4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
1. The table shows the number of costumes a store sold each week during a 3-week period.
Part A
Compare the value of the digit 6 in 764 to the value of the digit 6 in 627. Use what you know about place value to
explain your answer.
Part B
How many costumes were sold during the 3-week period? Round the total to the nearest hundred. Show your work
and explain your answer.
Part C
During the same 3-week time period last year, the store sold 1,425 costumes. Copy the table below and fill in the
number of costumes that could have been sold each week. Use these rules to choose your numbers.
♦ More costumes were sold in week 1 than any other week.
♦ The value of the hundreds digit in week 1 was ten times the value of the tens digit in week 2.
♦ A total of 1,425 costumes were sold.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
2. The top of Stone Mountain in Georgia is 1,683 feet above sea level. The top of Sassafras Mountain in South
Carolina is 3,560 feet. Which statement about the value of the digit 3 in 3,560 is true?
A. It is ten times the value of 3 in 1,683.
B. It is one hundred times the value of 3 in 1,683.
C. It is one thousand times the value of 3 in 1,683.
D. It is two thousand times the value of 3 in 1,683.
3. Maria earns $25 working after school. She decides to spend the $25 at the school store to buy gifts for her friends.
Part A
The total price of how many key chains equals the price of 1 T-shirt? Show your work or explain your answer.
Part B
Maria decides to buy 4 key chains. She then buys as many book covers as possible. Explain if Maria can buy anything
else after she buys the book covers. Show your work.
Part C
Maria goes to the school store again with $25. She buys the greatest number of different items that she can buy. Her
purchase is equal to all of the money she brought this time. Which items can Maria buy and spend all $25? Explain
your answer.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
4.
What is the place value of the underlined digit in 172,482.03?
A. hundreds
B. hundredths
C. thousands
D. thousandths
5. Alicia saved three thousand, seven hundred twenty-four pennies.
Part A
Write the number of pennies Alicia saved in standard and expanded forms.
Part B
If Alicia trades in all of her pennies for nickels, what is the greatest number of nickels she can get? How many
pennies will Alicia have left over? Show work or explain how you got your answer.
Part C
Alicia stated that she would get 10 times as many dimes as nickels if she traded her pennies for dimes. Is her
statement true? Why or why not? Show your work or explain your answer.
Part D
Alicia plans to cash in her pennies at the bank. What is the number of dollars and cents she should receive from all of
her pennies? Show your work.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
6. A fourth grade class is learning about veterans. A veteran is a person who has served in the military. The table
shows the information they collected about the number of people who are veterans in several states.
Which expression correctly compares the number of veterans in two of the states listed in the table?
A.
B.
C.
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
7. Marcus has 145 songs on his music player. Cory has 435 songs on his music player.
Part A
Write each number in word form.
Part B
Write an inequality using
know your answer is correct.
to compare the numbers of songs on each music player. Explain how you
Part C
Write each number in expanded form.
Part D
Cory added 24 new songs on his music player. Marcus added 6 times as many new songs on his player as Cory
added. What is the total number of songs on Marcus’s music player after this addition? Show your work.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
8. The table shows the weights of 3 giraffes.
Part A
What is the weight, in kilograms, of Giraffe 2 in expanded form? Explain your answer.
Part B
Does Giraffe 1 or Giraffe 3 weigh more? Explain your answer and use place value in your explanation.
Part C
What is the weight of each giraffe, rounded to the nearest 100 kilograms?
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9. Round 8,246 to the nearest hundred.
A. 8,000
B. 8,200
C. 8,250
D. 8,300
10. There were 75,631 people at a concert. What is that number rounded to the nearest ten thousand people?
A. 60,000
B. 70,000
C. 80,000
D. 90,000
Permission has been granted for reproduction by the Virginia Department of Education
© Virginia Department of Education
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
11. The table shows the distance that each of three trains traveled in a given number of days. The trains all traveled
the same number of hours each day.
Part A
Copy the table, round each distance to the nearest thousand kilometers, and fill in the spaces with your rounded
distances.
Part B
Use your rounded distances from Part A to estimate the number of kilometers each train traveled per day. Show your
work.
Part C
If the three trains traveled an equal number of days, which train would go the longest distance? Explain your answer.
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12.
The census of a city counts 99,896 families with 378,533 children and 121,323 adults. According to this census, what
is the best estimate of the city's population?
A. 600,000 people
B. 500,000 people
C. 121,000 people
D. 100,000 people
13. Which number is 4,718 rounded to the nearest thousand?
A. 4,000
B. 5,000
C. 6,000
D. 7,000
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
14. Three different reports give the number of people who attended a football game. Each report correctly rounds the
actual attendance to a different place value.
• Report A says the attendance was 192,000.
• Report B says the attendance was 200,000.
• Report C says the attendance was 190,000.
Which number could be the actual attendance at the football game?
A. 190,220
B. 191,804
C. 192,820
D. 199,018
15. A report stated that 281,305,769 people visited U.S. national parks in 2010. The author of a travel guide rounded
the number of visitors to 281,300,000. To which place value did the author round the number of people who visited
U.S. national parks in 2010?
A. ten millions
B. ten thousands
C. hundred millions
D. hundred thousands
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
16. The table shows the weights of several zebras.
Part A
Yolanda rounded each weight to the nearest hundred and said the combined weight was about 2,000 pounds. Does
Yolanda’s statement make sense? Use what you know about rounding to explain your answer.
Part B
The zebras were moving to a different zoo and needed to be transported on a trailer in 2 trips. Which zebras would be
on the trailer each trip if 2 of the zebras were taken at one time, and the total weight was no more than 1,025 pounds
on each trip? Show your work.
Part C
The rectangle shows the 135-square-foot watering hole for the zebras.
What is the value of w ? Show your work.
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17. What is 7,648 rounded to the nearest hundred?
A. 8,000
B. 7,700
C. 7,650
D. 7,600
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
18. The number of people who attended a big race on Friday was 111,283. On Saturday, 94,345 people attended
another race at the same race track.
