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Math resources Algebra Number patterns

Input output tables

Input/output tables

Here you will learn about input/output tables, including what input/output tables are, how to generate a number pattern using input/output tables, and how to use input/output tables to plot coordinates on a coordinate plane.

Students will first learn about input/output tables as a part of operations and algebraic thinking in 4 th grade and will expand on their learning in 5 th grade and into middle school.

What are input/output tables?

An input/output table is a table that shows the relationship between a set or sets of numbers. An input/output table will show you pairs of numbers that all follow the same rule. Input/output tables can contain integers (whole numbers), fractions, decimals, and negative numbers.

For example,

Output tables 1 US

If you look at the relationship between the numbers in the table, they all follow the same number pattern, or rule, of adding 2. You put a number “in,” apply the rule, and then the output comes “out.”

Sometimes various terms within the input/output table are missing, and you will have to determine what the rule is to find the missing numbers.

Let’s look at the table below.

There are two missing outputs that need to be solved for.

Output tables 2 US

Use the relationship between 9 and 5 and 22 and 18 to help find the missing values.

To find the relationship between the two numbers, determine the pattern.

\begin{aligned} & 9-5=4 \\\\ & 22-18=4 \end{aligned}

The rule is to subtract 4. Use that rule to find the missing values in the table.

\begin{aligned} & 14-4=10 \\\\ & 35-4=31 \end{aligned}

Output tables 3 US

Input/output tables and coordinate planes

Input/output tables can also be used to create ordered pairs from the corresponding terms in each pattern and graph them on the coordinate plane.

An ordered pair (x, y), is a pair of numbers used to locate a point on a coordinate plane.

The first number tells how far to move horizontally on the x -axis and the second number tells how far to move vertically on the y -axis.

For example,

Let’s use the input/output table from above.

Output tables 4 US

The input is the x value and the output is the y value. This can be used to create coordinate pairs.

Output tables 5 US

Next, you can graph each set of ordered pairs on the coordinate plane as a point. Then draw a line from the origin to connect the points.

Output tables 6 US

What are input/output tables?

What are input/output tables?

Common Core State Standards

How does this relate to 4 th grade math and 5 th grade math?

  • Grade 4: Operations and Algebraic Thinking (4.OA.C.5)
    Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

    For example, given the rule Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

  • Grade 4: Measurement and Data (4.MD.A.1)
    Know relative sizes of measurement units within one system of units including km, \, m, \, cm; \, kg, \, g; \, lb, \, oz.; \, l, \, ml; \, hr, \, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table.

    For example, know that 1~{ft} is 12 times as long as 1~{in}. Express the length of a 4~{ft} snake as 48~{in}. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36).

  • Grade 5: Operations and Algebraic Thinking (5.OA.B.3)
    Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

    For example, given the rule Add 3” and the starting number 0, and given the rule Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

[FREE] Number Patterns Check for Understanding Quiz (Grade 4 to 5)

[FREE] Number Patterns Check for Understanding Quiz (Grade 4 to 5)

[FREE] Number Patterns Check for Understanding Quiz (Grade 4 to 5)

Use this quiz to check your grade 4 to 5 students’ understanding of number patterns. 10+ questions with answers covering a range of 4th and 5th grade number patterns topics to identify areas of strength and support!

DOWNLOAD FREE
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[FREE] Number Patterns Check for Understanding Quiz (Grade 4 to 5)

[FREE] Number Patterns Check for Understanding Quiz (Grade 4 to 5)

[FREE] Number Patterns Check for Understanding Quiz (Grade 4 to 5)

Use this quiz to check your grade 4 to 5 students’ understanding of number patterns. 10+ questions with answers covering a range of 4th and 5th grade number patterns topics to identify areas of strength and support!

DOWNLOAD FREE

How to find the missing values in an input/output table

In order to find the missing values in an input/output table:

  1. Identify the number pattern and state the rule.
  2. Using the rule, find the missing values in the table.

Input/output tables examples

Example 1: missing values in an input/output table

Find the missing values in the given input/output table.

Output tables 7 US

  1. Identify the number pattern and state the rule.

To identify the pattern, analyze the given values within the table. The input value, 2, turns into the output value, 6, which means either adding 4 or multiplying by 3. In order for it to be a rule, it must be true of all values within the table.

