grade 6 math formula sheet...10. rebecca made this graph to show the colors of shirts students wore...

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Grade 6 Math Formula Sheet

Geometry

Perimeter: the distance around a polygon

Rectangle P 5 2l 1 2w

Area: the two-dimensional space inside of a polygon

Rectangle A 5 lw

Parallelogram A 5 bh

Triangle A 5 1 } 2 bh

Surface Area: the sum of the areas of the flat surfaces (called faces) of a three-dimensional figure

Volume: the amount of space inside of a three-dimensional figure

Right Rectangular Prism

V 5 lwh or V 5 Bh

Statistics

Mean (average): the sum of all the values in a data set divided by the number of values

Interquartile Range (IQR): the difference between the upper quartile (Q3) and lower quartile (Q1)

of a data set

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Assessment 2

©Curriculum Associates, LLC Copying is not permitted.

Assessment 222

Section 1, Part AYou may not use a calculator on this part of the test.

1. Consider the numbers 58.3 and 12.08.

What is the sum of the two numbers?

A. 6.038B. 60.38C. 70.38D. 703.8

2. Alden’s fish tank has 28 fish. There are 11 goldfish in the tank and the rest of the fish are tetras. Which ratio represents the number of goldfish in the tank to the number of tetras?

A. 11:17B. 11:28C. 17:11D. 28:11

3. Hailey is making 15 gift bags for a party. She has 345 marbles to put in the bags. How many marbles will Hailey put in each bag?

A. 15 B. 23C. 42 D. 69


Assessment 2 23

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4. What is the value of 43 1 52?

A. 22B. 37C. 54D. 89

5. The elevation of the floor of Little Neck Trench has changed from 232 feet to 227 feet. Which statement BEST describes this change?

A. The trench has become shallower because 232 is farther from 0 on a number line than 227.

B. The trench has become shallower because 232 is closer to 0 on a number line than 227.

C. The trench has become deeper because 232 is farther from 0 on a number line than 227.

D. The trench has become deeper because 232 is closer to 0 on a number line than 227.

6. On a number line, point A is located opposite of 2 7 } 4

. What is the location of point A on the number line?

A. 2 4 } 7

B. 0

C. 4 } 7

D. 7 } 4


Assessment 224

7. A statistical survey about a book included the question, “How long did it take you to read the book?”

Which BEST explains why the question from the survey is a statistical question?

A. The answers must all be different.B. It has only one answer.C. The answers can vary.D. There is no answer to it.

8. A piece of fabric is 3 } 4

yard long. Beni cuts strips that are each 1 }} 12 yard long. Which

expression can be used to determine how many strips Beni makes?

A. 3 } 4 3 1 }}

12

B. 3 } 4 3 12 }}

1

C. 12 }} 1 3 4 }

3

D. 1 }} 12

3 4 } 3

STOP


Assessment 2 25

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Section 1, Part BYou may use a calculator on this part of the test.

9. On one day, the temperature outside did not get above 6°F. Which number line represents the possible temperatures that day?

A. 5 6 7 8 9 10 11 12 13 14

B.

5 6 7 8 9 10 11 12 13 14

C.

–2 –1 0 1 2 3 4 5 6 87

D. –2 –1 0 1 2 3 4 5 6 87

10. Rebecca made this graph to show the colors of shirts students wore to school one day.

Num

ber

of S

tude

nts

Color

Shirt Colors

30

4035

25

15

5

20

10

White Blue Red Green

Which could group of students could Rebecca have examined?

A. Students in her math classB. Students in the cafeteria at lunchC. Students sitting in the officeD. Students playing in one basketball game


Assessment 226

11. Which expression represents the statement?

“A number multiplied by 4 is subtracted from the difference of the same number and 65.”

A. 4x 2 (x 2 65)B. 4x 2 x 2 65C. (x 2 65) 2 4xD. x 2 65 1 4x

12. Jacob wants to order pizzas for his party. He compares the cost of pizzas from four restaurants.

Pizza Prices

Restaurant Offer

Sal’s Pizzeria 8 pizzas for $68

Regina’s Restaurant 12 pizzas for $99

Hal’s House of Pizza 6 pizzas for $51

Barb’s Big Slice 14 pizzas for $98

Which statement is correct?

A. Sal’s Pizzeria charges $8.25 per pizza.B. Regina’s Restaurant charges $8.50 per pizza.C. Hal’s House of Pizza charges $8.00 per pizza.D. Barb’s Big Slice charges $7.00 per pizza.

