Unit 1.5  Patterns and relationships in tables
what we need to know
 What a pattern represents
 How a pattern is used to create a PATTERN RULE
 A TERM:represents the relation when we substitute the variable in it, and a TERM NUMBER represents the variable.
 A relation is the expression that relates the variable with the expression that contains it
 Input/output tables used to determine the relation expression.
 The INPUT column is made up of the the TERM NUMBERS, which are the variable we substitute on the relation to obtain each TERM . These terms form the OUTPUT column.
 How a pattern is used to create a PATTERN RULE
 A TERM:represents the relation when we substitute the variable in it, and a TERM NUMBER represents the variable.
 A relation is the expression that relates the variable with the expression that contains it
 Input/output tables used to determine the relation expression.
 The INPUT column is made up of the the TERM NUMBERS, which are the variable we substitute on the relation to obtain each TERM . These terms form the OUTPUT column.
class notes


more information
Just like in the previous lesson, in this lesson we will learn how to determine the relation expression between the terms and terms numbers, but this time we will use INPUT/OUTPUT tables to get the information..
what is the input/output table
Before getting to this important definition, let's review:
An input/output table gives pairs of numbers that follow a certain pattern or rule. In this input/output table, the rule is that 2 has been added to each input.
To determine the rule for a table, simply look at one pair of input/output numbers and figure out what number has been added, subtracted, multiplied, or divided by it.
Then, make sure that pattern matches the rest of the numbers.
Once you know the rule for a table, you can finish filling in the rest of it.
Look at the input and apply the rule.
Input/output tables can be written horizontally as well as vertically. The table above is an example of a VERTICAL table. Let's look the am example of a HORIZONTAL table (look at the following. This is how it looks:
In this case, $2 is the first term of the input, and it represents the variable since it changes from one term number to another. The second term will depend on the pattern rule. The $12 is part of the OUTCOME, which results from substituting each of the INPUT numbers into the relation,.
Last class we said that:
 In the INPUT COLUMN, you must input the TERM NUMBERS, which represent a variable. On the OUTPUT COLUMN, each of the TERM NUMBERS is obtained by substituting the TERM NUMBERS or variable, into the given relation.
Now, let's see how we can write expressions using tables:
 In the INPUT COLUMN, you must input the TERM NUMBERS, which represent a variable. On the OUTPUT COLUMN, each of the TERM NUMBERS is obtained by substituting the TERM NUMBERS or variable, into the given relation.
Now, let's see how we can write expressions using tables:
Example 1
What is the rule for this table?
Looking at the first pair (5 and 15), we can tell that either 10 was added to 5 or 5 was multiplied by 3.
Let's see which pattern works for the rest of the table.
 For the second pair (4 and 12) we can see that 10 was NOT added (only 8 was added.) But, 4 times 3 is 12. So, it appears the rule is "multiply by 3."
 Let's make sure this rule works for the rest of the table.
2 x 3 = 6 and 7 x 3 = 21, so yes, the rule is "multiply by 3."
If you needed to write this rule using a variable, you would say "3 times x" which can be written as 3x.
 Remember that a number next to a variable means multiplication.
That's because x stands for the input. So the output is always 3 times the input (x).
Let's see which pattern works for the rest of the table.
 For the second pair (4 and 12) we can see that 10 was NOT added (only 8 was added.) But, 4 times 3 is 12. So, it appears the rule is "multiply by 3."
 Let's make sure this rule works for the rest of the table.
2 x 3 = 6 and 7 x 3 = 21, so yes, the rule is "multiply by 3."
If you needed to write this rule using a variable, you would say "3 times x" which can be written as 3x.
 Remember that a number next to a variable means multiplication.
That's because x stands for the input. So the output is always 3 times the input (x).
example 2
The results check out!
example 3
FINALLY, LET'S REVIEW THE GRAPH FOR THE PREVIOUS LESSON
From here, we are reminded that:
 The INPUT is the TERM NUMBERS, which are assigned a variable. For example, I can assign the variable as s. Then, term number 1 is s =1, term number 2 is s = 2, etc.
 When in doubt, your input will probably numbers in consecutive order. (They vary > variables).
 The OUTPUT column is is made up of the TERMS which are made of the each of the term numbers substituting the variable in the determined relation.
INPUT (First column) > TERM NUMBERS = VARIABLES
OUTPUT > TERMS = Relations with the term numbers substituted in.
 The INPUT is the TERM NUMBERS, which are assigned a variable. For example, I can assign the variable as s. Then, term number 1 is s =1, term number 2 is s = 2, etc.
 When in doubt, your input will probably numbers in consecutive order. (They vary > variables).
 The OUTPUT column is is made up of the TERMS which are made of the each of the term numbers substituting the variable in the determined relation.
INPUT (First column) > TERM NUMBERS = VARIABLES
OUTPUT > TERMS = Relations with the term numbers substituted in.
videos that may help
In this video, x = Term number (variable), and y = Term
online interactive ACTIVITIES
worksheets





review  workbook
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