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Algebra 1 4-3 Complete Lesson: Patterns and Nonlinear Functions

By Matt Richardson
Last updated almost 3 years ago
36 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
Solve It! The table below shows the relationship between the number of steps in the staircase below and the number of blocks needed to build the staircase.

Solve It! How many blocks are required to build 4 steps? Enter only a number.

Solve It! What is the ordered pair associated with 4 steps?

Solve It! How many blocks are required to build 5 steps? Enter only a number.

Solve It! What is the ordered pair associated with 5 steps?

Problem 1 Got It? The table shows the fraction A of the original area of a piece of paper that remains after the paper has been cut in half n times. Graph the function represented by the table.

A.REI.10

Problem 1 Got It? Is the function represented by the table and graphed in the previous item linear or nonlinear?
Enter a one-word response.

F.IF.4
A.REI.10

Problem 1 Got It? Reasoning: Will the area, A, ever reach zero? Explain.

F.IF.4
A.REI.10

Problem 2 Got It? Enter a number to fill the table.

Problem 2 Got It? Enter a number to fill the table.

Problem 2 Got It? Represent the relationship using words.

Problem 2 Got It? Represent the relationship using an equation.

Problem 2 Got It? Represent the relationship using a graph.
NOTE: Not all points from the table must be on your graph.

Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

F.IF.4
A.REI.10

Problem 3 Got It?

A.REI.10

Graph the function represented by the table.

A.REI.10

Is the function you graphed in the item above linear or nonlinear?

A.REI.10

This set of ordered pairs represent a function.
What is a rule that represents this function?

A.REI.10

Which rule could represent the function shown by the table?

A.REI.10

Vocabulary: Does the graph represent a linear function or a nonlinear function?

Explain.

Vocabulary: Does the graph represent a linear function or a nonlinear function?

Explain.

Error Analysis: A classmate says that the function shown by the table can be represented by the rule y = x + 1. Describe and correct your classmate's error. Use ^2 notation for exponents, if necessary.

A.REI.10

Review Lesson 1-2: Evaluate the expression for x = -3.

Review Lesson 1-2: Evaluate the expression for x = 0.
Enter only a number.

Review Lesson 1-2: Evaluate the expression for x = 2.5.
Enter only a number in decimal form.

Review Lesson 1-2: Evaluate the expression for x = -3.
Enter only a number.

Review Lesson 1-2: Evaluate the expression for x = 0.
Enter only a number.

Review Lesson 1-2: Evaluate the expression for x = 2.5.
Enter only a number in decimal form.

Vocabulary Review: Find the next number in the pattern.
Enter only a number.

F.LE.2

Vocabulary Review: Find the next number in the pattern.
Enter only a number.

F.LE.2

Vocabulary Review: Find the next number in the pattern.
Enter only a number.

F.LE.2

Vocabulary Review: Find the next number in the pattern.
Enter only a number, in this format: 1/9.

F.LE.2

Vocabulary Review: The next shape in the pattern below has __?__ blocks.

Enter only a number to fill in the blank.

F.LE.2

Use Your Vocabulary: Identify the graphs that represent a nonlinear function.
Select all that apply.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

F.IF.4
A.REI.10