13. These temperatures were recorded one day in January.

• Denver 212°F

• Chicago 217°F

• Philadelphia 214°F

Which statement is true?

A. Since 214 , 212, it was colder in Philadelphia than in Denver.B. Since 214 . 212, it was colder in Philadelphia than in Denver.C. Since 214 , 217, it was colder in Philadelphia than in Chicago.D. Since 214 . 217, it was colder in Philadelphia than in Chicago.


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14. Square QRST has vertices Q(2, 8), R(24, 8), S(24, 2), and T(2, 2). Triangle QTU shares 2 vertices with square QRST.

Which ordered pair describes a possible point U if the area of triangle QTU is the same as the area of square QRST?

A. (8, 2)B. (14, 8)C. (8, 8)D. (2, 14)

15. Zane made this table to show equivalent ratios for x and y, but realized that he made a mistake. He wants to change one number to make the table correct.

x y

6 48

8 96

Which change to the values in the table would make the table correct?

A. change 6 to 2B. change 8 to 10C. change 48 to 72D. change 96 to 56


Assessment 228

16. A map of locations in Mia’s town is shown on the coordinate grid. Each grid mark represents 1 mile.

y

x0 1 2 3 4 5 -5 -4 -3 -2 -1

-1

-2

-3

-4

-5

5

4

3

2

1

Mia’s House

SchoolLibrary

If Mia rides her bike in a straight line from her house to school and then to the library, how many miles does she ride?

A. 5B. 6C. 10D. 11


Assessment 2 29

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17. Whitney made 14 bracelets for her friends using a total of 168 beads. The number of beads she used for each bracelet, x, can be determined using the equation 14x 5 168. How many beads did Whitney use for each bracelet?

A. 12B. 16C. 154D. 182

18. A rectangular prism is 6 1 } 2

inches long, 3 inches wide, and 4 1 } 2

inches tall. What is the

volume of the prism, in cubic inches?

A. 14

B. 28

C. 72 1 }

4

D. 87 3 } 4


Assessment 230

19. The point (4, 3) is reflected across the x-axis and then across the y-axis.

Which coordinate grid shows the reflected point?

-1

-2

-3

-4

-5

-5 -4 -3 -2 -1 1 2 3 4 50

5

4

3

2

1

y

x

P(4, –3)

-1

-2

-3

-4

-5

-5 -4 -3 -2 -1 1 2 3 4 50

5

4

3

2

1

y

x

P(–4, 3)

A. B.

-1

-2

-3

-4

-5

-5 -4 -3 -2 -1 1 2 3 4 50

5

4

3

2

1

y

x

P(4, 3)

-1

-2

-3

-4

-5

-5 -4 -3 -2 -1 1 2 3 4 50

5

4

3

2

1

y

x

P(–4, –3)

C. D.


Assessment 2 31

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20. A painter charges $20 for every hour that he paints. Let h equal the number of hours he paints and e represent his earnings.

Select TWO equations that represent the situation.

A. e 5 20h

B. h 5 20 1 e

C. 20 5 h 1 e

D. 20 5 h 3 e

E. e } h 5 20

21. Carmen bakes and sells pies. She sells each pie for $12.99. The ingredients for 1 apple pie cost $8.75.

Part A: After accounting for the cost of the ingredients, how much money does Carmen earn when she sells 5 apple pies? Show or explain your work and write your answer in the space provided.


Assessment 232

Part B: The ingredients for a chocolate cream pie cost $2.85 less than the ingredients for an apple pie. After accounting for the cost of the ingredients, how much money does Carmen earn when she sells 5 chocolate cream pies? Show or explain your work and write your answer in the space provided.

STOP


Assessment 2 33

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Section 2You may use a calculator on this part of the test.

22. Which statement about a data set provides the most information about the variability of the data?

A. The mean of the data set is 28.B. The median of the data set is 30.C. The maximum of the data set is 40.D. The range of the data set is 18.

23. It takes Marion’s printer 4 minutes to print 14 pages. Which statement is true?

A. It takes 12 minutes to print 45 pages.B. It takes 22 minutes to print 77 pages.C. It takes 26 minutes to print 81 pages.D. It takes 28 minutes to print 95 pages.

