           ## Absolute Value

Materials: index cards

Preparation: make cards for I have…Who Has?

• Say: You'll remember that absolute value is the distance from 0 of a number, no matter which direction from zero it is.

• Ask: Can someone write on the board an equation that means 24 is the absolute value of the number that is 6 less than x?
The equation, 24 = |x - 6|, represents the situation.

• Ask: What can be the value of the expression inside the absolute value symbols?
Students will readily see that x - 6 can have a value of 24. Help them to see that the expression can also have a value of 24. If necessary, remind them of your previous discussion about directed distance from zero as opposed to absolute distance from zero.

• Ask: If the expression can have a value of 24 or 24, what values can x have?
If x equals 30, then x - 6 = 24. If x = 18, then x - 6 = 24. Since |24| = | 24| = 24, there are two possible values for x, 30 and 18. Emphasize that you're asking for the absolute value of an expression, not of the variable itself.

• Repeat the last three questions using a variety of absolute value expressions:
|13 - x| = 14 (x = 1 or x = 27) |25 + x| = 25 (x = 0 or x = 50) 42 = |2x| (x = 21 or x = 21) 1 = | | (x = 36 or x = 36) 0 = |36/x| (There is no value for x that satisfies this equation.)

Wrap-Up and Assessment Hints

• Ask students to write and share their own definitions and real-life examples of absolute value situations.
• Play I have, who has? Make up a set of 15 index cards with absolute value expressions and 15 index cards containing values for the variable:

 Absolute Value Cards Variable Value Cards |x + 5| = 20 x = 15 |5 - x| = 30 x = 25 |x + 6| = 41 x = 35 | 27 - x| = 20 x = 47 7 + |x| = 0 x = 7 |25 - x| = 18 x = 7 |x + 5| = 38 x = 43 |37 - x| = 70 x = 33 114 - |x| = 7 x = 107 | x + 100| = 21 x = 121 |1 + x| = 80 x = 79 |x| = 81 x = 81 |x + 3| = 84 x = 81 |25 + x| = 62 x = 87 |x - 26| = 11 x = 37

Each Absolute Value Card listed has two values for x. These values overlap so that each Variable Value Card satisfies two of the given absolute value equations (the first and second values satisfy the first equation, the second and third values satisfy the second equation, and so on until the last and first values satisfy the last equation). Shuffle the deck and distribute the cards. Be sure they've all been distributed. Choose a student to say "I have" and then read the value or equation on his or her card. Then have the student say "Who has a match for my card?" Either student with a match should say "I have…Who has…" and the game should proceed until all cards have been read. You might have students stand when the game starts and sit as they offer a response. To keep seated students engaged, offer a reward for successful completion of the game, encouraging challenges to suspect responses.

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