Algebra 1 4-3 Guided Practice: Patterns and Nonlinear Functions

 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?

Take Note: Define nonlinear function.

Take Note: Sketch an example of a linear function and an example of a nonlinear function on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: Categorize each graph based on the type of function it represents.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Linear functions
Nonlinear functions

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 in the indicated space of the table.

Problem 2 Got It? Describe the relationship between the number of the figure, x, and the number of new branches, y.

Problem 2 Got It? Represent the relationship between x and y using an equation.

Problem 2 Got It? Represent the relationship between x and y using a graph.

⚠️ NOTE: All points from the table should be represented on your graph. Plan your x and y scales appropriately.

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

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?

Take Note: Define nonlinear function.

Take Note: Sketch an example of a linear function and an example of a nonlinear function on the canvas. You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: Categorize each graph based on the type of function it represents.You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

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.

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.

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

Problem 2 Got It? Enter a number to fill in the indicated space of the table.

Problem 2 Got It? Enter a number to fill in the indicated space of the table.

Problem 2 Got It? Describe the relationship between the number of the figure, x, and the number of new branches, y.

Problem 2 Got It? Represent the relationship between x and y using an equation.

Problem 3 Got It?

Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Sketch an example of a linear function and an example of a nonlinear function on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: Categorize each graph based on the type of function it represents.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

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.