Reviewing Quantitative Relationships

Reviewing Quantitative Relationships

Graph of Pumping Water

Opening

Graph of Pumping Water

The graph shows the amount of water pumped over time.

  • What does the point (10, 200) tell you?
  • At what rate is the water being pumped?

Math Mission

Opening

Represent rates in different ways.

Graph the Relationships

Work Time

Graph the Relationships

Below are four situations describing the rate of water flowing through a pump.

Situation 1: Pump 1 pumps water at a rate of 125 gallons per minute.

Situation 2: Pump 2 pumps water at a constant rate. Pump 2 pumps 364 gallons in 7 minutes.

Situation 3: Pump 3 pumps at a constant rate, represented by the table.

Situation 4: Pump 4 pumps at a constant rate, represented by the double number line.

For each situation, do the following.

  1. Write a formula that represents the rate relationship.
  2. Graph all four relationships on a single graph.

Situation 3:

Situation 4:

 

Hint:

  • What rate will you find gallons per minute or minutes per gallon?
  • How will you represent this rate as a formula?
  • Why should you represent time on the x -axis?

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation about the four situations.

  • Compare the situations. What is similar, and what is different?
  • What did you notice about two of the situations?

Challenge Problem

  • Which line on your graph of the rate relationships is the steepest? Explain why.
  • In this problem, the time is considered the independent variable and the volume the dependent variable. Explain why.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes as you listen to your classmates’ solutions.

Hint:

As your classmates present, ask questions such as the following:

  • What strategies did you use to make sense of the four situations?
  • Whose method makes most sense to you? Why?
  • Where do you see the rate in each representation (table, double number line, graph, formula)?
  • Which representation of the rate situation is easiest for you to understand? Why?
  • What conclusions can you draw from interpreting the graph?
  • Which pump is the fastest? How do you know?
  • Which pump is the slowest? How do you know?
  • How does the graph show that each pump works at a constant rate?

Summarize Your Learning

Formative Assessment

Summary of the Math: Summarize Your Learning

Summarize the mathematics you learned about graphing rates.

Hint:

Check your summary.

  • Does your summary explain what each point on your graph represents?
  • Does your summary include the term constant rate ?
  • Does your summary describe the two rates for each situation and their related formulas?

Check Your Understanding

Formative Assessment

Check Your Understanding

Use the graph to answer the questions.

  1. Does this graph most likely show the speed of a garden snail or a cheetah?
  2. How far did this creature travel in 8 minutes?
  3. How far did this creature travel in 3 minutes?
  4. What is this creature’s rate of speed in inches per minute?
  5. Solve an equation to find the distance the creature travels in 12 minutes.
  6. Solve an equation to find the time it takes the creature to travel 2 inches.

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

One thing I know about representing rate relationships is …