gps grade 6 sample questions - cobb county school district · gps grade 6 sample questions ... new...

GPS Grade 6 Sample Questions

Georgia Department of Education Kathy Cox, State Superintendent of Schools

MATHEMATICS GRADE 6 SAMPLE MULTIPLE CHOICE QUESITONS OCTOBER 15, 2007 of 18

Copyright 2007 © All Rights Reserved

The Georgia Department of Education has developed sample questions, in a multiple choice format, to illustrate the types of questions that might be seen on a standardized test such as the CRCT.

These are not intended to be a comprehensive means of assessment; instead teachers should use a variety of methods and strategies for assessing students. Tasks within the GPS frameworks along with additional resources including textbooks also offer a diverse assortment of assessments.

Unit 1: Gathering and Using Data KEY STANDARDS:

M6D1. Students will pose questions, collect data,

represent and analyze the data, and interpret

results.

a. Formulate questions that can be answered by

data. Students should collect data by using

samples from a larger population (surveys), or

by conducting experiments.

b. Using data, construct frequency distributions,

frequency tables, and graphs.

c. Choose appropriate graphs to be consistent with

the nature of the data (categorical or

numerical). Graphs should include pictographs,

histograms, bar graphs, line graphs, circle

graphs*, and line plots.

d. Use tables and graphs to examine variation that

occurs within a group and variation that

occurs between groups.

e. Relate the data analysis to the context of the

questions posed.

*Circle graphs will be addressed after the unit on

rational numbers in order to connect data, rational

numbers and geometry. Circle graphs should not be

addressed in this unit organizer.

1. (M6D1d)

The line plot below shows the ages of

teachers in your school.

Which of the following statements are

true according to the data?

I. The oldest teacher is 28 years

older than the youngest teacher.

II. Most of the teachers are over the

age of 46.

III. The most common age is 47.

A. Statements II and III

B. Statements I and III

C. None of the statements

D. All three statements*





Unit 2: Fun and Games: Extending and Applying Number Theory KEY STANDARDS:

M6N1. Students will understand the meaning of

the four arithmetic operations as related to

positive rational numbers and will use these

concepts to solve problems.

a. Apply factors and multiples.

b. Decompose numbers into their prime

factorization (Fundamental Theorem of

Arithmetic).

c. Determine the greatest common factor (GCF)

and the least common multiple (LCM) for

a set of numbers.

1. (M6N1c)

Justin is organizing his trophy

case. He has 30 baseball trophies

and 45 soccer trophies. He wants

to arrange the trophies so each

row has the same number of

trophies from only one sport.

What is the greatest number of

trophies that can be in each row?

A. 3

B. 5

C. 15*

D. 30





Unit 3: Fractions, Decimals, Ratios, and Percents

KEY STANDARDS:

M6N1. Students will understand the meaning of the

four arithmetic operations as related to positive

rational numbers and will use these concepts to solve

problems.

d. Add and subtract fractions and mixed numbers

with unlike denominators.

e. Multiply and divide fractions and mixed numbers.

f. Use fractions, decimals, and percents

interchangeably.

g. Solve problems involving fractions, decimals, and

percents.

M6Al. Students will understand the concept of ratio

and use it to represent quantitative relationships.

M6A2. Students will consider relationships between

varying quantities.

c. Use proportions (a/b=c/d) to describe

relationships and solve problems, including

percent problems.

1. (M6N1g)

Ralf and his best friend want to buy 3

DVDs normally priced at $20 each in

stores A, B, and C. Today, stores A,

B, and C have the DVDs on sale. At

which store(s) will the friends spend

the LEAST money if they buy 3

DVDs?

Store Sale

A

Buy one at regular price

and get two for half price

each.

B Each DVD is on sale at a

35% discount.

C Buy two at regular price

and get one free.

