Multiplication Properties of Equality

Multiplication Properties of Equality

Multiplication Property of Equality

Opening

Multiplication Property of Equality

The definition of the multiplication property of equality states:

If a = b, then ac = bc.

Discuss the following with your classmates.

  • Where is the multiplication property of equality used in this example?
  • How would you use a ratio table to solve this problem?

“Ask Myself” Questions

Opening

“Ask Myself” Questions

When working by yourself, you should:

  • Make sense of the problem.
  • Use “ask myself” questions to see what you need to understand before starting.
  • Persevere through difficulty by using what you do know.

Read the worked problem. Then watch your teacher give an example of how to use “ask myself” questions to understand the problem.

  • Solve the problem using a ratio table and using an equation.
  • Describe how you used the multiplication property of equality to solve the equation.

Hint:

Here are ideas for “ask myself” questions:

  • What does ____ mean?
  • What is this problem talking about?
  • What kinds of comparisons is the problem looking at?
  • What are the numbers in the problem and what do they mean?
  • What is the problem asking for?

Here are ideas for what to do if you get stuck:

  • Look at similar problems you have solved previously.
  • Model the problem using counters or other materials.
  • Sketch a diagram or other representation.
  • Write what you do know.
  • Write down questions to ask later.
  • Check other resources.

Math Mission

Opening

Compare different strategies for solving a ratio problem.

Use Different Strategies

Work Time

Use Different Strategies

Work on your own to solve this problem using a ratio table and using an equation. Then work with a partner.

A local hospital has a rule that the ratio of nurses to patients must be 1 : 12. A hospital expands to fit 672 patients. How many nurses does the hospital need?

  • Explain your strategies to your partner. Challenge your partner to have clear and complete explanations.
  • Describe how you used the multiplication property of equality to solve the equation.

Hint:

  • What questions did you ask yourself before you worked on this problem?
  • Remember to multiply both ratio quantities by the same value to preserve equality.
  • The multiplication property of equality states that if you multiply both sides of an equation by the same quantity, the sides remain equal.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Compare how your strategies for solving the problem are similar and different.
  • Justify your solution using the multiplication property of equality.
  • Identify any mistakes you made and what you learned from them.
  • Include any questions your partner asked about your explanation.

Challenge Problem

Tips at a restaurant are split among employees. The ratio of tips earned by servers to greeters to clean-up team is 11 : 5 : 2. The clean-up team earned $20.80 from tips one night.

How much did the servers and greeters earn from tips in the same night?

  • Solve the problem using a ratio table.
  • Solve the problem using an equation.
  • Identify where you use the multiplication properties of equality in your solutions.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about how your own strategies to solve the ratio problem are similar to and different from your classmates’ strategies.

Hint:

As your classmates present, ask questions such as:

  • Did you find it more difficult to use the ratio table or the equation to solve the problem?
  • How is your way of solving the problem with an equation similar to using a ratio table?
  • Why does the multiplication property of equality help you solve the equation?

What Is a Good Summary?

Formative Assessment

Summary of the Math: What Is a Good Summary?

A good summary clearly explains important mathematics of today's lesson.

  • Write a summary comparing different strategies for solving the ratio problem.

Hint:

Check your summary.

  • Do you describe how the different strategies for solving the ratio problem are similar and different?
  • Do you explain why the multiplication property of equality is useful for solving ratio problems?
  • Do you define justify?

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 multiplication property of equality is useful because…