LINR 1 | Lesson 1 | Try This!

Try This!

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

  1. Examine Steps 1, 2, and 3.  Draw Step 0 and Step 4 on the worksheet provided.
  2. By how many shaded squares does the pattern grow for each step? Describe the growth pattern in words.
  3. 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.
  4. Graph the number of shaded squares for each step.
  5. Write an equation to determine the number of shaded squares \((n)\) given any step number \((s)\).
  6. Determine the number of shaded squares in Step 100.
  7. 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

  1. Examine Steps 1, 2, and 3.  Draw Step 0 and Step 4 on the worksheet provided.
  2. By how many shaded squares does the pattern grow for each step? Describe the growth pattern in words.
  3. 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.
  4. Graph the number of shaded squares for each step.
  5. Write an equation to determine the number of shaded squares \((n)\) given any step number \((s)\).
  6. Determine the number of shaded squares in Step 100.
  7. 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

  1. Examine Steps 1, 2, and 3.  Draw Step 0 and Step 4 on the worksheet provided.
  2. By how many shaded squares does the pattern grow for each step? Describe the growth pattern in words.
  3. 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.
  4. Graph the number of shaded squares for each step.
  5. Write an equation to determine the number of shaded squares \((n)\) given any step number \((s)\).
  6. Determine the number of shaded squares in Step 100.
  7. 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

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

Making Connections

 

 

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