Rules For Computing A Value

Rules For Computing A Value

Revise and Extend Your Work

Opening

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.

Independent and Dependent

Opening

Independent and Dependent

Read and Discuss

  • You’ve seen many quantitative relationships—for example, the relationship between distance and time when you’re riding your bike. In these relationships, the quantity that changes independently is called the independent variable, and the quantity that is calculated is called the dependent variable.
  • In the above relationship, distance is the dependent variable because your distance depends on the amount of time that has passed. Time is the independent variable because the amount of time that has passed really does not depend on how far you have gone.
  • You graph the independent variable on the horizontal axis, the x-axis, and the dependent variable on the vertical axis, the y-axis. There isn’t any great mystery behind this; it’s just something mathematicians and scientists agreed on so that everyone would graph things the same way.

Math Mission

Opening

Summarize what you know about using rates, graphs of rates, and formulas.

Cost Versus Weight

Work Time

Cost Versus Weight

  • Graph the formula c = 0.4w. Label the x-axis “weight” and the y-axis “cost.”
  • Write a problem using the information from the graph.
  • What is the independent variable in your problem?
  • Share your problem with a partner. Discuss whether your partner agrees that your problem can be answered using the information from the graph.
  • Challenge your partner to use the graph to answer your problem.

Hint:

For an idea for a word problem, look at the exercises from Lesson 2 that had to do with price.

Volume Versus Time

Work Time

Volume Versus Time

  • Graph the formula v = 4t. Label the x-axis “time” and the y-axis “volume.”
  • Write a problem using the information from the graph.
  • What is the independent variable in your problem?
  • Share your problem with a partner. Discuss whether your partner agrees that your problem can be answered using the information from the graph.
  • Challenge your partner to use the graph to answer your problem.

Distance Versus Time

Work Time

Distance Versus Time

  • Graph the formula d = 35t. Label the x-axis “time” and the y-axis “distance.”
  • Write a problem using the information from the graph.
  • What is the independent variable in your problem?
  • Share your problem with a partner. Discuss whether your partner agrees that your problem can be answered using the information from the graph.
  • Challenge your partner to use the graph to answer your problem.
     

Challenge Problem

  • Write a problem that requires making and using information from graphs to find solutions, similar to the problems you just worked on.
  • Set up the problem with a blank graph, and trade problems with a partner.
  • Make the graph and solve your partner’s problem.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes as you listen to problems your classmates wrote to match the formula and the graph.

Hint:

As your classmates present, ask questions such as:

  • How did you use the formula to make a graph?
  • Where do you see the rate in the formula? On the graph?
  • What strategy did you use to make sense of your partner’s word problem?
  • If you graph any rate formula, do you think it will be a straight line? Why or why not?

Summarize Your Learning

Formative Assessment

Summary of the Math: Summarize Your Learning

Take a moment to summarize the concept of rate.

Hint:

Check your summary.

  • Does your summary explain how to represent quantitative relationships involving rates using graphs and formulas?
  • Does your summary talk about how to create one such representation given another?

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.

The most important thing I learned about rates and quantitative relationships in this unit is…