Part A
What was the total number of people who attended both races? Explain your answer using what you know about
place value.
Part B
How many fewer people attended the Saturday race than the Friday race? Explain your answer using what you know
about place value.
Part C
What was the attendance at the Friday race rounded to the nearest hundred? Explain your answer.
Part D
What was the attendance on Saturday rounded to the nearest thousand?
Explain your answer.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
19. This table shows the number of students in some of the grades at an elementary school.
Part A
What is the total number of students in grades K through 3? Show your work.
Part B
The elementary school has 697 students in all. What is the total number of students in grades 4 and 5 together? Show
your work.
Part C
Grade 4 has 30 more students than grade 5. How many students are in grade 4, and how many students are in grade 5?
Part D
A table in the cafeteria can have up to 9 students. How many tables are needed for each grade?
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
20. Each month Aiden pays his bills. Answer each question about Aiden’s bills.
Part A
Aiden has $3,942. He pays $362 for his electricity. He also pays $1,070 for his house. How much money will he have
left after he pays these two bills? Show your work.
Part B
Aiden is writing 2 checks to pay for his electricity and house.
Write each amount in words.
Part C
In 6 months, Aiden pays a total of $162 for his home phone and a total of $618 for his cell phone. He pays an equal
amount each month. What is the amount he pays in one month for his home phone and cell phone together?
Part D
Aiden pays $89 each month for cable TV. He worked the multiplication problem below and stated that he pays $267
for the whole year.
What is the error that Aiden made? Give a complete explanation of your answer.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
21. Joel is practicing his multiplication skills. He is looking for patterns when he multiplies a number by 35.
Part A
Joel multiplied
using the area model shown.
Complete the area model and write the value of
Part B
Joel found the product of
. Show your work.
.
in a different way. Use a way other than an area model to find the product of
Part C
Joel multiplied more numbers by 35 and made the table below.
The answers from Part A and Part B will complete the table. What do you notice about the last digit for all the
multiples of 35?
Part D
Joel guessed that 35 times an even number always has a last digit of 0. Explain in words why the area model in Part A
shows that Joel’s guess is correct.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
22. The numbers of tickets sold at different prices for a baseball game are listed in the table.
Part A
How much money was received for selling tickets that cost less than $8? Show your work.
Part B
Compare the value of the digit 4 in 5,417 to the value of the digit 4 in 1,034. How many times greater is one value
than the other value? Explain your answer.
Part C
Andrew made this table to show the prices of several tickets at different prices. Create a copy of the table below and
fill in the missing dollar amounts.
Andrew spent $62 on tickets. He bought at least 1 of each ticket price. How many of each ticket price could he have
bought? Show your work or explain your answer.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
23. A sheet of scented stickers has 18 stickers. There are 36 sheets of scented stickers in one package.
Part A
How many scented stickers are in one package? Show your work.
Part B
A store has 20 packages of the scented stickers. What is the total number of scented stickers the store has? Show your
work.
Part C
The store also sells star-shaped stickers. The total number of star-shaped stickers in one package can be calculated
using the expression
Based on this expression, how many star-shaped stickers are on one
sheet and how many sheets are in one package? Label your answers.
Part D
The store always keeps between 1 and 20 whole packages of stickers of each type of sticker. Is it possible for the
store to have the same total number of scented and star-shaped stickers? Explain your answer and show your work.
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24. Chen Li buys sports equipment for the City Park. One carton of tennis balls costs $49. If she needs to buy 17
cartons, how much will she pay for the tennis balls?
A. $68
B. $441
C. $733
D. $833
25. Jan has 40 bags of marbles. There are 70 marbles in each bag. How many marbles does Jan have?
A. 110
B. 280
C. 1110
D. 2800
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
26. A bookstore had 3,200 copies of a new book. Every copy was sold for $16 per copy.
What was the total amount of the bookstore's sales from this book?
A. $22,400
B. $32,000
C. $50,200
D. $51,200
This online assessment item contains material that has been released to the public by the Massachusetts Department of Education.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
27. Sophie has candy hearts to give to classmates. She makes the array shown to help group the candy.
Part A
How many groups of 7 candy hearts can be made with the hearts in the array? Show your work.
Part B
Write a division equation showing how many groups of 7 candy hearts Sophie can make.
Part C
Sophie eats 6 candy hearts. How many groups of 7 candy hearts are left in the array now? What does the remainder
mean for this situation? Show your work and explain your answer.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
28. A restaurant owner has $1,000 to spend on vegetables at a farmers’ market.
Part A
How many baskets of cucumbers could the owner buy if she only buys cucumbers? Explain how you got your answer
using an equation.
Part B
If the owner buys 25 baskets of tomatoes, how much money will she have left? Show your work.
Part C
Baskets of carrots are also for sale at the farmers’ market for $6 each. How much more would 45 baskets of peppers
cost than 45 baskets of carrots?
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
29. The table shows the numbers of cows in Rhode Island during two years.
Part A
Rhode Island has 5 counties. About how many cows were in each county in Rhode Island during 2011? Show how
you got your answer by writing an equation.
Part B
The state of Delaware had more than 4 times but less than 5 times as many cows as Rhode Island. What could be the
number of cows Delaware had in 2012? Show your work or explain your answer.
Part C
Alaska had more cows in 2012 than Rhode Island had in 2011 and 2012 combined. What could be the number of
cows Alaska had in 2012? Show your work or explain your answer.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
30. A season of baseball lasts 6 months. The table shows the number of baseballs 3 different teams used during one
season.
Part A
About how many baseballs did each team use in 1 month if the team used an equal number each month? Explain how
you got your answer.
Part B
Team B played another 2 weeks during the playoffs. Use your answer in Part A to estimate the number of balls they
used during the playoffs. Show your work.
Part C
Team B played 8 games in the 2 weeks of playoffs. About how many balls did they use in each game? Show your
work.
