Cool Down
Here are three patterns of dots.
Pattern A
Pattern B
Pattern C
Which pattern shows a quadratic relationship between the step number and the number of dots? Explain how you know algebraically and in complete sentences.
Compare your answer:
Pattern B shows a quadratic relationship.
- The number of dots is the step number squared plus 1, or .
- Pattern A is growing linearly. It is growing by 2 each time. Pattern C is growing by a factor of 3 each time, so it is growing exponentially.
- Pattern B is growing by 1, then by 3, and then by 5, which is the pattern we saw in other examples of quadratic relationships in the lesson.