Common Core: 3rd Grade Math : Solving Problems Involving the Four Operations, and Identifying and Explaining Patterns in Arithmetic

Study concepts, example questions & explanations for Common Core: 3rd Grade Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Solve Two Step Word Problems Using The Four Operations: Ccss.Math.Content.3.Oa.D.8

Jessica has been collecting beads all summer. She started with \displaystyle 50 beads and by the end of the summer she was able to add \displaystyle 34 more beads to her collection.  On the first day of school she wants to evenly split the beads up amongst her \displaystyle 4 friends.  How many beads will each friend get? 

Possible Answers:

\displaystyle 21

\displaystyle 16

\displaystyle 4

\displaystyle 12.5

\displaystyle 8.5

Correct answer:

\displaystyle 21

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number of beads she will have by the end of the summer and the number of beads each of her friends will receive. We can set up equations for these unknowns by letting \displaystyle T represent the beads that she has at the end of the summer and \displaystyle F represent the number of beads each of her friends will receive. 

 \displaystyle T=50+34 because she gets \displaystyle 34 more beads by the end of the summer.

\displaystyle T=84

\displaystyle F=84\div4 because she is splitting up her total amount of beads between \displaystyle 4 friends. When you split something up evenly you divide.  

\displaystyle F=21

Example Question #1 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Emily has been collecting beads all summer. She started with \displaystyle 62 beads and by the end of the summer she was able to add \displaystyle 18 more beads to her collection.  On the first day of school she wants to evenly split the beads up amongst her \displaystyle 5 friends.  How many beads will each friend get? 

Possible Answers:

\displaystyle 20

\displaystyle 16

\displaystyle 18

\displaystyle 80

\displaystyle 35

Correct answer:

\displaystyle 16

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number of beads she will have by the end of the summer and the number of beads each of her friends will receive. We can set up equations for these unknowns by letting \displaystyle T represent the beads that she has at the end of the summer and \displaystyle F represent the number of beads each of her friends will receive. 

 \displaystyle T=62+18 because she gets \displaystyle 18 more beads by the end of the summer.

\displaystyle T=80

\displaystyle F=80\div5 because she is splitting up her total amount of beads between \displaystyle 5 friends. When you split something up evenly you divide.  

\displaystyle F=16

Example Question #2 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Justin loves to run and is training for a marathon at the end of the month. His training program has him running \displaystyle 8 miles three times during the week, and \displaystyle 16 miles on a weekend day. How many miles does he run in a week? 

Possible Answers:

\displaystyle 40

\displaystyle 50

\displaystyle 30

\displaystyle 20

\displaystyle 60

Correct answer:

\displaystyle 40

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number of miles he runs during the week and the total miles that he runs. We can set up equations for these unknowns by letting \displaystyle M represent the miles that he runs during the weekdays and \displaystyle T represent the total miles that he runs in \displaystyle 1 week. 

 \displaystyle M=8\times3 because he is running \displaystyle 8 miles \displaystyle 3 times.

\displaystyle M=24

\displaystyle T=24+16 because to find the total we need to add the miles he runs during the week and on the weekend.

\displaystyle T=40

 

Example Question #771 : Operations & Algebraic Thinking

Jason loves to run and is training for a marathon at the end of the month. His training program has him running \displaystyle 12 miles three times a week, and \displaystyle 18 miles one time a week. How many miles does he run in a week? 

Possible Answers:

\displaystyle 66

\displaystyle 52

\displaystyle 54

\displaystyle 68

\displaystyle 50

Correct answer:

\displaystyle 54

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number of miles he runs during the week and the total miles that he runs. We can set up equations for these unknowns by letting \displaystyle M represent the miles that he runs during the weekdays and \displaystyle T represent the total miles that he runs in \displaystyle 1 week. 

 \displaystyle M=12\times3 because he is running \displaystyle 12 miles \displaystyle 3 times.

\displaystyle M=36

\displaystyle T=36+18 because to find the total we need to add the miles he runs during the week and on the weekend.

\displaystyle T=54

Example Question #1 : Solve Two Step Word Problems Using The Four Operations: Ccss.Math.Content.3.Oa.D.8

Hannah is making a red fruit salad because red is her favorite color. She cuts up \displaystyle 28 pieces of watermelon and puts it in a bowl. Because she really loves strawberries, she wants \displaystyle 4 times as many pieces of strawberries as pieces of watermelon. Then she adds half as many raspberries as strawberries. How many pieces of fruit are in her fruit salad? 

Possible Answers:

\displaystyle 147

\displaystyle 196

\displaystyle 143

\displaystyle 158

\displaystyle 168

Correct answer:

\displaystyle 196

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number strawberries and raspberries she puts in the fruit salad. We can set up equations for these unknowns by letting \displaystyle S represent strawberries and \displaystyle R represent raspberries. 

 \displaystyle S=28\times4 because she has \displaystyle 4 times as many strawberries than watermelon. 

\displaystyle S=112

 \displaystyle R=112\div2 because when we half something we always divide by \displaystyle 2.

\displaystyle R=56

Now we need to add the watermelon, strawberries, and raspberries together to find our total. 

\displaystyle 28+112+56=196

Example Question #3 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Hannah is making a red fruit salad because red is her favorite color. She cuts up \displaystyle 22 pieces of watermelon and puts it in a bowl. Because she really loves strawberries, she wants \displaystyle 3 times as many pieces of strawberries as pieces of watermelon. Then she adds half as many raspberries as strawberries. How many pieces of fruit are in her fruit salad? 

