Grade 3 Practice Problems: Numbers
Examples from Standards Revision and GLEs
3N66) Which picture goes with the number sentence 18, 3?
A.
B.
C.
D.
3N65) Juan was getting ready to play a game using marbles. He has 24 marbles and wants to share them with his 4 friends. Which fact could he use to find how any marbles he will give each friend?
A. 24 ¸ 4 B. 24 – 4 C. 4 ¸ 24 D. 4 x 24
3N64) Lisa bought 37 bananas and Mary bought 44 apples. About how many pieces of fruit did they buy together? Which number sentence gives the most REASONABLE estimate?
A. 40 + 50 B. 40 + 40 C. 30 + 40 D. 30 + 50
Explain why your answer is reasonable.
3N63) Kate found 5 hats and 3 scarves in her closet. Then she found 1 hat and 2 more scarves on a shelf. How many scarves did she find all together?
3N62) Sarah has 83 basketball cards in her collection. About how many cards does she have? Which would be the best estimate and why?
A. 85 B. 95 C. 80 D. 90
3N61) Draw a picture that represents this number sentence. 5 x 6 = 30
3N60) Write a division sentence for this picture.
3N59) Joe rode his bicycle 28 miles one day. He rode 12 miles the next day. About how many more miles did ride the first day?
A. 10 B. 20 C. 30 D. 40
3N58) At the pet store, there are 15 kinds of fresh water fish, 6 kinds of salt water fish, and 8 kinds of birds. How many kinds of fish are there at the pet store?
3N57) Susan made $15.00 delivering newspapers. She spent $11.45 on a birthday present. ABOUT how much does she have left?
A. A little more then $2.00
B. A little more than $3.00
C. A little less than $4.00
D. A little less than $5.00
3N56) Cleo and Roger rented videotapes for $15.00 and spent $38.00 to buy cassette tapes. Which statement shows the most REASONABLE estimate for what they spent?
A. $10 + $40 B. $10 + $30 C. $20 + $30 D. $20 + $40
3N55) Mrs. Penny divided 18 colored markers equally among three students. Which expression could be used to find the number of markers each student received?
A. 18 + 3 B. 3 ¸ 18 C. 18 ¸ 3 D. 18 x 3
3N54) Complete each fact family.
2 x 5 = 10 4 x 3 = 12
5 x 2 = 10 12 ¸ 3 = 4
10 ¸ 5 = 2 3 x 4 = 12
_________ __________
3N53) Write a multiplication sentence for this picture.
3N52) Which number sentence goes with this picture?
A. 8 ¸ 2 B. 4 ¸ 2 C. 8 x 2 D. 2 + 4
3N51) Write a division sentence for this picture.
3N50) Write a multiplication sentence for this picture.
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3N49) There were 45 soccer players in a league. 28 new players joined the league. To find out how many players are in the league, you should:
A. Divide 45 by 28 B. Subtract 28 from 45 C. Multiply 28 by 45 D. Add 28 to 45
3N48) The phone store has 25 different phones. 16 phones are black. How many phones are not black?
3N47) Mrs. Jones is beginning an exercise program. She plans to walk 2 miles for 2 days, 3 miles for 3 days, 4 miles for 4 days, and continue the pattern until she is walking 6 miles per day. In how many days will she first walk 6 miles? Show your work and Explain your thinking.
3N46) Shana’s teacher asked her to create a design; she needs to use four colors to divide a square into parts, and to color the parts as follows:
1/2 is colored red 1/4 is colored blue
1/8 is colored green Any other part is to be left white.
On the squares below, draw three different designs to help Shana. Each square must contain all four colors.
Circle one of your designs and explain to Shana how you know that the parts you colored are the correct fractions.
3N45) Carla has $10.00 and must go shopping and buy one quart of milk costing $1.50, a loaf of bread costing $.89 and two Twinkies costing $.69 each. Solve for how much money is left and support your answer.
3N44) In the number  4,183  the digit in the hundreds’ place is:
A. 4 B. 1 C. 8 D. 3
3N43) Four hundred four can be written as:
A. 4004 B. 40004 C. 404 D. 4040
3N42) How much of this figure is shaded?
3N41) A bag contains 2 white marbles, 3 red marbles, and 5 green marbles. What fraction of all of the marbles are red?
3N40) Which numbers are written in order from least to greatest?
