From Pattern to Formula
Turn a growing shape pattern into a general rule for pattern number x.
Equation
y = 1*x + 1
Graph
Table
| x | y |
|---|---|
| 1 | 2 |
| 2 | 3 |
| 3 | 4 |
| 4 | 5 |
| 5 | 6 |
What this lesson covers
What you do
You shape the function y = a*x + 1 and watch the graph answer.
Challenges to clear
- Pattern 1 uses 3 blocks. Slide a until the rule gives y = 3 at x = 1.
- The SAME rule must fit the whole pattern: pattern 5 uses 11 blocks. Check that x = 5 gives y = 11.
- A new pattern: 5, 8, 11, 14 … Some blocks are there before the pattern even starts growing. Slide c to 2.
- Now the growth. Slide a until pattern 1 uses 5 blocks — then check pattern 4 uses 14, exactly as the pattern says.
Check yourself
We found the rule y = 2x + 1. What does the '2' represent in our block pattern?
And what does the '+ 1' in y = 2x + 1 represent?
- The number of blocks added each time the pattern grows. — correct
- The number of blocks in the very first pattern.
- The total number of blocks in the last pattern.
- The height of the block tower.
- The starting block that is there before the pattern grows. — correct
- One extra block added at the end of every pattern.
- The pattern number itself.
- A mistake — the rule should be y = 2x.
Think about it
- x is the pattern number and y is how many blocks it uses. Once you find the right a, how many blocks should pattern 4 use? Check your prediction in the table.