A. Store A

B. Store B*

C. Stores A and B

D. Stores A and C

2. (M6N1g)

Mark wants to buy a scooter that

sells for $250.00. He can pay 20%

down and the rest in 12 payments

each of $24.37. How much more

does the bicycle cost buying it this

way than paying for it all at once?

A. $24.37

B. $42.44

C. $69.44

D. $94.44*

Continued…





Unit 3: Fractions, Decimals, Ratios, and Percents

KEY STANDARDS:

M6N1. Students will understand the meaning of the

four arithmetic operations as related to positive

rational numbers and will use these concepts to solve

problems.

d. Add and subtract fractions and mixed numbers




interchangeably.


percents.

M6Al. Students will understand the concept of ratio

and use it to represent quantitative relationships.

M6A2. Students will consider relationships between

varying quantities.



percent problems.

Continued…

3. (M6A1)

For her birthday, Jenna received 5

stuffed animals, 3 DVDs, 2 books, 1

game, 8 CDs, 1 shirt, and 2 pair of

jeans.

What is the ratio of DVDs to her

total number of gifts?

A. 1:3

B. 3:8

C. 3:19

D. 3:22*

4. (M6A2c)

Your best friend plays the drums in a

new popular band. Each song is 3 to

5 minutes long. Which is the best

estimate for the total number of

songs that the band could play in a 2-

hour concert?

A. 8 songs

B. 12 songs

C. 20 songs

D. 30 songs*





Unit 4: One-Step Equations KEY STANDARDS:

M6A2. Students will consider relationships

between varying quantities.

a) Analyze and describe patterns arising from

mathematical rules, tables, and graphs.

M6A3. Students will evaluate algebraic

expressions, including those with exponents, and

solve simple one-step equations using each of the

four basic operations.

1. (M6A2a)

Tommy and Terry have developed a

program to help them prepare for a long

distance bike trip. They are increasing

the number of miles that they ride each

week so they will be successful on this

trip. The table below shows the number

of miles each traveled for the first half

of the program.

Week Tommy Terry

1 6 3

2 6.5 4

3 7 5

4 7.5 6

5

6

7

8

If both Tommy and Terry continue to

increase the number of miles traveled

each week at the constant rates shown in

the table, which of the following is a

true statement about week 8?

A. Terry will travel more miles

than Tommy.*

B. Tommy and Terry will travel

the same number of miles.

C. Terry will travel a total of 13

miles.

D. Tommy and Terry will travel

a total of 20 miles.

Continued…





Unit 4: One-Step Equations KEY STANDARDS:



a) Analyze and describe patterns arising from






Continued…

2. (M6A3)

Sam picks a apples, and Sally

picks 7a+ 2 apples. If Sam picks

8 apples, how many apples does

Sally pick?

A. 7

B. 9

C. 58*

D. 80





Unit 5: Circles and Graphs

KEY STANDARDS:



results. b. Using data, construct frequency distributions,


c. Choose appropriate graphs to be consistent with the

nature of the data (categorical or numerical).

Graphs should include pictographs, histograms, bar

graphs, line graphs, circle graphs, and line plots.


occurs within a group and variation that occurs

between groups.


questions posed.




concepts to solve problems. d. Add and subtract fractions and mixed numbers




interchangeably.


percents.

M6M2. Students will use appropriate units of

measure for finding length, perimeter, area and

volume and will express each quantity using the

appropriate unit. a. Measure length to the nearest half, fourth, eighth

and sixteenth of an inch.

b. Select and use units of appropriate size and type to

measure length, perimeter, area and volume.

M6A1. Students will understand the concept of

ratio and use it to represent quantitative

relationships.





1. (M6D1c)

The results of a survey of sixth grade

students indicated that 34% preferred

math, 23% preferred science, 18%

preferred social studies, and 15%

preferred language arts. All other

students either did not have a favorite

subject or picked a connections/elective

class.

Which type of data display would be

MOST appropriate for showing the

data?

