Eligible Content M3.D.1.2.1 

Help Me To:   

Determine the missing element in a function table.  Functions may use + , - , or x.
Allowable multiples are 2, 3 or 5. Tables must have 3 INs and 3 OUTs listed.

Did You Know?

Sometimes you can find a number pattern in a table.  Number patterns can be found
in a table because the data is organized and so the pattern is clear.  You can use a table to show a
number pattern that describes a relationship between numbers.

Look at the example below.

One spider has eight legs.  If you have two spiders, multiply 2 x 8 to get 16 legs.
The rule is multiply by 8.  If you have three spiders multiply 3 x 8 to get 24 legs.
Continue to multiply by 8 to get the answers 32, 40 and 48 for the last three boxes

Check What You Know First

Number Patterns in Tables

Look at this table and write a rule for the function table going from column x to column y.
For example, the rule might be Add 2, Subtract 2, Multiply by 2 or Divide by 2.
Then write the missing number.

What is the missing value in the function table?

What is the missing value in the function table?

Look here for the answer... 40 is the missing value

Key Vocabulary

A function table is a table of ordered pairs.  Number patterns are found
in tables because the data is organized.

Learn About It Now

Number Patterns in Tables

Look at the first pair of numbers 1 and 5 to find a number relationship.  Also think about the number
operations: add, subtract, multiply and divide. Consider what numbers and what number operations
you could you use to go from 1 to 5.

First think of these rules:
When going from a smaller number to a larger number, try adding or multiplying.
When going from a larger number to a smaller number, try subtracting or dividing.

Now try a number and an operation.  In this table, you are not going from a larger number to a smaller
number, so you would not subtract or divide.  Since you are going from a smaller number to a larger
number try adding or multiplying.

In this table, each number in column y is 4 more than the number in column x.  The rule going from
x to y is  + 4  or add 4.   When you add 4 to 7, you get the answer 11 for the missing value in column y.

In the following table, you are not going from a smaller number to a larger number, so you would not add
or multiply.  Since you are going from a larger number to a smaller number try subtracting or dividing.

In this table, the rule going from x to y is  ÷  by 5 or divide by 5.   When you divide 40 by 5, you
get the answer 8 for the missing value in column y.

Solving Problems Using Number Patterns In Tables

Number patterns in tables can also be helpful when you try to solve math problems.
Let’s look at an example.

Tom practiced his multiplication tables the same number of minutes every day for five days.
He made a table to show the total number of minutes he had practiced after each of the five days.
What is the total number minutes Tom had practiced after 5 days?

From the table, you can see that the rule for going from the first row to the second row
is to multiply by 5.  Tom practiced 5 minutes each day. To find out how many total minutes Tom had practiced after 5 days,
multiply 5 X 5 = 25. Tom had practiced 25 minutes after 5 days.

Try This

If Tom continues to practice the same number of minutes every day, how many total
minutes will he have practiced after 30 days?

Look here for the answer... 150

How did Tom get this answer? 

For the solution... Click Here... The rule for the table is to multiply by 5.  Multiply 5 X 30 =150.

More Practice

For the following problems, find the rule for the function table going from column x  to column y.
Use the following words:  Add, Subtract, Multiply by or Divide by followed by a number.
Then write just the number for the missing value.

What is the missing value in the function table?

Look here for the answer... 9 is the missing value

What is the missing value in the function table?

Look here for the answer... 9 is the answer

What is the missing value in the function table?

Look here for the answer... 0 is the answer

What is the missing value in the function table?

Look here for the answer... The answer is 3

Websites to Check Out For Extra Practice

Read the directions below first and then click on the website to practice finding a missing number and operation that makes a
number sentence true in the Function Machine. In the Function Machine, students investigate very simple functions by trying
to guess the algebraic form from inputs and outputs.
http://www.shodor.org/interactivate/activities/fm/index.html

Directions for the Function Machine Game: 
For the variable x, type a number and click on enter. 
Under the question, (Can you guess the function?), select an operation. Then type a number in the box that follows. 
To see if you are correct, click on check formula. 
To begin a new problem, click on the button – Set new function. 
You can also see your score by clicking on the button – Keep score.

Also try these websites, for further work on function table skills.

Whole Number Cruncher - Similar to "Number Cruncher" but only generates multiplication and addition functions to avoid
outputting any negative numbers.
http://www.shodor.org/interactivate/activities/pnumbercruncher/index.html

Number Cruncher - Similar to the original "Function Machine" but lists input and output in a table and will not let the user attempt
to guess the rule on without at least having two data points.
http://www.shodor.org/interactivate/activities/numbercruncher/index.html

Ambleweb Function Machine – Input and Output to determine the rule
http://www.amblesideprimary.com/ambleweb/mentalmaths/functionmachines.html