Let’s look at the second input value, 6, and apply both possible rules: adding 4 and multiplying by 3.

6+4=10 and 6 \times 3=18

Multiplying by 3 holds the rule true.

Now try the final given input 12.

12+4=16 and 12 \times 3=36

Again, multiplying by 3 holds the rule true.

The rule for this input/output table is to multiply by 3.

2Using the rule, find the missing values in the table.

You can now find the missing value by using the rule: multiplying by 3.

Output tables 8 US

9 \times 3=27

The missing value is 27. You can now fill in the missing value.

Output tables 9 US

Example 2: missing values in an input/output table

Find the missing values in the given input/output table.

Output tables 10 US

Identify the number pattern and state the rule.

Using the rule, find the missing values in the table.

Example 3: missing values in an input/output table word problem

Miss Grace’s 3 rd grade classes stretch for 3 minutes before math class. For 5 days, they continued this practice. How many minutes do they spend stretching during that time? Use the given input/output table to help solve.

Output tables 13 US

Identify the number pattern and state the rule.

Using the rule, find the missing values in the table.

How to plot points on a coordinate plane using input/output tables

In order to find the missing values in an input/output table:

  1. Use pairs of corresponding terms to create an ordered pair.
  2. Graph each set of ordered pairs on the coordinate plane.
  3. Draw a line from the origin to connect the points.

Example 4: plot points on a coordinate plane using input/output tables

The table below represents the number of sodas that Sammy drank for the last 6 weeks. Graph the data on the coordinate plane.

Output tables 16 US

Use pairs of corresponding terms to create an ordered pair.

Graph each set of ordered pairs on the coordinate plane.

Draw a line from the origin to connect the points.

Example 5: plot points on a coordinate plane using input/output tables

The table below represents the number of baseball cards Phillip has collected for the last 6 months. Graph the data on the coordinate plane.

Output tables 20 US

Use pairs of corresponding terms to create an ordered pair.

Graph each set of ordered pairs on the coordinate plane.

Draw a line from the origin to connect the points.

Example 6: plot points on a coordinate plane using input/output tables word problem

Mrs. Vasek’s 6 th grade class recorded the growth of a class plant over time. The input/output table below represents the growth of the class plant over 6 weeks. Graph the data on a coordinate plane.

Output tables 24 US

Use pairs of corresponding terms to create an ordered pair.

Graph each set of ordered pairs on the coordinate plane.

Draw a line from the origin to connect the points.

Teaching tips for input/output tables

  • Instead of providing students with worksheets to practice with, allow students to create their own input/output tables, leaving blanks and having other students fill in the missing values.

  • Practice with mental math and place value can assist learners with identifying patterns and rules.

Easy mistakes to make

  • Confusing the input and output columns
    Always check how each column is labeled to be sure which column represents each set of data. Not doing so can lead to confusion or mistakes.

  • Not identifying the pattern
    There is always a rule or pattern in input/output tables. Carefully analyze each input/output table to ensure you identify the correct pattern.

  • Ignoring negative numbers or fractions
    Input/output tables can involve negative numbers and fractions. Ignoring these can lead to errors, so it’s important to pay attention to the signs and any fractional components of each value.

Practice input/output tables questions

1) What is the rule in the given input/output table?

 

Output tables 28 US

Add 12

GCSE Quiz False

Divide by 5

GCSE Quiz False

Subtract 12

GCSE Quiz False

Multiply by 5

GCSE Quiz True

To identify the pattern, analyze the given values within the table.

 

The input 3 turns into the output 15, which means either adding 12 or multiplying by 5. In order for it to be a rule, it must be true of all values within the table.

 

Try with the remaining inputs:

 

4+12=16 or 4 \times 5=20 \rightarrow multiplying by 5

 

5+12=17 or 5 \times 5=25 \rightarrow multiplying by 5

 

6+12=18 or 6 \times 5=30 \rightarrow multiplying by 5

 

7+12=19 or 7 \times 5=35 \rightarrow multiplying by 5

 

The rule is: multiply by 5.

2) What is the missing value in the given input/output table?