A. 548, 692, 136, 428
B. 345, 456, 123, 789
C. 110, 101, 125, 138
D. 285, 392, 516, 773
3N39) Answer: $1.63
Jill bought 2 packages of crayons for 59 cents each. She also bought one package of crayons for 45 cents. How much did Jill spend? Write to help explain your best thinking using words, numbers, or pictures.
3N38) Answer: 40 pennies
Joe collects coins. He has 84 coins in his collection. There are 14 dimes and 30 quarters. The rest are pennies. How many pennies? Write to help explain your best thinking using words, numbers, or pictures.
3N37) Answer: 1/6 pizza
Three friends shared a pizza. Tim ate 2/6 of the pizza. Kate ate 3/6. How much pizza is left? Write to help explain your best thinking using words, numbers, or pictures.
3N36) Answer: 1.4 gallons
Pam’s car holds 10 gallons of gasoline. After filling the tank, she drove to the beach. She had used 8.6 gallons. How many gallons are left in her gas tank? Write to help explain your best thinking using words, numbers, or pictures.
3N35) Answer: .2 miles
Ed and Jason are hiking 1 mile to a waterfall. They walk .5 miles to a bridge. Then they walk .3 miles to a river. How much farther do they have to walk to the waterfall? Write to help explain your best thinking using words, numbers, or pictures.
3N34) Answer: 10
Ruth, Roz, and Gladys bought two boxes of golf balls. Each box contains five sleeves of three balls in each. How many golf balls will each person get? Write to help explain your best thinking using words, numbers, or pictures.
3N33) Answer: 5 groups two each or two groups 5 each
There are 10 children in the art club. The teacher put them into groups, so that each group has the same number of children. How many groups could there be? How many children will be in each group? Write to help explain your best thinking using words, numbers, or pictures.
3N32) Answer: 7 children
When Alex got on the school bus, there were 3 other children on the bus. At the next stop, 3 more children got on the bus. How many children were now on the bus? Write to help explain your best thinking using words, numbers, or pictures.
3N31) Answer: 3 cookies
Edna loves cookies. She had 4 cookies. She ate 2 of the cookies, and her mom gave her another one. How many cookies does she have now? Write to help explain your best thinking using words, numbers, or pictures.
3N30) Answer: 7 stamps, pattern of odd numbers
Phoebe was putting her collection of postage stamps into a scrapbook. She put one stamp on the first row. She put 3 stamps on the second row. She put 5 stamps on the third row. How many stamps do you think Phoebe will put on the next row? Why? Write to help explain your best thinking using words, numbers, or pictures.
3N29) Answer: 27 eggs
A basket contains more than 12 but fewer than 32 eggs. When you count the eggs by fours, you have three left over. When you count by fives, you have two left over. How many eggs are in this basket? Write to help explain your best thinking using words, numbers, or pictures.
3N28) Answer: when John has taken 4 steps
John and Jean have a foot race starting with their right feet at the starting line, stepping forward on the left foot. If John takes two steps to every three Jean takes, when will their right feet hit the ground together again? Write to help explain your best thinking using words, numbers, or pictures.
3N27) Answer: 27 glasses
Apple juice was served at the picnic. Each of 3 girls poured 9 glasses of juice. How many glasses of juice were there? Write to help explain your best thinking using words, numbers, or pictures.
3N26) Answer: 48 plates
Patty bought 6 packages of paper plates. There were 8 plates in each package. How many plates did she buy? Write to help explain your best thinking using words, numbers, or pictures.
3N25) Answer: 45
Tabby Tiger roars every time someone passes her home in the zoo. One day the zookeeper kept track of how many times Tabby roared in one hour. Here are the clues he gave: Tabby roared more than 39 times; she roared fewer than 46 times; she roared an odd number of times; you say the number when you count by threes and by fives. How many times did Tabby roar in one hour? Write to help explain your best thinking using words, numbers, or pictures.
3N24) Answer: 44
In Bird Hotel, there are 46 nests for guests. Bird families stop in for a rest on their way south. Big Bird wants to know how many empty nests there are in the hotel today. Here are the clues his workers gave; not all of the nests are empty today; more than 40 nests are empty; an even number of nests are empty; the empty nests could be counted by fours, with none left over. How many of the nests in Bird Hotel are empty today? Write to help explain your best thinking using words, numbers, or pictures.
3N23) Answer: 2 yellow, 7 purple
Stuart and Marsha are playing a game called Pirates. They get 3 points every time they draw a yellow card, and 5 points every time they draw a purple card. Whoever gets 75 points first wins the game. Stuart has 41 points now, and he has 9 cards. How many cards does he have of each color? Write to help explain your best thinking using words, numbers, or pictures.