Part D
Each of the baseballs used in the playoffs cost $13. Use your answer in Part C to determine the total amount spent on
baseballs during one playoff game. Show your work.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
31. The diagram shows counters on place-value cards.
Part A
What number is represented by the counters? Divide this number by 3. Show your work or explain your answer in
words.
Part B
Round the number represented by the counters to the nearest ten. Explain your answer.
Part C
Make a model of a different number using place-value cards like the ones shown. Put an equal number of counters on
the thousands card and the tens card. Write the number that your model represents. How many times greater is the
value of the digit in the thousands place than the value of the digit in the tens place?
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32.
18,416 – 5,037 =
A. 13,339.
B. 13,379.
C. 13,429.
D. 13,479.
Permission has been granted for reproduction by the Virginia Department of Education
© Virginia Department of Education
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
33. Tammy is playing a math game. She has a card with the fraction model shown.
She needs to find another card with a different fraction model that represents the same fraction as her card. Which
fraction model represents the same fraction as Tammy’s fraction model?
A.
B.
C.
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
34. Valerie baked one full pan of muffins. She gave
of the muffins to a neighbor. Which model could represent the
pan Valerie used for baking and the muffins that she has left?
A.
B.
C.
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
35. Two fraction models are shown.
Part A
What fractions are represented by these models? Are the fractions equivalent? Explain your answer.
Part B
Compare the fraction shown in each model to
Use
in each comparison. Explain your answers.
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36. Which letter best represents 3
on the number line below?
A. U
B. V
C. W
D. X
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
37. Erica made a blanket using 12 cloth squares. She sewed decorations on the squares. All of the squares had more
than one decoration. Use the diagram shown to answer the questions.
Part A
Erica sewed flowers on
of the squares and birds on
of the squares.
Are there more squares with flowers or with birds? Explain your answer.
Part B
Erica made
of the squares pink and
of the squares purple. Fill in the number sentence to show the relationship
between the number of pink and purple squares using
Explain your answer.
Part C
There were more squares with stars than squares with flowers. Select the fraction that could represent the fraction of
squares with stars. Explain why you chose this fraction.
Part D
There were more squares with stars than squares with flowers. What is the fewest number of squares that must have
both a flower and a star? Show your work or explain your reasoning.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
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38. Jackie bought a bag of oranges.
•
She used
of the oranges to make orange juice.
She used
of the oranges to make a fruit salad.
•
•
She put
of the oranges in a bowl on the table.
She put
of the oranges in the refrigerator.
•
Which statement is true?
A. Jackie left more oranges on the table than she put in the refrigerator.
B. Jackie used fewer oranges to make orange juice than she left on the table.
C. Jackie put fewer oranges in the refrigerator than she used to make the fruit salad.
D. Jackie used more oranges to make a fruit salad than she used to make orange juice.
39.
A group of people ordered pizza for lunch. At the end of lunch, there were 2
left over. How much total pizza was left over?
A. 2
cheese pizzas and
pepperoni pizza
pizzas
B. 2 pizzas
C. 3 pizzas
D. 4 pizzas
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
40. Use this equation to answer Part A and Part B.
Part A
Each fraction in the equation should have a different numerator. Zero cannot be one of the numerators. What 3
numerators will make the equation true?
Part B
Draw a model to represent the equation. Use at least one numerator in your model that you did not use in Part A.
Part C
Evaluate the expression below. Show your work or explain your thinking.
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41. Jack painted a picture using three colors.
•
of the picture is green.
•
of the picture is blue.
• The rest of the picture is purple.
Which fraction shows the part of Jack’s picture that is purple?
A.
B.
C.
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
42. A teacher has two pieces of ribbon. One piece is
of a meter long. The other piece is
of a meter long.
Part A
What is the total length, in meters, of the two ribbons? Show your work.
Part B
What is the total length, in centimeters , of the ribbon? Show your work.
Part C
The teacher plans to use the shorter piece of ribbon to glue around the outside of a square picture. If no space around
the picture is left, what is the greatest length, in centimeters, that one side of the square can be? Show your work or
explain your answer.
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43.
Julia performs the computation of
Part A
Julia’s computation gave her an incorrect sum,
Explain what Julia did incorrectly to get the incorrect sum.
Part B
What is the correct value of
Show your work.
Part C
Write
as the product of a whole number and a fraction. Explain your answer.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
44. Emily makes a necklace with three types of beads. The length and width of each bead is shown in centimeters
(cm).
Part A
The striped bead is
cm long. Write this length as a decimal.
Part B
The widths of the striped bead and the white bead are
using the symbols
cm and
cm. Write a comparison of these two widths
Part C
Emily does the work shown below to determine how much longer the striped bead is than the white bead.
Do you agree with Emily’s work? Explain why you agree or disagree.
Part D
The length of the gray bead is more than 4.65 cm but less than
Explain your answer.
cm. What could be the length of the gray bead?
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
45.
Which of the following numbers is between
and 4.77?
A.
B. 4.8
C. 4.78
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
46. Jon runs or walks the same distance around his neighborhood every day for exercise. One complete circle around
his neighborhood is 2.5 miles starting and ending at his home.
Part A
On Monday, Jon ran and walked in this order.
• He started by running 0.8 mile.
• He then walked 0.6 mile.
• Jon finished the circle by running the rest of the way home.
How far did Jon run to finish his exercise on Monday? Express the distance as a fraction. Show your work. You may
use the tape diagram below to help answer the question.
Part B
Jon changed his exercise pattern on Tuesday so that he ran three times and walked two times.
• He started running and then switched between walking and running.
• Each section that he walked or ran was the same distance.
Describe the pattern Jon used on Tuesday to complete one circle around his neighborhood. You may use the tape
diagram below to help describe the pattern.
Part C
Jon likes to run more than walk. Think of a new pattern for Jon to run and walk one complete circle around his
neighborhood.
• For this pattern Jon will run twice and walk twice.
• Make each section a different distance.
• Make Jon’s total running distance longer than his total walking distance.
