Rate of Change Exploration - Part 1

Objective:

At the end of this exploration you should be able to create and label a t-table and linear graph.

Directions:

At your table, work to solve each of the problems below. As you answer each question, be sure to answer parts a-d thoroughly, then label your t-table and graph appropriately.

1. Dr. Klein is a super doctor! He saves lives at a rate of 10 people per hour. In one hour he has saved 10 people.

a) Create and complete a t-table and identify/label the variable(x) and total amount/distance (y) for your given scenario.

b) Draw an x/y axis making sure to label each axis & title the graph

c) Plot the points from the t-table above and create a line connecting all of the points.

d) Create a rule based on your findings and explain your rule in words.

2. Jared has $5 in his bank account. Every week he saves $4 and deposits it in the bank. After one week he has $9 in his account.

a) Create and complete a t-table and identify/label the variable(x) and total amount/distance (y) for your given scenario.

b) Draw an x/y axis making sure to label each axis & title the graph

c) Plot the points from the t-table above and create a line connecting all of the points.

d) Create a rule based on your findings and explain your rule in words.

3. Mrs. Garcia’s husband put her on a coffe budget. She has $40 in her bank account. Every week he spends $4 to buy a coffee. In two weeks she has $32 leftover.

a) Create and complete a t-table and identify/label the variable(x) and total amount/distance (y) for your given scenario.

b) Draw an x/y axis making sure to label each axis & title the graph

c) Plot the points from the t-table above and create a line connecting all of the points.

d) Create a rule based on your findings and explain your rule in words.

Name: _____________________________ Date: _________ Period: ____

Part 2

Objective:

At the end of this exploration you should be able to create and label a t-table and linear graph.

1. Julie can run at a rate of 7 miles per hour. After two hours Julie has run 14 miles.

a) Create and complete a t-table and identify/label the variable(x) and total amount/distance (y) for your given scenario.

b) Draw an x/y axis making sure to label each axis & title the graph

c) Plot the points from the t-table above and create a line connecting all of the points.

d) Create a rule based on your findings and explain your rule in words.

2. A pumpkin has an initial size of 5cm when it was first recorded. The next month the pumpkin grew at a rate of 10cm per month.

a) Create and complete a t-table and identify/label the variable(x) and total amount/distance (y) for your given scenario.

b) Draw an x/y axis making sure to label each axis & title the graph

c) Plot the points from the t-table above and create a line connecting all of the points.

d) Create a rule based on your findings and explain your rule in words.

3. Sophia is saving up to buy a bike. She already has $50 in her bank account, and every week she earns $10 per month. By the end of three weeks she had $80.

a) Create and complete a t-table and identify/label the variable(x) and total amount/distance (y) for your given scenario.

b) Draw an x/y axis making sure to label each axis & title the graph

c) Plot the points from the t-table above and create a line connecting all of the points.

d) Create a rule based on your findings and explain your rule in words.

4. Amelia is digging a hole in the backyard to make a pool. She starts digging the hole is able to dig a hole at a rate of 9 yards per week.

a) Create and complete a t-table and identify/label the variable(x) and total amount/distance (y) for your given scenario.

b) Draw an x/y axis making sure to label each axis & title the graph

c) Plot the points from the t-table above and create a line connecting all of the points.

d) Create a rule based on your findings and explain your rule in words.

Debrief Questions:

• 1. What does the x axis represent for each question?

  2. What does the y axis represent for each question?

  3. What does the point that lies on the y-axis represent?

  4. What is the rate of change for your line? Explain your reasoning.

  5. What does the rate of change represent?

  6. How do your points change as you go from one point to another? Is your sentence true for all points?