A. bar graph

B. circle graph*

C. histogram

D. pictograph

2. (M6N1g)

The table below shows Marie’s results

on a 50-question social studies test.

Results of Marie’s

Social Studies Test

Multiple-

Choice

Questions

True/False

Questions

Number of

Questions

Answered

Correctly

28 12

Number of

Questions

Answered

Incorrectly

2 4

Of the questions Marie answered

correctly, what percent were true-false

questions?

A. 30%*

B. 40%

C. 67%

D. 75% Continued…






KEY STANDARDS:











between groups.


questions posed.








interchangeably.


percents.










relationships.





Continued… 3. (M6M2b)

You are sending a blanket to your

friend’s brother in Iraq.

In determining the cost for mailing the

package, the post office needs to know

the dimensions of the package and the

total weight.

Which units would be MOST

appropriate for measuring the package?

A. cubic inches

B. feet

C. inches*

D. square feet

4. (M6A1)

Fifty-six students submitted entries to

the Reflections competition sponsored

by the PTA. Twelve students won the

opportunity to progress to the state level.

Which is the ratio of students who

progressed to the state level to those

who submitted entries?

A. 1 to 12

B. 3 to 14*

C. 3 to 25

D. 1 to 56

Continued…






KEY STANDARDS:











between groups.


questions posed.








interchangeably.


percents.










relationships.





Continued…

5. (M6A3)

At her job, Paula is paid $15.00 per

hour. When she drives her car for work,

she is paid an additional 48.5 per mile.

The expression below can be used to

find the amount she is paid, in dollars,

when she works for h hours and drives

m miles in her car.

15h + 0.485m

How much is Paula paid when she

works 2

118 hours and drives 348 miles

in her car?

A. $63.50

B. $188.10

C. $446.28*

D. $366.50





Unit 6: Symmetry KEY STANDARDS:

M6G1. Students will further develop their

understanding of plane figures.

a. Determine and use lines of symmetry.

b. Investigate rotational symmetry, including

degree of rotation.

1. (M6G1)

Which is true about the figure

below?

A. The figure has rotational

symmetry after a 45o turn.

B. The figure has rotational

symmetry after a 90o turn.*

C. The figure has rotational

symmetry after a 120o turn.

D. The figure does not have

rotational symmetry.





Unit 7: Scale Factor

KEY STANDARDS:

M6M1. Students will convert from one unit to

another within one system of measurement

(customary or metric) by using proportional

relationships.




appropriate unit.

a. Measure length to the nearest half, fourth,

eighth and sixteenth of an inch.

b. Select and use units of appropriate size and

type to measure length, perimeter, area and

volume.

c. Compare and contrast units of measure for

perimeter, area, and volume.



c. Use the concepts of ratio, proportion and

scale factor to demonstrate the relationships

between similar plane figures.

d. Interpret and sketch simple scale drawings.

e. Solve problems involving scale drawings.



relationships.

1. (M6M1)

A soft drink can holds 350 mL of cola. If

the machine at the canning company

contains 700 L of cola, how many cans

may be filled before the machine is

empty?

A. 2

B. 20

C. 200

D. 2000*

2. (M6M2c)

Nathan has a rectangular 15ft x 30ft

garden.

His next door neighbor has a garden

measuring 10yd x 20yd.

Which statement accurately compares the

areas of the two gardens?

A. The area of Nathan’s garden is

exactly 1.5 times larger than

the area of his neighbor’s

garden.

B. The area the neighbor’s

garden is exactly 2 times

larger than the area of

Nathan’s garden.

C. The area of Nathan’s garden is

exactly 2.25 times larger than

the area of his neighbor’s

garden.

