Common Core: 3rd Grade Math : Representing and Solving Problems Involving Multiplication and Division

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

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Example Questions

Example Question #1 : Common Core Math: Grade 3

\displaystyle \frac{\begin{array}[b]{r}2\\ \times 2\end{array}}{ \ \ \ \space}

Possible Answers:

\displaystyle 6

\displaystyle 8

\displaystyle 12

\displaystyle 10

\displaystyle 4

Correct answer:

\displaystyle 4

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 2\times2 means adding \displaystyle 2 two times. 

\displaystyle 2+2=4 and \displaystyle 2\times2=4

Or we can think of this as grouping objects. We have \displaystyle 2 groups, with \displaystyle 2 objects in each group. We can count up the total number of objects, in this case triangles. 

 

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Example Question #1 : Interpret Products Of Whole Numbers: Ccss.Math.Content.3.Oa.A.1

\displaystyle \frac{\begin{array}[b]{r}3\\ \times 6\end{array}}{ \ \ \ \space}

 

Possible Answers:

\displaystyle 21

\displaystyle 30

\displaystyle 12

\displaystyle 15

\displaystyle 18

Correct answer:

\displaystyle 18

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 3\times6 means adding \displaystyle 6 three times. 

\displaystyle 6+6+6=18 and \displaystyle 3\times6=18

Or we can think of this as grouping objects. We have \displaystyle 3 groups, with \displaystyle 6 objects in each group. We can count up the total number of objects, in this case triangles. 


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Example Question #1 : Common Core Math: Grade 3

\displaystyle \frac{\begin{array}[b]{r}5\\ \times 3\end{array}}{ \ \ \ \space}

 

Possible Answers:

\displaystyle 5

\displaystyle 15

\displaystyle 20

\displaystyle 25

\displaystyle 10

Correct answer:

\displaystyle 15

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 5\times3 means adding \displaystyle 3 five times. 

\displaystyle 3+3+3+3+3=15 and \displaystyle 5\times3=15

Or we can think of this as grouping objects. We have \displaystyle 5 groups, with \displaystyle 3 objects in each group. We can count up the total number of objects, in this case triangles. 

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Example Question #2 : Common Core Math: Grade 3

\displaystyle \frac{\begin{array}[b]{r}7\\ \times 7\end{array}}{ \ \ \ \space}

 

Possible Answers:

\displaystyle 42

\displaystyle 35

\displaystyle 28

\displaystyle 49

\displaystyle 21

Correct answer:

\displaystyle 49

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 7\times7 means adding \displaystyle 7 seven times. 

\displaystyle 7+7+7+7+7+7+7=49 and \displaystyle 7\times7=49

Or we can think of this as grouping objects. We have \displaystyle 7 groups, with \displaystyle 7 objects in each group. We can count up the total number of objects, in this case triangles. 

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Example Question #1 : Operations & Algebraic Thinking

\displaystyle \frac{\begin{array}[b]{r}8\\ \times 9\end{array}}{ \ \ \ \space}

 

Possible Answers:

\displaystyle 72

\displaystyle 56

\displaystyle 64

\displaystyle 48

\displaystyle 80

Correct answer:

\displaystyle 72

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 8\times9 means adding \displaystyle 9 eight times. 

\displaystyle 9+9+9+9+9+9+9+9=72 and \displaystyle 8\times9=72

Or we can think of this as grouping objects. We have \displaystyle 8 groups, with \displaystyle 9 objects in each group. We can count up the total number of objects, in this case triangles. 

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Example Question #4 : Common Core Math: Grade 3

\displaystyle \frac{\begin{array}[b]{r}9\\ \times 10\end{array}}{ \ \ \ \space}

 

Possible Answers:

\displaystyle 90

\displaystyle 63

\displaystyle 81

\displaystyle 72

\displaystyle 54

Correct answer:

\displaystyle 90

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 9\times10 means adding \displaystyle 10 nine times. 

\displaystyle 10+10+10+10+10+10+10+10+10=90 and \displaystyle 9\times10=90

Or we can think of this as grouping objects. We have \displaystyle 9 groups, with \displaystyle 10 objects in each group. We can count up the total number of objects, in this case triangles. Screen shot 2015 08 18 at 7.36.32 am

Example Question #3 : Operations & Algebraic Thinking

\displaystyle \frac{\begin{array}[b]{r}10\\ \times 1\end{array}}{ \ \ \ \space}

 

Possible Answers:

\displaystyle 50

\displaystyle 40

\displaystyle 20

\displaystyle 30

\displaystyle 10

Correct answer:

\displaystyle 10

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 10\times1 means adding \displaystyle 1 ten times. 

\displaystyle 1+1+1+1+1+1+1+1+1+1=10 and \displaystyle 10\times1=10

Or we can think of this as grouping objects. We have \displaystyle 10 groups, with \displaystyle 1 object in each group. We can count up the total number of objects, in this case triangles. Screen shot 2015 08 18 at 7.41.41 am

Example Question #1 : Interpret Products Of Whole Numbers: Ccss.Math.Content.3.Oa.A.1

\displaystyle \frac{\begin{array}[b]{r}11\\ \times 2\end{array}}{ \ \ \ \space}

 

Possible Answers:

\displaystyle 44

\displaystyle 11

\displaystyle 22

\displaystyle 33

\displaystyle 55

Correct answer:

\displaystyle 22

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 11\times2 means adding \displaystyle 2 eleven times. 

\displaystyle 2+2+2+2+2+2+2+2+2+2+2=22 and \displaystyle 11\times2=22

Or we can think of this as grouping objects. We have \displaystyle 11 groups, with \displaystyle 2 objects in each group. We can count up the total number of objects, in this case triangles. Screen shot 2015 08 18 at 7.51.17 am

Example Question #5 : Common Core Math: Grade 3

\displaystyle \frac{\begin{array}[b]{r}12\\ \times 3\end{array}}{ \ \ \ \space}

 

Possible Answers:

\displaystyle 36

\displaystyle 60

\displaystyle 48

\displaystyle 12

\displaystyle 24

Correct answer:

\displaystyle 36

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 12\times3 means adding \displaystyle 3 twelve times. 

\displaystyle 3+3+3+3+3+3+3+3+3+3+3+3=36 and \displaystyle 12\times3=36

Or we can think of this as grouping objects. We have \displaystyle 12 groups, with \displaystyle 3 objects in each group. We can count up the total number of objects, in this case triangles. Screen shot 2015 08 18 at 8.00.16 am

Example Question #1 : Common Core Math: Grade 3

\displaystyle \frac{\begin{array}[b]{r}1\\ \times 9\end{array}}{ \ \ \ \space}

 

 

Possible Answers:

\displaystyle 27

\displaystyle 36

\displaystyle 18

\displaystyle 9

\displaystyle 1

Correct answer:

\displaystyle 9

Explanation:

Multiplication can be thought of as repeated addition, or as objects in a group. 

\displaystyle 1\times9 means adding \displaystyle 9 one time. 

\displaystyle 9=9 and \displaystyle 1\times9=9

Or we can think of this as grouping objects. We have \displaystyle 1 group, with \displaystyle 9 objects in each group. We can count up the total number of objects, in this case triangles. 

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