3N22) Answer: 63
People boarded the train at each stop in the animal park. A few people got on at the alligators. Three more people got on at the buffaloes than at the alligators. Later the train stopped at the camels, the donkeys, the elephants, and the giraffes. At each stop, 3 more people got on the train than at the stop before. At the giraffes, 18 people got on the train. How many people in all boarded the train? Write to help explain your best thinking using words, numbers, or pictures.
3N21) Answer: 42
Sam and Mary have their own secret recipe for ice cream. They will tell you how much cream they put in, but they won't tell you how many marshmallows they put in. Sam will give you a few clues. She says, "We put in more than 36. We put in fewer than 43. Mary always puts the marshmallows in 3 at a time, with none left over. I always put the marshmallows in 2 at a time, with none left over." How many marshmallows do Sam and Mary put into their ice cream? Write to help explain your best thinking using words, numbers, or pictures.
3N20) Answer: 50 blocks; 30 flags
Here are ten children. Each child is pulling a wagon. There are five blocks in each wagon. Each child holds three flags. How many blocks? How many flags? Write to help explain your best thinking using words, numbers, or pictures.
3N19) Answer: Varies; example: Jack has $8 and Bob has $1 less than Jack. How much do they have together?
Write a story to go with this number sentence, including a question. Make a picture to match. Then provide the answer. 8 + 7 = ____ Write to help explain your best thinking using words, numbers, or pictures.
3N18) Answer: Kim 9 cows, Bud 8 cows, Sam 10 cows; 27 cows in all  herds not equal  Sam should give Bud a cow
Kim, Bud, and Sam each have a herd of cows. Kim has two black cows, four brown cows, and three red cows. Bud has three black cows, one brown cow, and four red cows. Sam has five black cows, three brown cows, and two red cows. How many cows does each person have? How many cows in all? Are the herds equal? How can we make them equal? Write to help explain your best thinking using words, numbers, or pictures.
3N17) Answer: If I have 9 dollars, how much more do I need to have 14 dollars in all.
Write a story to go with this number sentence. Make a picture to match. Then provide the answer. 9 + ___ = 14 Write to help explain your best thinking using words, numbers, or pictures.
3N16) Answer: 6 kickballs, 11 footballs, 17 baseballs; 9 balls/1st, 12 balls/3rd, 13 balls/4th
The firstgraders have three kickballs, two footballs, and four baseballs. The thirdgraders have two kickballs, four footballs, and six baseballs. The fourthgraders have one kickball, five footballs, and seven baseballs. How many of each kind of ball are there? Kickballs ___ Footballs ___ Baseballs ___ How many balls in each grade? Write to help explain your best thinking using words, numbers, or pictures.
3N15) Answer: 29(Blue); 28(Green); 25(B); 22(B & G); 19(G); 16(G); 15(B); 13(G); 10(G); 8(B); 7(G); 4(G); 1(B & G)
Make a number line from 30 to 0. Starting with 29, put a blue dot over every seventh number. Starting with 28, put a green dot under every third number. Write to help explain your best thinking using words, numbers, or pictures.
3N14) Answer: girls, 30 balloons; boys, 50 balloons; 80 balloons in all; 64 balloons left
There are three girls and five boys. Each child has ten balloons. How many balloons do the girls have? How many balloons do the boys have? How many balloons in all are there? If each child loses two balloons, how many balloons will be left? Write to help explain your best thinking using words, numbers, or pictures.
3N13) Answer: Sam has 2 more plants; 13 tomato plants + 13 lettuce plants
Frank planted five tomato plants and seven lettuce plants. Sam planted eight tomato plants and six lettuce plants. Who has more plants? How many more? How many tomato plants are there? How many lettuce plants are there? Write to help explain your best thinking using words, numbers, or pictures.
3N12) Answer: 3 orange trees; 3 pine trees
Draw pictures of 12 trees. 1/2 of them are apple trees. 1/4 of them are pine trees. The rest are orange trees. How many of the trees are orange trees. How many pine trees are there? Write to help explain your best thinking using words, numbers, or pictures.
3N11) Answer: 8; 6; 4; 3; 2
There are 24 slices of pizza. How many slices would each person get if there were: three people?...four people?...six people?...eight people?...twelve people? Write to help explain your best thinking using words, numbers, or pictures.