 

Output tables 29 US

10
GCSE Quiz True

6
GCSE Quiz False

12
GCSE Quiz False

8
GCSE Quiz False

To identify the pattern, analyze the given values within the table.

 

The input 22 turns into the output 18, which means either subtracting 4. In order for it to be a rule, it must be true of all values within the table.

 

Try with the remaining inputs:

 

\begin{aligned} & 18-4=14 \\\\ & 10-4=6 \\\\ & 6-4=2 \end{aligned} 

 

The rule is subtracting 2. Use this to find the missing value.

 

14-4=10

 

The missing value is 10.

3) Stefan is renting a scooter to get around town. It costs \$7 for each hour he rents the scooter. If he rents the scooter for 5 hours, how much will Stefan pay?

 

Output tables 30 US

\$12
GCSE Quiz False

\$27
GCSE Quiz False

\$31
GCSE Quiz False

\$35
GCSE Quiz True

To identify the pattern, analyze the given values within the table.

 

Each hour that Stefan keeps the scooter will cost him \$7. For 1 hour, it’s 7 dollars. For the second hour, calculate 7 + 7 = 14, or 7 \times 2=14. The rule will be to multiply by 7.

 

Calculate the remaining outputs to find the total cost that Stefan paid.

 

\begin{aligned} & 7 \times 2=14 \\\\ & 7 \times 3=21 \\\\ & 7 \times 4=28 \\\\ & 7 \times 2=35 \end{aligned} 

 

Stefan paid \$35 to rent the scooter.

4) The table below represents the number of seashells that Cadace collected over 6 days at the beach. Which set of points represents the data shown in the table below?

 

Output tables 31 US

(3,1), \, (6,2), \, (9,3), \, (12,4), \, (15,5), (18,6)

GCSE Quiz False

(1,3), \, (2,6), \, (3,9), \, (4,12), \, (5,15), (6,18)

GCSE Quiz True

(1,4), \, (2,8), \, (3,12), \, (4,16), \, (5,20), (6,24)

GCSE Quiz False

(1,2), \, (3,4), \, (5,6), \, (3,6), \, (9,12), (15,18)

GCSE Quiz False

The data in the day column will represent the variable x, and the data in the shells column will represent the y variable.

 

Output tables 32 US

 

The coordinates for this table are: (1,3), (2,6), (3,9), (4,12), (5,15), (6,18).

5) Cameron goes to band camp each summer for 15 days. He goes for 5 consecutive years. Which coordinate plane shows the number of days Cameron spends at band camp?

 

Output tables 33 US

Output tables 34 US

GCSE Quiz True

Output tables 35US

GCSE Quiz False

Output tables 36 US

GCSE Quiz False

Output tables 37 US

GCSE Quiz False

The data in the day column will represent the variable x, and the data in the shells column will represent the y variable.

 

Use the data given to create points that will be graphed on the coordinate grid.

 

Output tables 38 US

 

Find the coordinate grid that contains the points (1,15), (2,30), (3,45), (4,60) and (5,75).

6) Nora’s 8 th grade teacher gives her 16 pencils at the beginning of each month. The chart below represents the number of pencils she uses each week. Which coordinate plane shows the number of pencils Nora has at the end of the month?

 

Output tables 39 US

Output tables 40 US

GCSE Quiz False

Output tables 41 US

GCSE Quiz False

Output tables 42 US

GCSE Quiz True

Output tables 43 US

GCSE Quiz False

The data in the week column will represent the variable x, and the data in the pencils column will represent the y variable.

 

Use the data given to create points that will be graphed on the coordinate grid.

 

Output tables 44 US

 

Find the coordinate grid that contains the points (1,13), (2,10), (3,7), (4,4) and (5,1).

Input/output tables FAQs

What is the difference between input/output tables and function tables?

The biggest difference lies in the emphasis on mathematical functions in function tables, including the presence of a function rule and the requirement for unique outputs for each input. Input/output tables may represent various types of relationships, and the terminology might be used more broadly depending on the educational context.

How are input/output tables and ratios related?

Input/output tables focus on the relationship between input and output values in a function; ratios provide a way to express and analyze the relationship between two quantities.

The next lessons are

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