Describe a pattern that fits all of these rules. How much farther does Jon run than walk in your pattern?
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
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47. Libby and George raced their miniature cars at home. Libby’s car went
meter.
meter and George’s car went
Part A
Write the decimal that represents how far Libby’s car went. Explain your answer.
Part B
Write the decimal that represents how far George’s car went. Explain your answer.
Part C
How far did both cars go together? Write your answer as a fraction and explain your answer.
Part D
Draw and label a number line to show how far Libby’s car went.
Be sure to complete ALL parts of the task.
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48. Which point on the number line below best represents 0.8?
A. point A
B. point B
C. point C
D. point D
This online assessment item contains material that has been released to the public by the Massachusetts Department of Education.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
49.
At the grocery store, Shana's father bought six items with the following prices: $2.49, $1.19, $0.99, $0.99,
$5.39, and $1.09. Assuming there is no sales tax, what is the best estimate of the total bill?
A. $9.00
B. $12.00
C. $13.00
D. $15.00
50. Which decimal is LEAST?
A. 0.09
B. 0.10
C. 0.9
D. 0.19
51. Leo and Benito each drew a model to show
Which statement best explains who made the correct model to compare the decimal values?
A. Neither student made a correct model because 0.5 is greater than 0.7.
B. Both students made a correct model because 0.5 is smaller in each model.
C. Leo made the best model because each decimal describes parts of a different whole.
D. Benito made the best model because both decimals describe parts of the same whole.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
52. Olivia compares 0.06 and 0.4.
Part A
Olivia says that
because
Explain why you agree or disagree with Olivia.
Part B
Draw a visual model to compare the two numbers.
Part C
Write 0.06 as a fraction. Explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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53. Which numbers are in order from greatest to least?
A. 32.14, 34.01, 31.24, 30.41
B. 31.24, 32.14, 30.41, 34.01
C. 34.01, 32.14, 31.24, 30.41
D. 30.41, 31.24, 32.14, 34.01
54.
Amy measured four leaves for a science report. The leaves were 2.9 cm, 3.33 cm, 3.9 cm, and 3.12 cm long. Which
lists the lengths in order from LONGEST to SHORTEST?
A. 2.9 cm, 3.12 cm, 3.33 cm, 3.9 cm
B. 2.9 cm, 3.9 cm, 3.12 cm, 3.33 cm
C. 3.9 cm, 2.9 cm, 3.12 cm, 3.33 cm
D. 3.9 cm, 3.33 cm, 3.12 cm, 2.90 cm
36
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
55. The list shows the amount of change each student received after buying lunch.
♦ Gabby received $0.50.
♦ Brandon received $0.46.
♦ Veronica received $0.34.
♦ Rick received $0.55.
Part A
Compare the change that Gabby received to the amount Rick received using the symbols
answer.
Explain your
Part B
If Rick’s lunch cost $1.45, how much money did he have before he paid for his lunch? Explain your answer.
Part C
Rewrite the amount of change each student received as a fraction using 10 or 100 as the denominator. Explain your
answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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56. The distance from Atlanta to McDonough is about 30 miles. The distance from McDonough to Macon is two
times the distance from Atlanta to McDonough. Which equation best represents the distance from McDonough to
Macon?
A.
B.
C.
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
57. Mr. Michaels has 32 students in his class. He wants to arrange the rows with the same number of students in each
row. Which table shows all of the ways Mr. Michaels can arrange the students?
A.
B.
C.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
D.
58. A club with 124 members is planning a camping trip. They need to rent cabins and tents for sleeping.
• Eight members can sleep in each cabin.
• Two members can sleep in each tent.
• They plan to rent as many cabins as they can fill.
How many tents does the club need to rent?
A. 2
B. 4
C. 15
D. 62
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
59. Amy has
packs of gum. Kim has
packs of gum. Each whole pack of gum has the same number of
pieces. A fraction model is shaded to represent this situation.
Which addition problem is equivalent to the one shown in the model?
A.
B.
C.
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
60. Which model is shaded to represent a fraction equivalent to
?
A.
B.
C.
D.
41
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
61. Dara made 12 fruit baskets for gifts. She put 2 peaches and 3 pears in each basket. Then she added apples, plums,
and oranges.
• Dara put four times as many apples as peaches in each basket.
• She put twice as many plums as pears in each basket.
• She put the same number of oranges in each basket.
Each basket has 23 pieces of fruit all together.
Part A
What is the total number of pieces of fruit in all the fruit baskets Dara made? Show your work.
Part B
How many oranges did Dara put in each fruit basket? Show your work or explain how you got your answer.
Part C
If Dara replaces 3 oranges from each basket with 2 grapefruit, what will be the total number of pieces of fruit in all of
the baskets? Show your work or explain how you got your answer.
Part D
Dara removes 3 oranges from each basket to fill sacks for the food bank. It takes 8 oranges to fill one sack. How
many full sacks of oranges can Dara give to the food bank? How many oranges will be left over? Show your work or
explain how you got your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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42
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
62. The length of a tree’s shadow was measured and recorded at three different times one day.
• The shadow was 32 feet long at 8:30 a.m.
• The shadow was 8 feet long at 12:00 noon.
• The shadow was 48 feet long at 5:00 p.m.
Part A
How many times longer was the shadow of the tree at 8:30 a.m. than it was at noon? Explain your answer.
Part B
At 5:00 p.m. the shadow was 3 times as long as the height of the tree. What was the height, in feet, of the tree? Show
your work or explain your answer.
Part C
Another tree has a shadow 6 feet long at 12:00 noon. Make a table showing the lengths of this tree’s shadow if it
increases by 4 feet every 2 hours beginning at 10:00 a.m. and ending at 6:00 p.m. Explain how you found the
unknown lengths.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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43
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
63. The two spinners shown are used for a math game. On each turn, a player spins the arrows on both spinners.
The product of the two numbers determines a player’s move.