3N10) Answer: Paul 11, James 8, Ann 14; Paul 17, James 14, Ann 14; Paul gives a fish to James & a fish to Ann
Paul has 17 fish. James had 16 fish. Paul gave 6 fish to Ann. James gave 8 fish to Ann. How many will each have now? Paul _____ James _____ Ann ______ Ann buys 12 fish and gives half to Paul and half to James. Now how many are in each tank? What would we need to do to get an equal number of fish in all three tanks? Write to help explain your best thinking using words, numbers, or pictures.
3N9) Answer: blue team has more pounds; Gloria changes with Sam or Sandy changes with Larry
The children are having a tug of war. For the blue team, Betsy weighs 60 pounds, Jess weighs 90 pounds, Gloria weighs 80 pounds, and Sandy weighs 60 pounds. For the red team, Kevin weighs 90 pounds, Larry weighs 50 pounds, Sam weighs 70 pounds, and Jane weighs 60 pounds. Which team has the advantage with more pounds? How can we make the teams equal? Write to help explain your best thinking using words, numbers, or pictures.
3N8) Answer: Bob has 42 balls. How many must be add to his collection to get a total of 67 balls?
Write a story to go with this number sentence. Make a drawing to match. Then provide the answer. 42 + ___ = 67 Write to help explain your best thinking using words, numbers, or pictures.
3N7) Answer: 32 acorns; 20 more; 5 squirrels
Eight squirrels each carry four acorns. How many acorns?___ They want to store fifty two acorns. How many more acorns do they need?____ How many squirrels, with each carrying four acorns, do they need?____ Write to help explain your best thinking using words, numbers, or pictures.
3N6) Answer: 3 boxes; yes; 10 clips
We are going to use paper clips for measuring. Each student will get 5 clips. There are 28 students in the class. There are 50 clips in each box. How many boxes will we need?____ Will there be clips left over?___ How many?___ Write to help explain your best thinking using words, numbers, or pictures.
3N5) Answer: 48 pencils; 2 pencils
There are 12 pencils in each box. There are 4 boxes on the table. How many pencils are on the table?___ There are 24 students in the class. If we divide the pencils evenly, how many will each one get?___ Write to help explain your best thinking using words, numbers, or pictures.
3N4) Answer: I have 6 stars with 5 points each. How many points on the 6 stars?
Using stars, make a picture to go with this number sentence. Then provide the answer. 5 x 6 = ___ Write to help explain your best thinking using words, numbers, or pictures.
3N3) Answer: red1 cup; orange2 cups; yellow4 cups; green6 cups; blue3 cups
Sylvia has five containers. The red one holds one cup. The orange one holds twice as much as the red one. The yellow one holds twice as much as the orange one. The green one holds as much as the orange and yellow ones together. The blue one holds half as much as the green one. Draw a picture of each container. Write to help explain your best thinking using words, numbers, or pictures.
3N2) Answer: red8 cups; orange4 cups; yellow2 cups; green6 cups; blue3 cups
Jay has five containers. The red one holds eight cups. The orange one holds half as much as the red one. The yellow one holds half as much as the orange one. The green one holds as much as the yellow and orange ones together. The blue one holds half as much as the green one. Draw a picture of each container showing what each one holds. Write to help explain your best thinking using words, numbers, or pictures.
3N1) Answer: 3 children each have 10 marbles. How many marbles all together?
Write a word problem about children and marbles, using multiplication. Then draw a picture of our word problem. Write to help explain your best thinking using words, numbers, or pictures.
Expectations & Examples of Numbers from the 2008 Math Standards Revision (draft)  Grade 3
Represent fractions with physical materials, pictures, numbers, or words, and translate among representations. Representations may include parts of a whole, parts of a set, or locations on a number line. Include numbers greater than, less than, and equal to 1. Use fractions with denominators of 2, 3, 4, 5, 6, 8, 9, 10, and 12. Compare and order fractions using physical materials, pictures, numbers, or number lines. Fractions may be compared using benchmarks, common numerators, or common denominators. Common benchmarks used for comparing fractions include 0, ½, 1, and 1½. Represent equivalent fractions using physical materials, pictures, numbers, or number lines, and translate among representations. Use fractions with denominators of 2, 3, 4, 5, 6, 8, 9, 10, and 12. Solve word problems that involve comparing fractions in a variety of contexts and explain solutions using physical materials, pictures, numbers, equations, or words.
Use place value to read, write, compare, and order numbers to at least 10,000 using numbers, words, and symbols. Symbols used to describe comparisons include <, >, =, ≠.
Round whole numbers through 10,000 to the nearest ten, hundred, and thousand.

