 are equal.
D) 20 cm
G) The sum of the areas of R2 and
R3 in the scale drawing is 22 in2.
E) 21 cm
F) 24 cm
H) The combined area of R2 and R3
is smaller than the area of R4.
7.G.2
7.G.1
Page 11 of 15
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
3´
Benchmark 3 Study Guide
Tommy helped paint a basketball key on the
neighborhood playground. Which of the
following statements are true about the
figure below?
4´
Which of the following statements are true
about the figure below?
(Note: Not drawn to scale)
Mark all correct answers.
A) 45º, 50º, and b are complementary angles.
B) 45º, 50º, and b are supplementary angles.
Select all that apply.
C) 50º and b are adjacent angles.
D) The measure of ∠b is 45º.
A) The area of the semicircle is 18π ft2.
E) The measure of ∠b is 85º.
B) The perimeter of the key (including the
semicircle) is approximately 70 ft.
F) The equation b + 45 + 50 = 180 could be used
to find the measure of ∠b.
C) The perimeter of the key (including the
semicircle) is approximately 60 ft.
G) The sum of the measures of angles a and b is 95º.
H) The measure of ∠a is 20º.
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.
7.G.5
F) The area of the entire key is
approximately 285 ft2.
7.G.4
Page 12 of 15
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
5´
Benchmark 3 Study Guide
Use two different methods to find the area of
the trapezoid below.
6´
Using the same table in example 6, identify
which of the following statements are true.
Mark all correct answers.
A) Four times as many students wrote essays about
the movies than about the beach.
Method 1: Break into smaller figures
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.
7.SP.2
Method 2: Area of a Trapezoid Formula
7.G.6
Page 13 of 15
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
7´
Benchmark 3 Study Guide
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.
8´
The double box plot below shows the speed
of cars recorded on two different roads in
Alameda County.
81, 90, 65, 77, 70, 100, 65, 75, 95, 82
Put in order from least to greatest:
79
65, 65, 70, 75, 77, 81, 82, 90, 95, 100
minimum
maximum
lower quartile
Which of the following statements are true?
upper quartile
Select all that apply.
minimum: 65
A) The difference between the medians of the two
data sets is 10.
maximum: 100
B) The median for Frontage Road is 52.5.
median: 79
lower quartile: 70
upper quartile: 90
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.
Box-and-Whisker Plot:
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.
6.SP.4
7.SP.4
Page 14 of 15
MCC@WCCUSD (WCCUSD) 01/16/15
WCCUSD Grade 7 Math
9´
Benchmark 3 Study Guide
The double dot plot below shows the daily
high temperatures for two cities in 12 days.
10´
Using the spinner to the left (question 9) and
the graphic above, indicate whether each
statement correctly describes the probability of
the outcome. The spinner is only spun once for
each statement.
Which of the following statements are true?
Mark all correct answers.
Select all that apply.
A) The probability of landing on the A is less than
.
A) The mean for Richmond is approximately 75.
B) The median for Richmond is 76.
B) The probability of landing on the C, D, E, or F
is less than 50%.
C) The mean for Oakland is greater than the mean
for Richmond.
C) The probability of landing on a vowel is more than 0.4.
D) The difference between the means of the two cities
is approximately 5.
D) It is likely that the spinner will land on a vowel.
E) It is impossible that the spinner will land on a Z.
E) The difference between the medians of the two cities
is approximately 8.
F) If one of your favorite letters is on the spinner, it is
unlikely that the spinner will land on that letter.
F) If you prefer warmer temperatures, based on the data
above, you probably would choose Oakland.
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
G) In the 12 days data was collected, only one of the
cities had a high of 72º.
is greater than
7.SP.4
Page 15 of 15
.
7.SP.5
MCC@WCCUSD (WCCUSD) 01/16/15