Reasoning to Identify Solutions

Reasoning to Identify Solutions

Reasoning to Find a Solution

Opening

Reasoning to Find a Solution

Look at this equation and think about its structure:

+ 5= 5+ 16

  • Does the structure give you a clue about the solution to the equation?
  • Find a solution and check to make sure your solution is in fact the solution.

Math Mission

Opening

Use reasoning and substitution to find solutions to equations.

Find Solutions

Work Time

Find Solutions

  • Take turns with your partner. Match an equation card with a solution card.
  • Explain to your partner how you know that the cards match. Your partner should agree with your explanation or challenge it if your explanation is not correct, clear, and complete.
  • Record the steps you took to find the solution for each equation.

HANDOUT: Card Sort

Hint:

  • There is a value of the variable that makes the two sides of the equation equal. Think about what this value could be.
  • Does the structure of the equation give you any clues about its solution?
  • Try substituting different numbers on the solution cards into an equation to find the solution to that equation.

Prepare a Presentation

Work Time

Prepare a Presentation

Be prepared to share your matches and explain how you know that those cards match.

Challenge Problem

  • Find a solution to this equation:

4+ 5 + 6− 3 = 4(+ 5)

  • Explain how you know your solution is correct and how you found it.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes as your classmates explain how they matched the solution cards to the equation cards.

Hint:

As your classmates present, ask questions such as:

  • How did you decide which number is a solution to
    that equation?
  • Are there other solutions to that equation?
  • Could you tell what the solution was from looking at the structure of the equation?
  • Why do you think that equation has no solutions?
  • Why do you think all numbers are a solution to that equation?

Solutions to Equations

Formative Assessment

Summary of the Math: Solutions to Equations

Write a summary about finding solutions to equations.

Hint:

Check your summary:

  • Do you explain how to find a solution to an equation?
  • Do you explain how looking at the structure of an equation can help you find the solution?
  • Do you explain how to show that a number is a solution to an equation?
  • Do you provide examples of equations that have more than one solution or no solutions?

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.

An equation can have more than one solution when …