Expectations and Examples of Operations from the 2008 Math Standards Revision (draft) – Grade 3
Represent multiplication as joining equal groups using words, numbers, pictures, physical materials, or equations, and translate among representations. Students may manipulate physical materials or draw pictures to find the total number of objects in equal sets or in an array. Picture representations may include finding the total distance resulting from equal jumps on a number line. Representations involving numbers and equations might include repeated addition, such as 3 x 4 = 4 + 4 + 4. Example: Represent division as equal sharing or forming equal groups using words, numbers, pictures, physical materials, or equations, and translate among representations. The same physical materials and pictures used to demonstrate multiplication can be used to find a missing factor. Representations involving numbers and equations might include finding quotients with repeated subtraction or division sentences. Representations in words might include the terms quotient and remainder. Represent and use the inverse relationship between multiplication and division. Write different multiplication and division sentences to express the relationships between the numbers in a fact family.
Explain and use strategies for learning basic multiplication and division facts. Strategies might include using repeated addition to learn multiplication facts, using the inverse relationship between multiplication and division (including fact families), or using the properties of whole numbers. The emphasis here is on using the properties rather than knowing the formal vocabulary.
Demonstrate mastery of multiplication and related division facts for at least the factors 0, 1, 2, 5, and 10, and determine the products and related quotients of other factors through at least 10 x 10. Create a problem situation that corresponds to a given multiplication or division equation. Solve word problems that involve multiplication or division in a variety of contexts and explain solutions using words, numbers, pictures, physical materials, or equations. Problems can be solved using various representations of multiplication and division; these representations can be used to justify solutions. Problems should include a variety of contexts that require interpretations of the remainder, such as determining the number of 20student buses needed for a field trip for 85 students. Problems might include using multiplication to count the number of possible outcomes, such as determining how many different outfits can be made with four shirts and three pairs of pants. Multiply the numbers from 11 to 19 by single digit numbers using place value and the distributive property. A student recognizes 6 x 12 as 6 tens and 6 twos. Add and subtract whole numbers efficiently using the standard algorithms and solve addition and subtraction word problems. Estimate sums and differences to predict results or determine reasonableness of answers. Determine the amount of money needed to make change up to a dollar and record amounts in dollarandcents notation. 
Examples of Number Sense from the 2006 GLEs – Grade 3
Represent a number to at least 10,000 in different ways, including numerals, words, pictures, and physical models; and translate from one representation to another. Represent and show numbers in standard and expanded forms. State equivalent representations for a given number by decomposing and composing into sums for that number. Represent and discuss place values of digits of whole numbers using words, pictures, or numbers. Sort and order whole number values to at least 10,000 from least to greatest. Order three or more numbers to at least 10,000 from least to greatest on number lines, symbolically, or with illustrations. Explain why one whole number is greater than or less than another whole number. Explain or show how the commutative property works for addition and not subtraction using words, pictures, physical models, or numbers. Identify equivalent expressions using the commutative property. Explain the identity property of addition and give examples. Show whether addition equations are true or false and provide an explanation, based on the commutative or identity property Illustrate multiplication and division using words, pictures, models, and/or numbers. Illustrate and explain the inverse relationship between multiplication and division using words, pictures, models, and/or numbers. Show and explain the relationship between multiplication and repeated addition. Show and explain the relationship between division and repeated subtraction. Explain the use of division to find the number of equal shares or the quantity in each equal share. Identify and explain fact families for multiplication and division. Explain the meaning of a remainder in a division problem. Select and/or use an appropriate operation to show understanding of addition, subtraction, multiplication, or division of whole numbers. Apply a variety of strategies to add and subtract 3 digit numbers in a given situation. Describe and show relationships between strategies and procedures for multiplying and dividing. Complete multi step computations that involve addition and subtraction and explain strategies. Explain and apply strategies or use procedures to add three 2 digit or two 3 digit numbers, and/or subtract numbers with 1, 2, or 3 digits. Explain and apply strategies or use procedures to add up to 5 one digit whole numbers. Select and use appropriate tools from among mental computation, estimation, calculators, manipulatives, and paper and pencil to compute in a given situation. Explain why a selected tool is most efficient for a given situation. Explain when an estimation or exact answer is or is not appropriate. Apply and explain a variety of estimation strategies, including multiples of 10 and 100, rounding, and compatible numbers prior to computation. Use estimation to check the reasonableness of calculated results. Explain an appropriate adjustment when an estimate and a calculation don’t agree. 