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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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All Common Core: 3rd Grade Math Resources

7 Diagnostic Tests 226 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Operations & Algebraic Thinking

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

Possible Answers:

$\displaystyle 6$

$\displaystyle 8$

$\displaystyle 10$

$\displaystyle 12$

$\displaystyle 4$

Correct answer:

$\displaystyle 4$

Explanation:

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

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

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

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.

Screen shot 2015 08 17 at 8.45.38 pm

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Example Question #203 : Operations

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

Possible Answers:

$\displaystyle 15$

$\displaystyle 18$

$\displaystyle 30$

$\displaystyle 12$

$\displaystyle 21$

Correct answer:

$\displaystyle 18$

Explanation:

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

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

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

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.

Screen shot 2015 08 17 at 9.00.58 pm

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Example Question #204 : Operations

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

Possible Answers:

$\displaystyle 15$

$\displaystyle 20$

$\displaystyle 25$

$\displaystyle 10$

$\displaystyle 5$

Correct answer:

$\displaystyle 15$

Explanation:

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

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

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

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.

Screen shot 2015 08 17 at 9.09.23 pm

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Example Question #2 : Operations & Algebraic Thinking

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

Possible Answers:

$\displaystyle 42$

$\displaystyle 35$

$\displaystyle 28$

$\displaystyle 21$

$\displaystyle 49$

Correct answer:

$\displaystyle 49$

Explanation:

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

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

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

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.

Screen shot 2015 08 18 at 7.26.23 am

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Example Question #2 : Operations & Algebraic Thinking

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

Possible Answers:

$\displaystyle 64$

$\displaystyle 56$

$\displaystyle 80$

$\displaystyle 72$

$\displaystyle 48$

Correct answer:

$\displaystyle 72$

Explanation:

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

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

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

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.

Screen shot 2015 08 18 at 7.32.06 am

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Example Question #205 : Operations

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

Possible Answers:

$\displaystyle 90$

$\displaystyle 72$

$\displaystyle 54$

$\displaystyle 81$

$\displaystyle 63$

Correct answer:

$\displaystyle 90$

Explanation:

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

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

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

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

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Example Question #206 : Operations

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

Possible Answers:

$\displaystyle 10$

$\displaystyle 30$

$\displaystyle 20$

$\displaystyle 40$

$\displaystyle 50$

Correct answer:

$\displaystyle 10$

Explanation:

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

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

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

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

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Example Question #207 : Operations

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

Possible Answers:

$\displaystyle 55$

$\displaystyle 44$

$\displaystyle 33$

$\displaystyle 22$

$\displaystyle 11$

Correct answer:

$\displaystyle 22$

Explanation:

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

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

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

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

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Example Question #3 : Operations & Algebraic Thinking

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

Possible Answers:

$\displaystyle 60$

$\displaystyle 24$

$\displaystyle 12$

$\displaystyle 36$

$\displaystyle 48$

Correct answer:

$\displaystyle 36$

Explanation:

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

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

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

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

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Example Question #211 : Operations

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

Possible Answers:

$\displaystyle 9$

$\displaystyle 36$

$\displaystyle 1$

$\displaystyle 18$

$\displaystyle 27$

Correct answer:

$\displaystyle 9$

Explanation:

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

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

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

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.

Screen shot 2015 08 18 at 8.03.43 am

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

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

All Common Core: 3rd Grade Math Resources

Example Questions

Example Question #1 : Operations & Algebraic Thinking

Example Question #203 : Operations

Example Question #204 : Operations

Example Question #2 : Operations & Algebraic Thinking

Example Question #2 : Operations & Algebraic Thinking

Example Question #205 : Operations

Example Question #206 : Operations

Example Question #207 : Operations

Example Question #3 : Operations & Algebraic Thinking

Example Question #211 : Operations

All Common Core: 3rd Grade Math Resources

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