Common Core: 3rd Grade Math : Operations & Algebraic Thinking

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

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Example Questions

Example Question #12 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

There were \displaystyle 5 families of meerkats that lived in the same burrows. Each family had \displaystyle 7 meerkats. \displaystyle 4 meerkats went out to find food, how many are left in the burrows?

Possible Answers:

\displaystyle 31

\displaystyle 8

\displaystyle 26

\displaystyle 6

Correct answer:

\displaystyle 31

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are how many meerkats there are total (T) and how many meerkats are left in the burrow (L).

\displaystyle T=5*7 because there are \displaystyle 5 families of meerkats and each of them has \displaystyle 7 members of the family. Each is a keyword for multiplication so that gives us a hint.

\displaystyle T=35

\displaystyle L=35-4 because there are \displaystyle 35 meerkats total in the burrows and \displaystyle 4 meerkats are subtracted because they left the burrow.

\displaystyle L=31

There are \displaystyle 31 meerkats left in the burrows.

Example Question #13 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Patrick got \displaystyle 40 baseball trading cards for his birthday from his best friend. The next day he received \displaystyle 20 more cards from his uncle. He decided to share them equally between himself and his two brothers. How many cards will each child receive?

Possible Answers:

\displaystyle 20

\displaystyle 57

\displaystyle 30

\displaystyle 63

Correct answer:

\displaystyle 20

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are how many baseball cards Patrick received in total (T) and how many cards each child will receive (C).

\displaystyle T=40+20 because he received \displaystyle 40 cards from his friend and then another \displaystyle 20 from his uncle. The cards would be added together to find the total.

\displaystyle T=60

\displaystyle C=60÷\displaystyle 3 because there are \displaystyle 60 cards total and they are being shared equally among Patrick AND his two brothers so there are \displaystyle 3 children total. "Shared equally" is a keyword for division.

\displaystyle C=20

Each child will receive \displaystyle 20 cards in total.

Example Question #14 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

In Denver, it snowed 5 inches on Monday, 6 inches on Tuesday, 3 inches on Thursday, and 1 inch on Friday. On Saturday, it snowed three times as much as the rest of the week. How much did it snow on Saturday?

Possible Answers:

\displaystyle 18 inches

\displaystyle 45 inches

\displaystyle 42 inches

\displaystyle 12 inches

Correct answer:

\displaystyle 45 inches

Explanation:

To solve this problem, we first have to find our unknowns. Our unknowns are how much did it snow during the weekdays (W) and how much did it snow on Saturday (S).

\displaystyle W=5+6+3+1 because we need to know how much it snowed during the weekdays in total. We must add together the amount of snow from Monday, Tuesday, Thursday, and Friday.

\displaystyle W=15

\displaystyle S=15*3 because it snowed \displaystyle 3 times as much on Saturday as it did the rest of the week. The total snow from the weekdays will be multiplied by \displaystyle 3 to find out how much it snowed on Saturday.

\displaystyle S=45

On Saturday it snowed a total of \displaystyle 45 inches.

Example Question #1 : Identify Arithmetic Patterns: Ccss.Math.Content.3.Oa.D.9

What is the pattern for the numbers in the X column to the numbers in the Y column? 


Screen shot 2015 09 23 at 10.33.26 am

Possible Answers:

Add \displaystyle 2

Subtract \displaystyle 3

Multiply \displaystyle 2

Add \displaystyle 3

Subtract \displaystyle 2

Correct answer:

Add \displaystyle 2

Explanation:

\displaystyle 2 is added to each X value to get the Y value. 

\displaystyle 1+2=3

\displaystyle 2+2=4

\displaystyle 3+2=5

\displaystyle 4+2=6

To find the rule, you may have to do some trial and error. The most important thing to remember is, once you think you have the rule, make sure to test the rule with all of the X values. 

Example Question #2 : Identify Arithmetic Patterns: Ccss.Math.Content.3.Oa.D.9

What is the pattern for the numbers in the X column to the numbers in the Y column? 

Screen shot 2015 09 23 at 10.33.31 am

Possible Answers:

Add \displaystyle 18

Add \displaystyle 19

Multiply \displaystyle 7

Add \displaystyle 20

Multiply \displaystyle 3

Correct answer:

Add \displaystyle 18

Explanation:

\displaystyle 18 is added to each X value to get the Y value. 

