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

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 #131 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}12\\ \times 9\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}12\\ \times 9\end{array}}{ \ \ \ \space}$

Possible Answers:

144 $\displaystyle 144$

108 $\displaystyle 108$

120 $\displaystyle 120$

$\displaystyle 96$

132 $\displaystyle 132$

Correct answer:

108 $\displaystyle 108$

Explanation:

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

$12\times9$ $\displaystyle 12\times9$ means adding $\displaystyle 9$ twelve times.

$\displaystyle 9+9+9+9+9+9+9+9+9+9+9+9=108$ and $12\times9=108$ $\displaystyle 12\times9=108$

Or we can think of this as grouping objects. We have $\displaystyle 12$ 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 19 at 12.32.57 pm

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Example Question #132 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}4\\ \times 2\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}4\\ \times 2\end{array}}{ \ \ \ \space}$

Possible Answers:

$\displaystyle 4$

$\displaystyle 8$

$\displaystyle 20$

$\displaystyle 16$

$\displaystyle 12$

Correct answer:

$\displaystyle 8$

Explanation:

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

$4\times2$ $\displaystyle 4\times2$ means adding $\displaystyle 2$ four times.

$\displaystyle 2+2+2+2=8$ and $4\times2=8$ $\displaystyle 4\times2=8$

Or we can think of this as grouping objects. We have $\displaystyle 4$ 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 9.04.25 pm

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Example Question #133 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}10\\ \times 3\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}10\\ \times 3\end{array}}{ \ \ \ \space}$

Possible Answers:

$\displaystyle 30$

$\displaystyle 20$

$\displaystyle 50$

$\displaystyle 40$

$\displaystyle 60$

Correct answer:

$\displaystyle 30$

Explanation:

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

$10\times3$ $\displaystyle 10\times3$ means adding $\displaystyle 3$ ten times.

$\displaystyle 3+3+3+3+3+3+3+3+3+3=30$ and $10\times3=30$ $\displaystyle 10\times3=30$

Or we can think of this as grouping objects. We have $\displaystyle 10$ 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 8.55.06 am

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Example Question #134 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}8\\ \times 4\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}8\\ \times 4\end{array}}{ \ \ \ \space}$

Possible Answers:

$\displaystyle 48$

$\displaystyle 32$

$\displaystyle 40$

$\displaystyle 64$

$\displaystyle 56$

Correct answer:

$\displaystyle 32$

Explanation:

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

$8\times4$ $\displaystyle 8\times4$ means adding $\displaystyle 4$ six times.

$\displaystyle 4+4+4+4+4+4+4+4=32$ and $8\times4=32$ $\displaystyle 8\times4=32$

Or we can think of this as grouping objects. We have $\displaystyle 8$ groups, with $\displaystyle 4$ objects in each group. We can count up the total number of objects, in this case triangles.

Screen shot 2015 08 18 at 8.45.43 am

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Example Question #135 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}2\\ \times 6\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}2\\ \times 6\end{array}}{ \ \ \ \space}$

Possible Answers:

$\displaystyle 24$

$\displaystyle 36$

$\displaystyle 30$

$\displaystyle 12$

$\displaystyle 18$

Correct answer:

$\displaystyle 12$

Explanation:

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

$2\times6$ $\displaystyle 2\times6$ means adding $\displaystyle 6$ two times.

6+6=12 $\displaystyle 6+6=12$ and $2\times6=12$ $\displaystyle 2\times6=12$

Or we can think of this as grouping objects. We have $\displaystyle 2$ 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 18 at 8.13.19 am

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Example Question #136 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}5\\ \times 8\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}5\\ \times 8\end{array}}{ \ \ \ \space}$

Possible Answers:

$\displaystyle 30$

$\displaystyle 25$

$\displaystyle 35$

$\displaystyle 45$

$\displaystyle 40$

Correct answer:

$\displaystyle 40$

Explanation:

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

$5\times8$ $\displaystyle 5\times8$ means adding $\displaystyle 8$ five times.

$\displaystyle 8+8+8+8+8=40$ and $5\times8=40$ $\displaystyle 5\times8=40$

Or we can think of this as grouping objects. We have $\displaystyle 5$ groups, with $\displaystyle 8$ objects in each group. We can count up the total number of objects, in this case triangles.

