Additional Properties of Equality

Additional Properties of Equality

Keep Balanced

Opening

Keep Balanced

  • Look at the balance scale in the Balance Scale interactive. 
  • Can you add a number to each side of the scale but still keep the scale balanced? Try it.
  • Based on your new scale, can you subtract a number from each side but still keep the scale balanced? Try it.

INTERACTIVE: Balance Scale

Find the Solution

Opening

Find the Solution

Set up the Balance Scale X interactive as your teacher instructs you. Ignore any instructions in the interactive. Then complete the following.

  • Write an equation that represents the balance scale.
  • Can you add or subtract something from both sides of the balance scale to find the value of x that makes the equation true? Experiment with the Balance Scale X interactive to see if you can find the solution using this method.
  • What is the solution?
  • Substitute your solution for x in your equation to check your answer.

INTERACTIVE: Balance Scale X

Math Mission

Opening

Use the addition property of equality to solve equations.

Apply the Property

Work Time

Apply the Property

Addition property of equality: If you add the same number to both sides of an algebraic equation or subtract the same number from both sides of an algebraic equation, the equations will be equivalent and the equations will have the same solution.

Look at the board to set up each problem in the Balance Scale X interactive. Ignore any instructions in the interactive. For each problem:

  • Write an equation that represents the balance scale.
  • Find the solution using the addition property of equality. Write down your solution steps.
  • Check your solution.

INTERACTIVE: Balance Scale X

Hint:

  • Try to get x by itself on one side of the balance scale.
  • How can you use substitution to check your solution?

Prepare a Presentation

Work Time

Prepare a Presentation

Select one of the problems from Task 4.

  • Explain how you wrote an equation to represent the balance scale.
  • Explain how you used the addition property of equality to find the solution.
  • Explain how you checked your solution.

Challenge Problem

Use the addition property of equality to solve the following equation. Show each step of your work.

  • + 6.7 = 9.45

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes about your classmates’ methods for solving equations using the addition property of equality.

Hint:

As your classmates present, ask questions such as:

  • How did you decide what to add or remove from each side of the equation?
  • Why do you need to do the same thing on both sides of an equation?
  • What could you do if you checked your solution and found that your solution was incorrect?

Solve the Equations

Work Time

Apply the Learning: Solve the Equations

Solve the equations using the addition property of equality.

Show each step of your work, and check your solutions.

  • + 29 = 67
  • x + 312 = 814          
  • + 7.5 = 8.3
  • 219 = x34

The Addition Property of Equality

Formative Assessment

Summary of the Math: The Addition Property of Equality

Write a summary about the addition property of equality and give an example.

Hint:

Check your summary:

  • Do you define the addition property of equality and provide a simple example of how it works? (Use an equation such as 8=8.)
  • Do you explain how to use the addition property of equality to solve equations that are similar to the ones you solved today (such as x+8=19)?

Reflect On Your Work

Work Time

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

One thing that confuses me about solving equations is …