## Steps and Squares

In this learning experience, you will represent linear trends in patterns, tables, graphs, and equations with a focus on the change in the number of shaded squares for each step.

### Pattern 1: Use the *Worksheet for Pattern 1 *and the instructions below to complete this task.

###### Pattern 1

- Examine Steps 1, 2, and 3. Draw Step 0 and Step 4 on the worksheet provided.
- By how many shaded squares does the pattern grow for each step? Describe the growth pattern in words.
- Create a table to record the number of shaded squares for each step. Let \(n\) represent the step number, and let \(s\) represent the number of shaded squares.
- Graph the number of shaded squares for each step.
- Write an equation to determine the number of shaded squares \((n)\) given any step number \((s)\).
- Determine the number of shaded squares in Step 100.
- Use Desmos.com to verify your results by entering your table and your equation.

### Pattern 2: Use the *Worksheet for Pattern 2* and the instructions below to complete this task.

###### Pattern 2

- Examine Steps 1, 2, and 3. Draw Step 0 and Step 4 on the worksheet provided.
- By how many shaded squares does the pattern grow for each step? Describe the growth pattern in words.
- Create a table to record the number of shaded squares for each step. Let \(n\) represent the step number, and let \(s\) represent the number of shaded squares.
- Graph the number of shaded squares for each step.
- Write an equation to determine the number of shaded squares \((n)\) given any step number \((s)\).
- Determine the number of shaded squares in Step 100.
- Use Desmos.com to verify your results by entering your table and your equation, or click
*here*to see a solution.

### Pattern 3: Use the *Worksheet for Pattern 3* and the instructions below to complete this task.

###### Pattern 3

- Examine Steps 1, 2, and 3. Draw Step 0 and Step 4 on the worksheet provided.
- By how many shaded squares does the pattern grow for each step? Describe the growth pattern in words.
- Create a table to record the number of shaded squares for each step. Let \(n\) represent the step number, and let \(s\) represent the number of shaded squares.
- Graph the number of shaded squares for each step.
- Write an equation to determine the number of shaded squares \((n)\) given any step number \((s)\).
- Determine the number of shaded squares in Step 100.
- Use Desmos.com to verify your results by entering your table and your equation.

### Pattern 4: Use the *Worksheet for Pattern 4 *and the instructions below to complete this task.

###### Pattern 4

- Examine Steps 1, 2, and 3. Draw Step 0 and Step 4 on the worksheet provided.
- Graph the number of shaded squares for each step.
- Write an equation to determine the number of shaded squares \((n)\) given any step number \((s)\).
- Determine the number of shaded squares in Step 100.
- Use Desmos.com to verify your results by entering your table and your equation, or click
*here*to see a solution.