Screen shot 2015 08 18 at 9.36.54 am

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Example Question #137 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}5\\ \times 4\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}5\\ \times 4\end{array}}{ \ \ \ \space}$

Possible Answers:

$\displaystyle 20$

$\displaystyle 15$

$\displaystyle 5$

$\displaystyle 25$

$\displaystyle 10$

Correct answer:

$\displaystyle 20$

Explanation:

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

$5\times4$ $\displaystyle 5\times4$ means adding $\displaystyle 4$ five times.

$\displaystyle 4+4+4+4+4=20$ and $5\times4=20$ $\displaystyle 5\times4=20$

Or we can think of this as grouping objects. We have $\displaystyle 5$ groups, with $\displaystyle 4$ objects in each group. We can count up the total number of objects, in this case triangles.

Screen shot 2015 08 18 at 10.34.31 am

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Example Question #138 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}7\\ \times 2\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}7\\ \times 2\end{array}}{ \ \ \ \space}$

Possible Answers:

$\displaystyle 14$

$\displaystyle 7$

$\displaystyle 21$

$\displaystyle 35$

$\displaystyle 28$

Correct answer:

$\displaystyle 14$

Explanation:

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

$7\times2$ $\displaystyle 7\times2$ means adding $\displaystyle 2$ seven times.

$\displaystyle 2+2+2+2+2+2+2=14$ and $7\times2=14$ $\displaystyle 7\times2=14$

Or we can think of this as grouping objects. We have $\displaystyle 7$ 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 3.45.49 pm

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Example Question #139 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}10\\ \times 2\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}10\\ \times 2\end{array}}{ \ \ \ \space}$

Possible Answers:

$\displaystyle 10$

$\displaystyle 20$

$\displaystyle 30$

$\displaystyle 40$

$\displaystyle 50$

Correct answer:

$\displaystyle 20$

Explanation:

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

$10\times2$ $\displaystyle 10\times2$ means adding $\displaystyle 2$ ten times.

$\displaystyle 2+2+2+2+2+2+2+2+2+2=20$ and $10\times2=20$ $\displaystyle 10\times2=20$

Or we can think of this as grouping objects. We have $\displaystyle 10$ groups, with $\displaystyle 2$ objects in each group. We can count up the total number of objects, in this case triangles.

Screen shot 2015 09 03 at 12.13.26 pm

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Example Question #140 : Operations & Algebraic Thinking

$\frac{\begin{array}[b]{r}9\\ \times 12\end{array}}{ \ \ \ \space}$ $\displaystyle \frac{\begin{array}[b]{r}9\\ \times 12\end{array}}{ \ \ \ \space}$

Possible Answers:

$\displaystyle 99$

$\displaystyle 90$

$\displaystyle 72$

$\displaystyle 81$

108 $\displaystyle 108$

Correct answer:

108 $\displaystyle 108$

Explanation:

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

$9\times12$ $\displaystyle 9\times12$ means adding $\displaystyle 12$ nine times.

$\displaystyle 12+12+12+12+12+12+12+12+12=108$ and $12\times9=108$ $\displaystyle 12\times9=108$

Or we can think of this as grouping objects. We have $\displaystyle 9$ groups, with $\displaystyle 12$ objects in each group. We can count up the total number of objects, in this case triangles.

Screen shot 2015 08 18 at 9.18.26 pm

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All Common Core: 3rd Grade Math Resources

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

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

All Common Core: 3rd Grade Math Resources

Example Questions

Example Question #131 : Operations & Algebraic Thinking

Example Question #132 : Operations & Algebraic Thinking

Example Question #133 : Operations & Algebraic Thinking

Example Question #134 : Operations & Algebraic Thinking

Example Question #135 : Operations & Algebraic Thinking

Example Question #136 : Operations & Algebraic Thinking

Example Question #137 : Operations & Algebraic Thinking

Example Question #138 : Operations & Algebraic Thinking

Example Question #139 : Operations & Algebraic Thinking

Example Question #140 : Operations & Algebraic Thinking

All Common Core: 3rd Grade Math Resources

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