IM Alg1.6.3 Lesson: Building Quadratic Functions from Geometric Patterns
Figure A is a large square. Figure B is a large square with a smaller square removed. Figure C is composed of two large squares with one smaller square added.
| Figure A | Figure B | Figure C |
 |  |  |
If the pattern continues, what will we see in Step 5 and Step 18?
Sketch or describe the figure in each of these steps.
How many small squares are in each of these steps? Explain how you know.
Write an equation to represent the relationship between the step number and the number of squares . Be prepared to explain how each part of your equation relates to the pattern. (If you get stuck, try making a table.)
Sketch the first 3 steps of a pattern that can be represented by the equation y = n² - 1.
For the original step pattern in the statement, write an equation to represent the relationship between the step number and the perimeter, .
For the step pattern represented by the equation , write an equation to represent the relationship between the step number and the perimeter, .
Are these linear functions?
Here is an image showing a pattern. Sketch the next step in the pattern.
Kiran says that the pattern is growing linearly because as the step number goes up by 1, the number of rows and the number of columns also increase by 1. Do you agree? Explain your reasoning.
To represent the number of squares after steps, Diego and Jada wrote different equations. Diego wrote the equation . Jada wrote the equation . Are either Diego or Jada correct? Explain your reasoning.