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 #8 : 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 10.32.25 am

Possible Answers:

Divide 

Add 

Multiply 

Add 

Subtract 

Correct answer:

Multiply 

Explanation:

Each X value is multiplied by  to get the Y value. 

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 #5 : 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 10.32.32 am

Possible Answers:

Multiply 

Multiply 

Add 

Add 

Add 

Correct answer:

Multiply 

Explanation:

Each X value is multiplied by  to get the Y value. 

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 #6 : 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 10.33.05 am

Possible Answers:

Multiply 

Add 

Add 

Multiply 

Multiply 

Correct answer:

Multiply 

Explanation:

Each X value is multiplied by  to get the Y value. 

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 #11 : 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 10.33.10 am

Possible Answers:

Add 

Add 

Multiply 

Subtract 

Multiply 

Correct answer:

Multiply 

Explanation:

Each X value is multiplied by  to get the Y value. 

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 #11 : 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 10.33.17 am

Possible Answers:

Add 

Multiply 

Multiply 

Divide 

Add 

Correct answer:

Multiply 

Explanation:

Each X value is multiplied by  to get the Y value. 

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 #791 : Operations & Algebraic Thinking

Fill in the missing number that completes the sequence:

1, 5, _____, 13

Possible Answers:

4

25

8

9

Correct answer:

9

Explanation:

The first step in solving this problem is identifying the pattern used to create the sequence. It could be any of the four operations (addition, subtraction, multiplication, or division). 

The first thing that may be noticed is that the numbers are increasing, which would likely mean the pattern is using addition or multiplication because this leads to larger numbers in the answer rather than smaller answers.

Let's focus on multiplication first, 1x____=5 would be the first step to see if multiplication is the pattern being used. 1x5=5, so this could be our pattern. We must try the rule again with the next digit to see if it follows in sequence. 5x5=25, which is larger than the last number (13) in the series, so multiplication is not the operation used. We can eliminate multiplication.

This leaves us with addition. 1+___=5 reveals that 4 can be added to make 5. To see if the pattern holds, we can try it with 5+4=9 and then use the sum from the attempted pattern to try and make 13. 9+4=13, so we see that 4 works again. This means that the rule is to add each number by 4 to reveal the next number in the sequence.

The missing number in the sequence is 9.

Example Question #792 : Operations & Algebraic Thinking

Fill in the missing number that completes the sequence:

16, 12, 8, ______

Possible Answers:

3

4

2

6

Correct answer:

4

Explanation:

The first step in solving this problem is identifying the pattern used to create the sequence. It could be any of the four operations (addition, subtraction, multiplication, or division). 

The first thing that may be noticed is that the numbers are decreasing, which would likely mean the pattern is using subtraction or division because this leads to smaller numbers in the answer rather than larger answers.

Let's focus on division first, 16÷____=12 would be the first step to see if division is the pattern being used. There is no whole number that would give 12 as the quotient to this problem, so with that, we can eliminate division.

This leaves us with subtraction. 16-___=12 reveals that 4 can be subtracted to make 12. To see if the pattern holds, we can try it with 12-___=8 and 4 works again. This means that the rule is to subtract each number by 4 to reveal the next number in the sequence.

8-4=4 so the missing number in the sequence is 4.

Example Question #793 : Operations & Algebraic Thinking

What is the pattern used to create this numerical sequence?

500, 100, 20, 4

Possible Answers:

Subtract by 400

Add 80

Multiply by 5

Divide by 5

Correct answer:

Divide by 5

Explanation:

The first step in solving this problem is identifying the pattern used to create the sequence. It could be any of the four operations (addition, subtraction, multiplication, or division). 


Something that may be noticed is that the numbers are decreasing, which would likely mean the pattern is using subtraction or division because this leads to smaller numbers in the answer rather than larger solutions.


Let’s focus on subtraction first, 500-____=100 would be the way to identify the difference between the two numbers and a possible rule. 500-400=100, so the next term would need to be subtracted by 400 to make this rule accurate. 100-400 is NOT 20, so subtraction cannot be the pattern.


This leaves us with division. 500÷___=100 reveals that 5 can be inserted into the blank to make 100. 500÷5=100 is true. To see if the pattern holds, we can try it with 100÷5=20, and it works again. The final test is with the last number in the sequence, 20÷5=4, so the rule holds. Dividing by 5 will get the next term in the series.


The rule is to divide each term by 5.

Example Question #1 : Multiplying Within 100 To Solve Word Problems

There are  boxes of oranges. Each box contains  oranges. How many oranges are there? 

Possible Answers:

Correct answer:

Explanation:

Looking at the picture below, we have  groups, each with  oranges. To find the total we could add  to itself  times, or we could do multiplication. Remember, multiplication is the same thing as repeated addition. 

Let's let  equal the total number of oranges. 

Our equation is 

5x3

 

Example Question #2 : Multiplying Within 100 To Solve Word Problems

There are  boxes of oranges. Each box contains  oranges. How many oranges are there? 

 

Possible Answers:

Correct answer:

Explanation:

Looking at the picture below, we have  groups, each with  oranges. To find the total we could add  to itself  times, or we could do multiplication. Remember, multiplication is the same thing as repeated addition. 

Let's let  equal the total number of oranges. 

Our equation is 

4x3

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