Solving Problems Involving the Four Operations, and Identifying and Explaining Patterns in Arithmetic

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3rd Grade Math › Solving Problems Involving the Four Operations, and Identifying and Explaining Patterns in Arithmetic

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1

Jessica has been collecting beads all summer. She started with beads and by the end of the summer she was able to add more beads to her collection. On the first day of school she wants to evenly split the beads up amongst her friends. How many beads will each friend get?

Explanation

To solve this problem, we first have to find our unknowns. Our unknowns are the number of beads she will have by the end of the summer and the number of beads each of her friends will receive. We can set up equations for these unknowns by letting represent the beads that she has at the end of the summer and represent the number of beads each of her friends will receive.

because she gets more beads by the end of the summer.

because she is splitting up her total amount of beads between friends. When you split something up evenly you divide.

2

Jessica has been collecting beads all summer. She started with beads and by the end of the summer she was able to add more beads to her collection. On the first day of school she wants to evenly split the beads up amongst her friends. How many beads will each friend get?

Explanation

To solve this problem, we first have to find our unknowns. Our unknowns are the number of beads she will have by the end of the summer and the number of beads each of her friends will receive. We can set up equations for these unknowns by letting represent the beads that she has at the end of the summer and represent the number of beads each of her friends will receive.

because she gets more beads by the end of the summer.

because she is splitting up her total amount of beads between friends. When you split something up evenly you divide.

3

Emily has been collecting beads all summer. She started with beads and by the end of the summer she was able to add more beads to her collection. On the first day of school she wants to evenly split the beads up amongst her friends. How many beads will each friend get?

Explanation

To solve this problem, we first have to find our unknowns. Our unknowns are the number of beads she will have by the end of the summer and the number of beads each of her friends will receive. We can set up equations for these unknowns by letting represent the beads that she has at the end of the summer and represent the number of beads each of her friends will receive.

because she gets more beads by the end of the summer.

because she is splitting up her total amount of beads between friends. When you split something up evenly you divide.

4

Emily has been collecting beads all summer. She started with beads and by the end of the summer she was able to add more beads to her collection. On the first day of school she wants to evenly split the beads up amongst her friends. How many beads will each friend get?

Explanation

To solve this problem, we first have to find our unknowns. Our unknowns are the number of beads she will have by the end of the summer and the number of beads each of her friends will receive. We can set up equations for these unknowns by letting represent the beads that she has at the end of the summer and represent the number of beads each of her friends will receive.

because she gets more beads by the end of the summer.

because she is splitting up her total amount of beads between friends. When you split something up evenly you divide.

5

Hannah is making a red fruit salad because red is her favorite color. She cuts up pieces of watermelon and puts it in a bowl. Because she really loves strawberries, she wants times as many pieces of strawberries as pieces of watermelon. Then she adds half as many raspberries as strawberries. How many pieces of fruit are in her fruit salad?

Explanation

To solve this problem, we first have to find our unknowns. Our unknowns are the number strawberries and raspberries she puts in the fruit salad. We can set up equations for these unknowns by letting represent strawberries and represent raspberries.

because she has times as many strawberries than watermelon.

because when we half something we always divide by

Now we need to add the watermelon, strawberries, and raspberries together to find our total.

6

Hannah is making a red fruit salad because red is her favorite color. She cuts up pieces of watermelon and puts it in a bowl. Because she really loves strawberries, she wants times as many pieces of strawberries as pieces of watermelon. Then she adds half as many raspberries as strawberries. How many pieces of fruit are in her fruit salad?

Explanation

To solve this problem, we first have to find our unknowns. Our unknowns are the number strawberries and raspberries she puts in the fruit salad. We can set up equations for these unknowns by letting represent strawberries and represent raspberries.

because she has times as many strawberries than watermelon.

because when we half something we always divide by

Now we need to add the watermelon, strawberries, and raspberries together to find our total.

7

Fill in the missing number that completes the sequence:

16, 12, 8, ______

4

6

3

2

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.

8

Fill in the missing number that completes the sequence:

16, 12, 8, ______

4

6

3

2

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.

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

Multiply

Add

Add

Multiply

Subtract

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.

10

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

Multiply

Add

Add

Multiply

Subtract

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.

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