• 2 spaces forward if the product is a prime number
• 1 space forward if the product is even and composite
• 1 space backward if the product is odd and composite
Part A
List all the products that move the players 2 spaces forward.
Part B
List all the products that move the players 1 space forward.
Part C
List all the products that move the players 1 space backward.
Part D
The numbers on Spinner 2 were changed. The new products of the numbers on Spinner 1 and Spinner 2 are shown in
this chart. Each column of numbers follows a pattern.
Write the rules for the numbers in each column.
44
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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64. A group of students walk or run laps around the school track each day after school. The line plot shows the
distances, in miles, the group of students completed one day.
Part A
What is the total number of miles the group of students completed that day? Show your work or explain your answer.
Part B
What is the difference, in miles, between the longest distance completed by one student and the shortest distance
completed by one student? Show your work.
Part C
One lap is equal to
work.
mile. What is the total number of laps the group of students completed that day? Show your
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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45
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
65. A carpenter needs 16 pieces of painter’s tape that measure
foot each.
Part A
How many feet of painting tape does the carpenter need? Show your work or explain your answer.
Part B
The carpenter has 5 yards of painter’s tape. Does he have as much tape as he needs? Explain your answer by showing
your work or using a model.
Part C
The carpenter places two of the
-foot pieces of tape end-to-end. What is the total length, in inches , of the two
pieces of tape? Show your work or explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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46
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
66. Sherry drew a pizza with equal sized slices and labeled each slice with its topping.
Part A
What fraction of Sherry’s pizza has onions as a topping? What fraction of the pizza has a topping other than onions?
Explain your answers.
Part B
What fraction of the pizza has bacon or beef? Show your work or explain your answer.
Part C
Sherry’s favorite toppings are bacon, olives, and cheese. What fraction of the pizza has Sherry’s favorite toppings?
Show your work or explain your answer.
Part D
Which two different toppings were used for exactly
of the pizza? Show your work or explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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47
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
67. A candy shop sells fudge in two sizes. The weight of each type of box is shown in the picture below.
Part A
Gina is buying 2 small boxes and 3 large boxes of fudge from the shop. What is the total weight, in pounds, of these
boxes of fudge? Show your work.
Part B
A small box of fudge costs $12. A large box of fudge costs $20. What is the total cost of the boxes of fudge Gina is
buying? Show your work.
Part C
Last week Gina bought 1 large box of fudge and some small boxes of fudge. The cost of all the boxes of fudge was
$56. What was the total weight, in pounds, of the fudge she bought last week? Explain how you got your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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48
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
68. Wendy and her mother went to a yard sale. This sign was posted at the yard sale.
Part A
Wendy has $75. She wants to spend $15 on toys. She can use this equation to find how many toys she can buy with
$15.
Solve the equation to find the number of toys Wendy can buy. Show your work.
Part B
Wendy’s mother plans to spend up to $105 for chairs. Write an equation to find how many chairs she can buy. Use c
in the equation to represent the number of chairs she can buy.
Part C
Solve the equation you wrote in Part B. What is the greatest number of chairs Wendy’s mother can buy? Show your
work.
Part D
Wendy and her mother want to buy some other items with the money they have left over. They want to buy 5 golf
clubs, 4 shirts, and 5 books. Do they have enough money to buy all of these items? Show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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49
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
69. Mr. Johns bought 8 packages of hot dogs for a cook-out. The total cost of the hot dogs was $24.00. Which of the
following number sentences could be used to determine the cost of one package of hot dogs?
A.
B.
C.
D.
This online assessment item contains material that has been released to the public by the Massachusetts Department of Education.
70.
There are 2,457 boxes of pencils. There are 13 schools in a town. Each school will get the same number of boxes.
How many boxes will each school get?
A. 112
B. 118
C. 134
D. 189
71.
360 ÷ 30 yields the same quotient as
A. 36 ÷ 3.
B. 36 ÷ 12.
C. 360 ÷ 3.
D. 360 ÷ 12.
50
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
72. Rachel is making a wooden shelf for her garage. She plans to use a piece of wood that is 1.5 meters long. The
shelf will be attached to the wall, and Rachel needs to make two legs for support.
Part A
What is the total number of centimeters in 1.5 meters?
Part B
Rachel bought a piece of wood
meter long and had the store cut it into two equal pieces for the legs. Each piece
was
meter too short. What was the length Rachel needed each leg to be? Show your work and write your answer
as a fraction.
Part C
The width of Rachel’s shelf is
your work.
meter less than the length. What is the width of the shelf in centimeters? Show
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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73. Marvin and Tomas ran a 5-kilometer race.
Part A
How many centimeters long is a 5-kilometer race? Show your work or explain your answer in words.
Part B
Marvin ran the race in 24 minutes and 33 seconds. Tomas ran the race in 26 minutes and 15 seconds. How much
longer did it take Tomas to run the race than Marvin? Show your work.
Part C
The race started at exactly 8:45 a.m. What time did Tomas finish the race, to the nearest whole minute? Show your
work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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51
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
74. Mason used four rectangular pieces of wood to make a slide for his brother. Use these pieces to answer the
questions.
Part A
What is the difference, in square inches, in the areas of the top of piece B and the top of piece C? Show your work.
Part B
To keep the slide from moving, Mason put a piece of rubber around the perimeter of piece A. What was the length, in
inches, of the piece of rubber? Show your work.
Part C
Mason bought 48 square feet of wood. The price was $1 for 4 square feet of wood. What was the total cost of the
wood? Explain your answer.
Part D
Mason took $20 to the store to buy the wood. He used the money he had left to buy one bucket of paint and one paint
brush. Select one bucket of paint and one paint brush that Mason could have bought. Explain your choice.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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52
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
75. Teresa has a math worksheet to practice adding fractions. In the exercise shown, she needs to choose two of the
fractions or mixed numbers with a sum of
Part A
Which two fractions or mixed numbers have a sum of
Show your work.
Part B
Solve the subtraction problem
Make a fraction model to support your answer.
