Possible or Impossible?

Possible or Impossible?

Critique Denzel’s Statement

Opening

Critique Denzel's Statement

Denzel says that he is thinking of a number and its opposite that are both positive.

  • Is Denzel's statement possible?

In your argument, you should either provide an example that justifies Denzel’s statement or explain why his reasoning does not make sense.

Math Mission

Opening

Justify whether statements are possible or impossible by using the definitions of absolute value and the oppositeof a number.

Possible or Impossible?

Work Time

Possible or Impossible?

Sort the statements into two groups: Possible and Impossible.

  • If possible, give an example.
  • If impossible, explain why.

HANDOUT: Possible or Impossible?

Try different numbers to see if they satisfy the statement.

Value of Expressions

Work Time

Value of Expressions

  • Do the two expressions below have the same value? Explain your thinking.
    −|−3| and −(−3)
  • Is the following statement sometimes true, always true, or never true? Give an example to support your answer.

The opposite of a number is equal to the opposite
of the absolute value of the number.

  • Sort the cards to show whether the statements on the cards are possible or impossible. Provide an explanation.

INTERACTIVE: Card Sort: Opposite and Absolute Values

  • For the first question, do each step—start inside the absolute value symbols or inside the parentheses.
  • For the second question, test different numbers. Try positive and negative numbers and 0.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Present one statement you said was possible. Provide more than one example using integers, fractions, and decimals to support your reasoning.
  • Present one statement you said was impossible. Provide a complete explanation that the class will understand.

Challenge Problem

  • Write a statement like the ones in the card sort.
  • Give your statement to your partner. Have your partner either find a pair of numbers that satisfies the statement or explain why it is impossible to do so.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes on which statements belong in the Possible group and which statements belong in the Impossible group. Include examples and explanations in your notes.

As classmates present, ask questions such as:

  • What strategy did you use to decide if the statement was possible or impossible?
  • How do you know this statement is impossible?
  • How do you know your example fits the statement?
  • Can you sketch a diagram to help you justify the statement?
  • Explain each term in the statement and what it told you about the numbers.

Absolute Value and the Opposites of Numbers

Formative Assessment

Summary of the Math: Absolute Value and the Opposites of Numbers

Read and Discuss

  • Absolute value: The distance a number is from 0 on a number line. The symbol |a| is used to indicate the absolute value of a. |a| is a, if a is positive. |−a| is a, if a is negative.
  • Opposite of a number n: The number that is the same distance from 0 as n but on the other side of 0 on a number line; 0 is its own opposite. The opposite of a is −a.

Can you:

  • Write a definition for the terms absolute value and opposite of a number?
  • Explain what signs a number and its opposite have?
  • Explain what sign the absolute value of a number has?

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.

It was difficult to decide whether the statement about _____ was possible or impossible because...