24. What is the area of the shape in square centimeters?

8 cm[not drawn to scale]

8 cm

7.5 cm

7.5 cm

A. 30B. 60C. 90D. 120


Assessment 234

25. Which expression is equivalent to 4 1 8x?

A. 2(4 1 2x)B. 4x 1 2(2 1 2x)C. 8(x 1 1) 1 3D. 4x 1 2 1 2(x 1 1)

26. Look at the coordinate grid below.

-1

-2

-3

-4

-5

-5 -4 -3 -2 -1 1 2 3 4 50

5

4

3

2

1

y

x

P

S R

Q

Which point represents (25, 3)?

A. point PB. point QC. point RD. point S


Assessment 2 35

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27. Chandra wants to install new carpet on the floor of her attic storage closet. The shape of the closet floor is shown below.

6 ft

2 ft

4 ft6 ft

3 ft

What is the area of the closet floor?

A. 18 square feet B. 23 square feetC. 24 square feetD. 29 square feet

28. A diver is exploring in the ocean. When she is 3.25 feet below the surface, she sees a clownfish. When she is 8.75 feet below the surface, she sees a moray eel. Which statement correctly compares the depths?

A. The diver is deeper when she sees the clownfish than the moray eel because |23.25| , |28.75|.

B. The diver is deeper when she sees the moray eel than the clownfish because |23.25| . |28.75|.

C. The diver is closer to the surface when she sees the moray eel than the clownfish because |23.25| . |28.75|.

D. The diver is closer to the surface when she sees the clownfish than the moral eel because |23.25| , |28.75|.


Assessment 236

29. Look at the expression.

5x 2 3y2 1 4z

Which set of values would give the expression the least value?

A. x 5 2, y 5 3, z 5 1B. x 5 2, y 5 3, z 5 2C. x 5 3, y 5 1, z 5 2D. x 5 2, y 5 2, z 5 3

30. The figure represents the net of a right triangular prism.

6 cm

8 cm

8 cm

25 cm 25 cm

10 cm

10 cm

What is the surface area of the right triangular prism, in square centimeters?

A. 498B. 600 C. 648D. 696


Assessment 2 37

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31. The temperature at midnight was 232°F. At 6:00 am, the temperature was 227°F. Which statement BEST describes this change in temperature?

A. The temperature became colder because 232 is closer to 0 on a number line than 227.

B. The temperature became warmer because 232 is closer to 0 on a number line than 227.

C. The temperature became colder because 232 is farther from 0 on a number line than 227.

D. The temperature became warmer because 232 is farther from 0 on a number line than 227.

32. The line plot shows the time, in minutes, that customers waited to see the vet at an animal hospital last week.

8 9 10 11 12 13 14 15

XXXX

XXX

XXX

XX

Time (in minutes)

Animal Hospital Wait Time

Which data set is displayed in the line plot?

A. 8, 11, 14, 11, 15, 13, 11, 13, 15, 8, 8, 15B. 15, 14, 13, 15, 8, 8, 11, 9, 15, 13, 8, 11C. 14, 15, 15, 13, 8, 9, 13, 8, 9, 11, 8, 15, 13D. 8, 9, 11, 8, 13, 13, 14, 8, 15, 15, 15, 8


Assessment 238

33. A sculptor draws a net to represent the square pyramid he is planning to build as part of a display at a park. He plans to paint all of the surfaces of the pyramid blue. What is the total area, in square feet, that he needs to paint?

10 ft

13 ft

12 ft

A. 340B. 360C. 580D. 620

34. The dot plots show the numbers of hours two different groups of students spend online each week.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Group A

Time Spent Online

Number of Hours

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Group B

Time Spent Online

Number of Hours

Which statement correctly compares the data?

A. The variability in Group A is greater than the variability in Group B.B. The measures of center are higher for Group A than for Group B.C. The measures of center are closer to each other for Group B than for Group A.D. The variability in Group A is less than the variability in Group B.


Assessment 2 39

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35. Rammy has saved some money for a new bicycle helmet that costs $47, but needs to save more. He writes an addition equation with a variable to represent the amount of money that he still needs to save.

Which must be true about Rammy’s equation?

A. The amount he has saved and the cost of the helmet are on the same side of the equation.

B. The amount he has saved and the variable are on the same side of the equation.C. The cost of the helmet and the variable are on the same side of the equation.D. He cannot write an addition equation to represent the problem.

36. Ari waters his garden every 3 days and weeds it every Saturday.

Ari watered his garden this Saturday. How many days will it be until the next time Ari both waters and weeds his garden on the same day?

A. 14 daysB. 18 daysC. 21 daysD. 28 days

37. Consider the expression 2x2 1 5x 1 7y 2 6.

How many terms are there in the expression?

