ausd grade 7 benchmark 3 study guide - west contra ... the plane shown is parallel to the base....

AUSD Grade 7 Benchmark 3 Study Guide

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.



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.



2ft=

2 cm

x




2ft=

8 cm

x


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


D) The area of R2 in real life is 18 ft2.

E) The length of the longest side of


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



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


7.G.6



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



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



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



D) The area of the rectangular

portion of the key is 31 ft2.

E) The area of the rectangular


F) The area of the entire key is

approximately 285 ft2.



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



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


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.



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



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


F) The speed of cars is higher on

Highway 80.

G) The speed of cars is higher on

Frontage Road.



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.


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


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.



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 .



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?


possible outcomes if you flip the coin a

second time.

7.SP.8



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



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


B) The area of R4 in real life

is 336 ft2.

C) The length of the shortest side of


D) The area of R2 in real life is 18 ft2.

E) The length of the longest side of


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.



3´ Use two different methods to find the area of


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



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



C) The perimeter of the key



D) The area of the rectangular


E) The area of the rectangular


F) The area of the entire key is

approximately 285 ft2.



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


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


will write essays about going to a

theme park.



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


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


E) Frontage Road has less variation


F) The speed of cars is higher on

Highway 80.

G) The speed of cars is higher on

Frontage Road.


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


E) The difference between the medians


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.



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 .



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


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°

ausd grade 7 benchmark 3 study guide - west contra ... the plane shown is parallel to the base....

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