D. The area the neighbor’s

garden is exactly 4 times

larger than the area of

Nathan’s garden.*

Continued…





Unit 7: Scale Factor

KEY STANDARDS:

M6M1. Students will convert from one unit to

another within one system of measurement

(customary or metric) by using proportional

relationships.




appropriate unit.

a. Measure length to the nearest half, fourth,

eighth and sixteenth of an inch.

b. Select and use units of appropriate size and

type to measure length, perimeter, area and

volume.

c. Compare and contrast units of measure for

perimeter, area, and volume.



c. Use the concepts of ratio, proportion and

scale factor to demonstrate the relationships

between similar plane figures.

d. Interpret and sketch simple scale drawings.

e. Solve problems involving scale drawings.



relationships.

Continued…

3. (M6G1c)

Missy enjoys building model antique

cars.

If the actual car was 16 ¼ feet long and

her model is 3 ¼ inches long. What is the

scale factor of the model car?

A. ¼ inch = 1 foot

B. ½ inch = 3 feet

C. 1 inch = 5 feet*

D. 1 inch = 5 feet and 4 inches

4. (M6A1)

It takes your teacher 10 minutes to grade

3 of your class papers. Which pair of

ratios could be used to determine how

long will it take her to grade all 117 of

her students’ papers?

A. p

117

10

3*

B. 10117

3 p

C. 310

117 p

D. 3

10117

p





Unit 8: Solids KEY STANDARDS:

M6M3: Students will determine the volume of

fundamental solid figures (right rectangular

prisms, cylinders, pyramids, and cones.)

a. Determine the formula for finding the volume

of fundamental solid figures.

b. Compute the volumes of fundamental solid

figures, using appropriate units of measure.

c. Estimate the volumes of simple geometric

solids.

d. Solve application problems involving the

volume of fundamental solid figures.

M6M4: Students will determine the surface area

of solid figures (right rectangular prisms and

cylinders.)

a. Find the surface area of right rectangular

prisms and cylinders using manipulatives and

constructing nets.

b. Compute the surface area of right rectangular

prisms and cylinders using formulae.

c. Estimate the surface areas of simple geometric

solids.

d. Solve application problems involving surface

area of right rectangular prisms and cylinders.

M6G2: Students will further develop their

understanding of solid figures.

a. Compare and contrast right prisms and

pyramids.

b. Compare and contrast cylinders and cones.

c. Interpret and sketch front, back, top, bottom

and side views of solid figures.

d. Construct nets for prisms, cylinders, pyramids,

and cones.

1. (M6M3d)

The BuyDirt/SellDirt Company uses a

truck with a rectangular prism bed that

is 24 feet long, 8 feet wide, and 6 feet

high. They charge $288 per truck load

to take dirt away, and they sell the dirt

they have moved for $192 per truck

load. Each truck is considered full

when the bed of the truck is filled so

that the dirt is level with the top. If they

have a customer that needs 1280 cubic

feet of dirt moved and another customer

that will buy the dirt; how much money

will the company make?

A. $480

B. $4,800*

C. $48,000

D. $480,000

Continued…

Bed of the truck Bed of truck





Unit 8: Solids KEY STANDARDS:

M6M3: Students will determine the volume of

fundamental solid figures (right rectangular

prisms, cylinders, pyramids, and cones.)

e. Determine the formula for finding the volume

of fundamental solid figures.

f. Compute the volumes of fundamental solid

figures, using appropriate units of measure.

g. Estimate the volumes of simple geometric

solids.

h. Solve application problems involving the

volume of fundamental solid figures.

M6M4: Students will determine the surface area

of solid figures (right rectangular prisms and

cylinders.)

e. Find the surface area of right rectangular

prisms and cylinders using manipulatives and

constructing nets.

f. Compute the surface area of right rectangular

prisms and cylinders using formulae.

g. Estimate the surface areas of simple geometric

solids.

h. Solve application problems involving surface

area of right rectangular prisms and cylinders.

M6G2: Students will further develop their

understanding of solid figures.

e. Compare and contrast right prisms and

pyramids.

f. Compare and contrast cylinders and cones.

g. Interpret and sketch front, back, top, bottom

and side views of solid figures.

h. Construct nets for prisms, cylinders, pyramids,

and cones.