A. 2B. 3C. 4D. 7


Assessment 240

38. Kelly is reading a book with 12 chapters. The number of pages in each chapter is listed below.

9, 19, 25, 13, 17, 17, 15, 22, 24, 20, 15, 18

Which histogram BEST displays these data?

Pages in Book

Num

ber

of C

hapt

ers

Number of Pages

6

4

2

7

5

3

01

0-9 10-19 20-29

10

89

Pages in Book

Num

ber

of C

hapt

ers

Number of Pages

6

4

2

7

5

3

01

0-9 10-19 20-29

10

89

A. B.

Pages in Book

Num

ber

of C

hapt

ers

Number of Pages

6

4

2

7

5

3

01

0-9 10-19 20-29

10

89

Pages in Book

Num

ber

of C

hapt

ers

Number of Pages

6

4

2

7

5

3

01

0-9 10-19 20-29

10

89

C. D.


Assessment 2 41

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39. Thomas creates a flag in the shape of a triangle. He represents the flag on a coordinate plane, locating the vertices of the base of the triangle at (2, 24) and (26, 24). The area of the triangle is 24 square units. What is the height of the triangle?

A. 3 units B. 4 units C. 6 unitsD. 8 units

40. An art museum has been keeping track of the number of visitors it has each day, week, month, and year.

During a particular week, the art museum had 1,600 visitors, and that was 40% of the total number of visitors for the month. How many total visitors did the art museum have that month?

A. 640B. 2,500C. 4,000D. 6,000

41. Which expression is equivalent to 3(2x 1 8) 2 4x?

A. 4(2x 1 6) 2 6xB. 2(x 1 20) 1 4C. 2(3x 1 12) 2 4D. 4(x 1 8) 2 2x


Assessment 242

42. A contractor digs a rectangular hole that is 10 1 } 2

feet deep. She removes 6,510 cubic feet of dirt.

Part A: If the length of the hole is 40 feet, what is the width? Show or explain your work and write your answer in the space provided.

Part B: The contractor will use the dirt from the hole to fill box garden beds in the city.

Each garden bed is 15 feet long, 4 1 } 2

feet wide, and 3 feet deep. How many full garden

beds can be filled with the dirt that was removed from the hole? Show or explain your work

and write your answer in the space provided.


Assessment 2 43

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43. The box plots below represent the weights of the players in two football divisions. Coach Gibson is the head coach of one of the teams in Division B. When choosing players for his roster, he wants to know how the weights of the players in Division B compare to the weights of the players in Division A.

250 260 280 300 310 320 330 340 350 360230 240 270 290220

Weight (pounds)

Player Weights by Division

Division B

Division A

Part A: Choose numbers from the set shown to describe the box plot for Division A.

220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360

Minimum: pounds 1st Quartile: pounds

Maximum: pounds 3rd Quartile: pounds

Median: pounds

Part B: Choose numbers from the set shown to describe the box plot for Division B.

220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360

Minimum: pounds 1st Quartile: pounds

Maximum: pounds 3rd Quartile: pounds

Median: pounds


Assessment 244

Part C: Compare the median of each data set. What does this tell Coach Gibson about the typical weight of players in each division?

Show or explain your work and write your answer in the space provided.

Part D: Compare the interquartile range and range of each data set. What does this tell Coach Gibson about the variation of weights in each division?

Show or explain your work and write your answer in the space provided.

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Assessment 2

TEACHER USE ONLY

21. 012

42. 0 1 2

43. 0 1 234

Section 1, Part A

1. ABCD

2. ABCD

3. ABCD

4. ABCD

5. ABCD

6. ABCD

7. ABCD

8. ABCD

Section 1, Part B

9. ABCD

10. ABCD

11. ABCD

12. ABCD

13. ABCD

14. ABCD

15. ABCD

16. ABCD

17. ABCD

18. ABCD

19. ABCD

20. ABCDE

21. See page 31 .

Section 2

22. ABCD

23. ABCD

24. ABCD

25. ABCD

26. ABCD

27. ABCD

28. ABCD

29. ABCD

30. ABCD

31. ABCD

32. ABCD

33. ABCD

34. ABCD

35. ABCD

36. ABCD

37. ABCD

38. ABCD

39. ABCD

40. ABCD

41. ABCD

42. See page 42 .

43. See page 43 .

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grade 6 math formula sheet...10. rebecca made this graph to show the colors of shirts students wore...

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