Part C
Compare the fractions
statement true?
and
Which symbol
should be placed in the box to make the number
Explain how you know which symbol to use.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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53
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
76. The table shows the lengths of some of the hiking trails at a state park.
Part A
Martin hiked the Sycamore trail and the Mountaintop trail last week. What was the total distance he hiked? Show
your work.
Part B
Merrilee hiked the Elkhorn trail and Kevin hiked the Meadowland trail. How much farther did Merrilee hike than
Kevin? Show your work.
Part C
Tynan wants to hike 3 different trails totaling at least 15 miles. Explain whether or not there is more than one
combination of 3 different trails she can choose that will be a distance of at least 15 miles. Show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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54
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
77. Alice starts and finishes her guitar lesson at the times shown.
Part A
How long is Alice’s guitar lesson? Show your work using a number line.
Part B
What fraction of the hour did Alice spend in the guitar lesson? Show your work or explain your answer.
Part C
Alice’s guitar teacher has to change the start time of the lesson to 3:30 p.m. If the length of the lesson remains the
same, at which time will the guitar lesson now finish? Show your work or explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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55
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
78. A box of pancake mix contains 40 ounces of mix. The amount of mix needed to make four 8-inch-diameter
pancakes is 2 cups.
Part A
How many ounces of mix are equal to 2 cups? Show your work.
Part B
How many 8-inch pancakes can be made using 40 ounces of pancake mix? Show your work or explain your answer.
Part C
More pancakes that have a 6-inch diameter can be made with 2 cups of pancake mix. What number of cups and what
number of pancakes would complete the table below? Explain your answer.
Part D
Which would use more cups of pancake mix?
• 14 pancakes with a 8-inch diameter
• 21 pancakes with a 6-inch diameter
Show your work or explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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56
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
79. Andrew has 10 quarters, 4 dimes, and 6 nickels in a jar.
Part A
If there are no other coins or bills in the jar, what is the amount of money in Andrew’s jar? Show your work.
Part B
How many $1 bills can Andrew exchange for the coins he has in the jar? Explain your answer.
Part C
How much additional money does he need for a $5 bill? Explain your answer.
Part D
What is the least number of coins equal to the amount you got in Part C, using any combination of quarters, dimes, or
nickels? Show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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57
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
80. A rectangular space on a wall at school is used to post school announcements. The space is 3 feet in length and
has a perimeter of 12 feet.
Part A
What is the width, in feet, of the rectangular space? Show your work.
Part B
What is the area, in square feet, of the rectangular space? Show your work.
Part C
The rectangular area needs to be enlarged. The new rectangular area will be two times the area you found in Part B. If
the width remains the same, what is the length of the larger rectangular area? Show your work.
Part D
Look at the following statement.
If the area of a rectangle is doubled, then the perimeter of the larger rectangle will be two times the original perimeter.
Is this statement always true? Explain your answer by giving an example.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
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58
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
81. A group of friends bought some pizzas. Each pizza was cut into 8 equal slices. The table shows the number of
slices of pizza taken by all the friends.
Part A
Everyone in the group took at least one slice of pizza. Based on the data in the table, how many people were in the
group? Explain your answer.
Part B
Create a line plot using the number line shown below and the data in the table.
Part C
If no pizza slices were leftover, how many pizzas did the group buy? Show your work or explain your answer.
Part D
The cost of each pizza was $13. What was the cost of the pizzas before tax was added? Show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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59
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
82. The line plot below shows the lengths, in inches, of several flower petals.
What is the difference, in inches, between the lengths of the second longest petal and the shortest petal?
A.
B.
C.
D.
83. Gino read 42 pages in one day. Tisha read 126 pages in one day. Which equation could be solved to find how
many times more pages Tisha read than Gino?
A.
B.
C.
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
84. Which shaded fraction model correctly shows the decomposition of
A.
B.
C.
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
85. Tamika calculated the number of hours she watched television, based on the number of minutes she had watched.
Which table shows the correct relationship of minutes and hours?
A.
B.
C.
D.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
86. Members of a school club sold bottled water and bags of popcorn at a basketball tournament. They had a total of
78 water bottles to sell for the 3-day tournament. They used the school’s popcorn machine to make as many bags of
popcorn as they could sell.
Part A
Before the tournament started, the club’s goal was to raise a total of $800. If they sold water bottles for $1 each and
popcorn for $2 each, how many total bags and bottles would they need to sell? Explain how you got your answer.
Part B
The club sold 5 packs of 6 bottles each on the first day. How many water bottles did they have left to sell after the
first day? Write an equation that could be solved to answer the question. Use n to represent the unknown quantity in
your equation.
Part C
The club sold bags of popcorn for $2 each. At the end of the third day, they had received a total of $588 selling the
bags of popcorn. How many bags of popcorn did they sell at the tournament?
If they sold the same number of bags each day of the tournament, how many bags did they sell in one day? Show
your work to find the total number of bags sold for the tournament and number of bags sold per day.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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63
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
87. A total of 12 girls are on a softball team. The shaded baseball gloves represent the number of girls who have a
black glove and the non-shaded gloves represent the number of girls who have a brown glove.
Part A
Angelica stated that
of the team has a black glove. Gabby stated that
whether or not each girl’s statement is correct.
of the team has a black glove. Explain
Part B
Coach Anders said that over
of the team did not have brown gloves. Is his statement correct? Explain what you
know about comparing fractions in your answer.
Part C
Each glove measures
of a meter in length. Write a different fraction that is equivalent to
answer using words or a model.
Explain your
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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64
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
88. Jessica jumped three times, and each time she jumped forward
of a yard.
Part A
Draw a model or a number line to represent one of Jessica’s jumps. Use the model or number line you drew to find
the total distance of Jessica’s three jumps.
