Understand number patterns and simple functions using input-output tables!
Scenario: You're helping organize a school fundraiser. For every 2 tickets sold, the school earns $5. Let's create a pattern to see how much money is earned for different numbers of tickets.
A pattern is a sequence of numbers that follows a specific rule. Once you find the rule, you can predict what comes next in the sequence.
2, 4, 6, 8, 10, 12, ...
This pattern adds 2 each time
Look at how the numbers change from one to the next
Apply the same rule to find the next numbers
Let's create an input-output table for our fundraiser scenario:
| Input (Tickets) | Output (Money Earned) |
|---|---|
| 2 | $5 |
| 4 | $10 |
| 6 | $15 |
| 8 | $20 |
| 10 | $25 |
The number of tickets sold (what goes in)
The money earned (what comes out)
Let's analyze our table to find the rule:
2 tickets → $5
$5 ÷ 2 = $2.50 per ticket
4 tickets → $10
$10 ÷ 4 = $2.50 per ticket
6 tickets → $15
$15 ÷ 6 = $2.50 per ticket
Pattern Found: Each ticket earns $2.50!
Now we can write a rule to find the money earned for any number of tickets:
Money Earned = 2.5 × Number of Tickets
Function rule
Or: y = 2.5x
Where x = tickets, y = money
Let's use our function rule to find how much money is earned for 12 tickets:
y = 2.5x
Our function rule
y = 2.5 × 12
Substitute x = 12
y = $30
12 tickets earn $30!
A book club charges $3 per person for each meeting. Complete the table and find the function rule.
| People (x) | Cost (y) |
|---|---|
| 1 | $3 |
| 2 | $6 |
| 3 | $9 |
| 4 | $12 |
Function Rule: y = 3x
Cost = $3 × number of people
Find the next 3 numbers: 5, 10, 15, 20, __, __, __
25, 30, 35
Rule: Add 5 each time
Find the next 3 numbers: 2, 4, 8, 16, __, __, __
32, 64, 128
Rule: Multiply by 2 each time