Continued…

2. (M6M4c)

A musical instrument to be used with

elementary school students is being

made out of cylinders that are ¼ full of

rice. Your art class has decided to

decorate the instruments. Cindy wants

to cover hers with cloth.

6cm

10cm

What is the BEST ESTIMATE for

amount cloth she will need to cover the

entire cylinder?

A. 32 cm2

B. 60 cm2

C. 120 cm2

D. 230 cm2*

3. (M6G2c)

If you were flying over Egypt in a

helicopter, what would a square-based

pyramid look like looking down from

the sky?

A. *

B.

C.

D.





Unit 9: Direct Proportion KEY STANDARDS:



a. Analyze and describe patterns arising from


b. Use manipulatives or draw pictures to solve

problems involving proportional relationships.



percent problems.

d. Describe proportional relationships

mathematically using y = kx, where k is the

constant of proportionality.

e. Graph proportional relationships in the form

y = kx and describe characteristics of the

graphs.

f. In a proportional relationship expressed as

y = kx, solve for one quantity given values of

the other two. Given quantities may be whole

numbers, decimals, or fractions. Solve problems

using the relationship y = kx.

g. Use proportional reasoning (a/b=c/d and

y = kx) to solve problems.





1. (M6A2c)

The Girl Scout troop sold 416 boxes of

cookies the first two days they sold

cookies. Which proportion could be

used to make the best estimate for the

number of cookies that the troop will

sell in 8 days?

A. x

2

8

416

B. x

416

2

8

C. 8416

2 x

D. x

8

416

2*

2. (M6A2f)

A spider crawled 25 cm in 6 seconds.

How long will it take the spider to

crawl 55 cm if it continues at the same

rate?

A. 51 minutes

B. 55 minutes

C. 4 minutes, 35 seconds *

D. 6 minutes, 55 seconds

Continued…














percent problems.






graphs.












Continued…

3. (M6A2g)

The circles below represent a cookie

cake and a regular cookie. The

diameter of the cookie cake is 42

centimeters. The ratio of the diameter

of the cookie cake to the diameter of

the cookie is 7:1.

What is the area, in square centimeters,

of the regular cookie?

A. 6π cm2

B. 9π cm2

C. 21π cm2

D. 42π cm2

Continued…

42 cm

Cookie Cake

Regular Cookie














percent problems.






graphs.












Continued…

4. (M6A3)

Amy earns d dollars for raking leaves

each week. She also receives an

allowance of $12 per week. The

expression below can be used to

calculate the amount of money she will

have at the end of 8 weeks.

(12 + d) x 8

What is the amount of money Amy will

have at the end of eight weeks if d =

$20?

A. $160

B. $172

C. $248

D. $256*





Unit 10: Games of Chance

KEY STANDARDS:

M6D2. Students will use experimental and simple

theoretical probability and understand the nature

of sampling. They will also make predictions from

investigations.

a. Predict the probability of a given event through

trials/simulations (experimental probability),

and represent the probability as a ratio.

b. Determine, and use a ratio to represent, the

theoretical probability of a given event.

c. Discover that experimental probability

approaches theoretical probability when the

number of trials is large.

1. (M6D2)

The students on your bus were excited

because not only did you have the

nicest bus driver in your district, but

she was going to have a baby and every

one of the riders wanted to pitch in to

purchase a nice baby gift. The problem

was trying to agree on a gift, so each

person wrote down what they thought

the group should buy on a piece of

paper and placed it in a box. The

results are shown in the chart below.

Gift

Ideas

Number

of

Student

Choices Car seat 18

Highchair 6 Playpen 8 Rocking

chair 14

Stroller 10

One of the students reached into the

box and drew out a paper at random.

What is the probability a piece of paper

that had the words ‘rocking chair’

written on it was drawn?

A. 56

1

B. 4

1*

C. 5

1

D. 5

14

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