Part B
Each one of Mark’s jumps was
work.
yards. How much farther did Mark jump in one jump than Jessica? Show your
Part C
The total of Tony’s three jumps was
yards. Tony jumped the same distance on each jump. Write an equation,
using multiplication only, to represent Tony’s total distance for three jumps.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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65
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
89. Each of the book shelves in a library is 2 yards long. The librarian created a table showing the lengths of the book
shelves when placed side by side.
Part A
Margie used a 12-inch ruler to check the measurements shown in the librarian’s table. Explain how many inches
Margie should measure for each measurement in the table, if both the librarian and the student’s measurements are
correct.
Part B
Each of the shelves can hold 48 textbooks. How many textbooks could 11 shelves hold? Show your work.
Part C
Margie checked out 36 textbooks during the first hour she worked at the library, as shown on the number line.
If she checks out the same number of textbooks each hour, how many textbooks will Margie check out in
Explain how you got your answer.
hours?
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
________________________________________________________________________
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66
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
90. Ms. Parker uses nails to finish a birdhouse she is making. The line plot shows the lengths of some of the nails in
Ms. Parker’s tool box.
Part A
Ms. Parker said she had a silver nail that was
silver nail? Show your work.
inch longer than the shortest nail in the line plot. How long was the
Part B
The bottom of Ms. Parker’s birdhouse is a rectangle. The area of the rectangle is 60 square inches. The length of the
rectangle equals the sum of the lengths of all of the nails shown in the line plot.
What is the width of the birdhouse? Explain how you got your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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67
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
91. The figure shows the front view of a door. A large glass window covers most of the top half of the door.
Part A
Marissa says the shaded figures in the window are rhombi because they each have 2 sets of parallel lines. Did Marissa
classify the shaded figures correctly? Explain your answer.
Part B
Based on the angles, what type of triangle is shown in the glass window on the door? Explain your answer.
Part C
Can a line of symmetry be drawn on the door? Explain why or why not.
Part D
The width of the door is 3 feet, and the height is
you got your answers.
feet. What are the dimensions of the door in inches? Show how
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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68
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
92. One bamboo plant is 8 feet tall. A second bamboo plant is 24 feet tall. Sarah says that the second bamboo plant is
3 times as tall as the first bamboo plant.
Part A
Write an equation that represents the relationship between the heights of these two bamboo plants. Explain why you
chose your equation.
Part B
Chase disagrees with Sarah and says that the second bamboo plant is 16 times as tall as the first plant. What mistake
do you think Chase made? Explain why he is incorrect.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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93. The table shows 2 number patterns.
Part A
What are the first four terms of Pattern A? Show or explain your work.
Part B
Ryan says all the terms in Pattern B are odd. Do you agree with Ryan? Explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
94. The table shows the amount of time Feliciano spent running for the last 2 weeks.
Part A
Use multiplication to find the total amount of time, in hours, that Feliciano ran in week 1. Express your answer as an
improper fraction and also as a mixed number. Show your work or explain your answers.
Part B
What is the total amount of time, in minutes, that Feliciano ran in week 2? Show your work or explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
95. The table shows the numbers of tickets needed to play different games at a festival.
Amelia had several tickets to spend.
Part A
Amelia spent half of her tickets on games that each cost 5 tickets. Then, she did the cake walk 3 times. She had 15
tickets left at this time. How many tickets did Amelia have at the start? Show your work or explain your answer.
Part B
Amelia sold her remaining 15 tickets to her friend for $0.50 each. How much money did she receive for 15 tickets?
Show your work or explain your answer.
Part C
The festival started at 10:30 a.m. and lasted 3 hours 30 minutes. What time did the festival end? Show your work or
explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
96. The table shows the fraction of months during one year that each of four friends went swimming at least once.
Part A
Chandrel said she swam more months than Gus. Copy the fraction bars below and shade each fraction bar to show the
fraction each friend swam.
Is Chandrel correct? Explain your answer.
Part B
Write an equivalent fraction with a denominator of 10 to show the part of the year Blake swam. What decimal
number could be used to describe the part of the year Blake swam? Show your work or explain your answer.
Part C
How many months did Allison swim during the year? Show your work or explain your answer by writing a
multiplication equation.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
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97. Melissa’s softball team has 15 players.
Part A
Melissa says
of the players wear their hats backwards. Using a model and multiplication, find the number of
players who wear their hats backwards. Show your work and explain your answer.
Part B
Melissa and 5 friends each got exactly 1 hit during the softball game. What fraction of the team got exactly 1 hit?
Show your work or explain your answer.
Part C
During the game,
of the players drank water and
drank a sports drink. Melissa said more players drank water
than a sports drink during the game, because 2 is greater than 1. Use what you know about equivalent fractions to
determine if Melissa is correct. Show your work or explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
98. Students in Mr. Kingston’s class are learning about the attributes of two-dimensional figures. He put up the
display shown so the students could study the figures.
Use the figures in Mr. Kingston’s display to answer the following questions.
Part A
List the figures that have at least one set of perpendicular lines. Explain your answer.
Part B
List the figures that have only acute angles. Explain your answer.
Part C
List the figures that have at least one set of parallel lines. Explain your answer.
Part D
Mr. Kingston had his students draw and name a shape that has more than two lines of symmetry and is not one of the
shapes shown above. Draw and name a shape, not shown above, that has more than two lines of symmetry. Draw in
the lines of symmetry of your shape and explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
99. A family made 48 cookies for a bake sale. They are deciding how many cookies to put in each bag so that all the
bags have an equal number of cookies.
Part A
The family lists the factor pairs of 48 to determine all the possible ways to divide the cookies into bags. List all the
factor pairs of 48. Explain your answer.
Part B
The family decides to eat 4 cookies before they put the remaining cookies in the bags. Will they be able to put all the
remaining cookies in 8 bags and still have an equal number in each bag? Explain why or why not using what you
know about factor pairs and multiples.
Part C
If 11 cookies of the 48 cookies are eaten or given away, how many cookies will be left to sell? Will the number of
cookies left be a prime or composite number? Explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
100. A fencing company uses different size pieces of wood, as shown in the table below.
Part A
Compare the sizes of Pickets A and C by writing an expression using the symbols
Explain your answer
using what you know about
Part B
Compare the sizes of Pickets A and B by writing an expression using the symbols
by using common denominators.