Possible Answers:

\displaystyle 133

\displaystyle 143

\displaystyle 130

\displaystyle 121

\displaystyle 99

Correct answer:

\displaystyle 121

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number strawberries and raspberries she puts in the fruit salad. We can set up equations for these unknowns by letting \displaystyle S represent strawberries and \displaystyle R represent raspberries. 

 \displaystyle S=22\times3 because she has \displaystyle 3 times as many strawberries than watermelon. 

\displaystyle S=66

 \displaystyle R=66\div2 because when we half something we always divide by \displaystyle 2.

\displaystyle R=33

Now we need to add the watermelon, strawberries, and raspberries together to find our total. 

\displaystyle 22+66+33=121

Example Question #4 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Ali is hanging up flyers around her school. She started with \displaystyle 96 flyers. She hung \displaystyle 30 flyers around the east side of the building, but she hung half as many flyers on the west side of the building. How many flyers does she have left? 

Possible Answers:

\displaystyle 66

\displaystyle 51

\displaystyle 61

\displaystyle 36

\displaystyle 42

Correct answer:

\displaystyle 51

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number of flyers that she hung on the west side of the building and the number of flyers she has left over. We can set up equations for these unknowns by letting \displaystyle W represent the flyers she hung on the west side and \displaystyle F represent the flyers that she has left. 

 \displaystyle W=30\div2 because she hung half as many flyers on the west side as she hung on the east side. When we half something we always divide by \displaystyle 2.

\displaystyle W=15 

To find the total number of flyers that she hung we add the amount of flyers on the east side and the amount on the west side. 

\displaystyle 30+15=45

To find how many flyers she has left, we subtract that total flyers that were hung from the \displaystyle 96 flyers that she started with. 

\displaystyle F=96-45

\displaystyle F=51

Example Question #5 : Solve Two Step Word Problems Using The Four Operations: Ccss.Math.Content.3.Oa.D.8

Sara is hanging up flyers around her school. She started with \displaystyle 100 flyers. She hung \displaystyle 44 flyers around the east side of the building, but she hung half as many flyers on the west side of the building. How many flyers does she have left? 

Possible Answers:

\displaystyle 66

\displaystyle 34

\displaystyle 70

\displaystyle 56

\displaystyle 60

Correct answer:

\displaystyle 34

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number of flyers that she hung on the west side of the building and the number of flyers she has left over. We can set up equations for these unknowns by letting \displaystyle W represent the flyers she hung on the west side and \displaystyle F represent the flyers that she has left. 

 \displaystyle W=44\div2 because she hung half as many flyers on the west side as she hung on the east side. When we half something we always divide by \displaystyle 2.

\displaystyle W=22 

To find the total number of flyers that she hung we add the amount of flyers on the east side and the amount on the west side. 

\displaystyle 44+22=66

To find how many flyers she has left, we subtract that total flyers that were hung from the \displaystyle 100 flyers that she started with. 

\displaystyle F=100-66

\displaystyle F=34

Example Question #2 : Solve Two Step Word Problems Using The Four Operations: Ccss.Math.Content.3.Oa.D.8

In Spot’s toy basket he has \displaystyle 4 balls. There are \displaystyle 3 more stuffed animals than balls and there is double the number of ropes than balls. How many toys does Spot have in his basket? 

Possible Answers:

\displaystyle 17

\displaystyle 19

\displaystyle 12

\displaystyle 7

\displaystyle 23

Correct answer:

\displaystyle 19

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number of ropes and stuffed animals that Spot has. We can set up equations for these unknowns by letting \displaystyle R represent ropes and \displaystyle S represent stuffed animals. 

\displaystyle S=4+3 because he has \displaystyle 3 more stuffed animals than his \displaystyle 4 balls. 

\displaystyle S=7

\displaystyle R=2\times4 because double means \displaystyle 2 times more. 

\displaystyle R=8

Now we need to add up our number of balls, stuffed animals and ropes to find our total. 

\displaystyle 4+7+8=19

 

Example Question #3 : Solve Two Step Word Problems Using The Four Operations: Ccss.Math.Content.3.Oa.D.8

Charlie swims laps in the pool every day during the week before school. On Monday and Tuesday he swims \displaystyle 28 laps each day. On Wednesday and Thursday he triples the number of laps he swims. By Friday, he does \displaystyle 10 less laps than he does on Monday. How many total laps does he swim during the week? 

Possible Answers:

\displaystyle 190

\displaystyle 164

\displaystyle 206

\displaystyle 218

\displaystyle 242

Correct answer:

\displaystyle 242

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are the number of laps he swims on Wednesday and Thursday and the number of laps he swims on Friday. We can set up equations for these unknowns by letting \displaystyle WT represent the laps that he swims on Wednesday and Thursday and \displaystyle F represent the number of laps he swims on Friday. 

\displaystyle WT=28\times3 because when we triple something we multiply by \displaystyle 3.

\displaystyle WT=84

\displaystyle F=28-10 because he is swimming \displaystyle 10 less laps than he did on Monday, which means we subtract. 

\displaystyle F=18

To find the total amount of laps that he swam, we need to add up the laps that he did each day. 

\displaystyle 28+28+84+84+18=242

Learning Tools by Varsity Tutors