\displaystyle 3+18=21

\displaystyle 5+18=23

\displaystyle 7+18=25

\displaystyle 9+18=27

To find the rule, you may have to do some trial and error. The most important thing to remember is, once you think you have the rule, make sure to test the rule with all of the X values. 

Example Question #2 : Identify Arithmetic Patterns: Ccss.Math.Content.3.Oa.D.9

What is the pattern for the numbers in the X column to the numbers in the Y column? 

Screen shot 2015 09 23 at 10.33.36 am

Possible Answers:

Add \displaystyle 20

Divide \displaystyle 2

Multiply \displaystyle 2

Divide \displaystyle 3

Add \displaystyle 49

Correct answer:

Add \displaystyle 20

Explanation:

\displaystyle 20 is added to each X value to get the Y value. 

\displaystyle 29+20=49

\displaystyle 35+20=55

\displaystyle 41+20=61

\displaystyle 53+20=73

To find the rule, you may have to do some trial and error. The most important thing to remember is, once you think you have the rule, make sure to test the rule with all of the X values. 

Example Question #3 : Identify Arithmetic Patterns: Ccss.Math.Content.3.Oa.D.9

What is the pattern for the numbers in the X column to the numbers in the Y column? 

Screen shot 2015 09 23 at 10.33.46 am

Possible Answers:

Add \displaystyle 7

Multiply \displaystyle 2

Multiply \displaystyle 3

Add \displaystyle 2

Add \displaystyle 14

Correct answer:

Add \displaystyle 7

Explanation:

\displaystyle 7 is added to each X value to get the Y value. 

\displaystyle 62+7=69

\displaystyle 75+7=82

\displaystyle 87+7=94

\displaystyle 94+7=101

To find the rule, you may have to do some trial and error. The most important thing to remember is, once you think you have the rule, make sure to test the rule with all of the X values. 

Example Question #19 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

What is the pattern for the numbers in the X column to the numbers in the Y column? 

Screen shot 2015 09 23 at 10.33.50 am

Possible Answers:

Add \displaystyle 4

Add \displaystyle 2

Divide \displaystyle 2

Add \displaystyle 5

Multiply \displaystyle 2

Correct answer:

Add \displaystyle 4

Explanation:

\displaystyle 4 is added to each X value to get the Y value. 

\displaystyle 14+4=18

\displaystyle 17+4=21

\displaystyle 20+4=24

\displaystyle 36+4=40

To find the rule, you may have to do some trial and error. The most important thing to remember is, once you think you have the rule, make sure to test the rule with all of the X values. 

Example Question #21 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

What is the pattern for the numbers in the X column to the numbers in the Y column? 


Screen shot 2015 09 23 at 11.03.32 am

Possible Answers:

Multiply \displaystyle 6

Add \displaystyle 5

Subtract \displaystyle 6

Add \displaystyle 6

Add \displaystyle 7

Correct answer:

Add \displaystyle 5

Explanation:

\displaystyle 5 is added to each X value to get the Y value. 

\displaystyle 1+5=6

\displaystyle 2+5=7

\displaystyle 3+5=8

\displaystyle 4+5=9

To find the rule, you may have to do some trial and error. The most important thing to remember is, once you think you have the rule, make sure to test the rule with all of the X values. 

Example Question #4 : Identify Arithmetic Patterns: Ccss.Math.Content.3.Oa.D.9

What is the pattern for the numbers in the X column to the numbers in the Y column? 

Screen shot 2015 09 23 at 10.32.19 am

Possible Answers:

Multiply \displaystyle 4

Multiply \displaystyle 2

Add \displaystyle 4

Add \displaystyle 2

Subtract \displaystyle 2

Correct answer:

Multiply \displaystyle 4

Explanation:

Each X value is multiplied by \displaystyle 4 to get the Y value. 

\displaystyle 2\times4=8

\displaystyle 4\times4=16

\displaystyle 6\times4=24

\displaystyle 8\times4=32

To find the rule, you may have to do some trial and error. The most important thing to remember is, once you think you have the rule, make sure to test the rule with all of the X values. 

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