Explain your answer
Part C
Compare the sizes of Pickets B and C by writing an expression using the symbols
by drawing a fraction model comparing Pickets B and C.
Explain your answer
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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76
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
101. A company is planting new grass on a lawn. The lawn is in the shape of a rectangle with the dimensions shown.
Part A
The company needs to know how many square feet of grass it needs to plant to cover the lawn. What is the area of the
lawn? Show your work or explain your answer.
Part B
The owner also wants to know the perimeter of the lawn to install a fence. What is the perimeter of the lawn? Show
your work or explain your answer.
Part C
The owner wants to place bricks against the longest side of the lawn as a walkway. The bricks are 2 feet long and will
be placed end-to-end. How many bricks can the owner fit against the longest side of the lawn? Show your work or
explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
102. A fourth grade class is learning about angles. Henry points out that when he opens his book, the inside edge
makes an angle, as shown in the picture below.
Part A
What fraction of the circle does the angle created by the open book cover equal? Explain your answer.
Part B
What is the measure in degrees of the angle of the open book? Explain your answer.
Part C
Henry’s friend said if he closes the book, the angle will be 180 degrees. Is Henry’s friend correct? Why or why not?
Explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
103. The table shows the sizes and costs of five different sunscreen containers.
Part A
Maggie wrote the equation
to find the cost of a 7-ounce container of sunscreen. Explain why Maggie
used this multiplication equation to find her answer.
Part B
Based on the pattern shown in the table, how many ounces of sunscreen would be in a sunscreen container that costs
$48? Show your work.
Part C
Nancy bought a total of 50 ounces of sunscreen for the members of her swim team. She bought one of the $48
containers from Part B. List two possible combinations of sunscreen containers Nancy could have bought. Show your
work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
104. The front view of a set of cubby holes in a bookshelf is shown. At 8:00 a.m., the teacher took this picture
showing the number of books in the bookshelf.
If all the cubby holes are completely filled, the total number of books in the bookshelf is 50.
Part A
Belinda said that at 8:00 a.m.,
of the cubby holes in the bookshelf had books in them. Name a fraction equivalent
to
that could be used to describe the part of the cubby holes that had books. Explain your answer using what you
know about equivalent fractions.
Part B
At 10:00 a.m., an additional
of the cubby holes were completely filled with books. What fraction of the cubby
holes had books then? Show your work.
Part C
How many books were in the cubby holes after 10:00 a.m.? Explain how you got your answer.
Part D
State the number of books from Part C as a fraction of the total number of books the bookshelf can hold.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
105. Blake and Andrea were on rope climbing teams in class. The table shows the lengths of several different ropes
the class used.
Part A
Copy and complete the table to show the missing equal lengths, in inches.
Part B
Andrea climbed
your work.
of the way up the 8-foot rope before she stopped. How many inches did Andrea climb? Show
Blake climbed
of the way up the 5-foot rope before he stopped. He said he climbed more inches than Andrea. Is
Blake’s claim true? Explain why or why not.
Part C
For each inch they climbed, Blake and Andrea earned 20 points for their teams. How many points did each person
earn? Show your work.
Part D
Blake earned
of his team’s total points. How many points did Blake’s team earn in all?
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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81
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
106. A rectangle has an area of 48 square centimeters. The length and width of the rectangle are both whole numbers.
Part A
What are all possible length-width pairs? Show or explain your work.
Part B
Which of the lengths or widths you found are prime numbers? Explain your answer.
Part C
For the length-width pairs you found in Part A, list all possible perimeters for the rectangle. Show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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82
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
107. Mr. Hanks is building a tree house and a playhouse. Each floor is in the shape of a rectangle. The tree house
floor is made of 10 boards that are all the same size as shown.
Part A
Each board has a length of 7 feet and a width of 6 inches. How many inches wide is the floor? Show your work or
explain how you got your answer.
Part B
The playhouse floor is wider than the tree house floor. It is made with 30 of the same type of boards used in the tree
house floor. How many inches wider is the playhouse floor than the tree house floor? Show your work.
Part C
What is the area, in square feet, of the tree house floor? Show your work or explain how you got your answer.
Part D
Mr. Hanks is going to paint the floor of the tree house and the playhouse. What is the total area that Mr. Hanks will
need to paint? Label your answer and show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
Answer Key
1.
2. C) It is one thousand times the value of 3 in 1,683.
3.
4. C) thousands
5.
6. B)
7.
8.
9. B) 8,200
10. C) 80,000
11.
12. B) 500,000 people
13. B) 5,000
14. B) 191,804
15. D) hundred thousands
16.
17. D) 7,600
18.
19.
20.
21.
22.
23.
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
24. D) $833
25. D) 2800
26. D) $51,200
27.
28.
29.
30.
31.
32. B) 13,379.
33. B)
34. A)
35.
36. B) V
37.
38. C) Jackie put fewer oranges in the refrigerator than she used to make the fruit salad.
39. C) 3 pizzas
40.
41. A)
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
42.
43.
44.
45. C) 4.78
46.
47.
48. C) point C
49. B) $12.00
50. A) 0.09
51. D) Benito made the best model because both decimals describe parts of the same whole.
52.
53. C) 34.01, 32.14, 31.24, 30.41
54. D) 3.9 cm, 3.33 cm, 3.12 cm, 2.90 cm
55.
56. D)
57. B)
58. A) 2
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4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
59. D)
60. B)
61.
62.
63.
64.
65.
66.
67.
68.
69. C)
70. D) 189
71. A) 36 ÷ 3.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
87
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
82. D)
83. C)
84. D)
85. A)
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
88
4th grade Numbers & Operations 2014 (Quarterman4thgrade2014)
98.
99.
100.
101.
102.
103.
104.
105.
106.
107.
89