Determine if each statement below is always true, sometimes true, or never true. If it is not always true, give a counter example to disprove the statement. For an extra challenge, rewrite the false statements to make them true. You can record your answers in your notes.

1. Based on the examples: twelve times one-half equals six; twelve times one-fourth equals three; twelve times two-thirds equals eight12 * 1 2 = 6, 12 * 1 4 = 3, 12 * 2 3 = 8, we get the following statement:
     “Multiplying a number by a fraction results in a smaller number than you started with.”

• Always true?  Sometimes true? Never true?
• Counter example?
• Rewrite?
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• Sometimes true.
• Counter example:twelve times three-halves equals eighteen 12 * 3 2 = 18
• Possible Rewrite: "Multiplying a positive number by a fraction less than one results in a smaller number than you started with."

2.“Every quadrilateral with two pairs of congruent sides is a parallelogram.”

• Always true?  Sometimes true? Never true?
• Counter example?
• Rewrite?
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• Sometimes true.
• Counter example: A quadrilateral with two pairs of congruent adjacent sides is a kite.
• Possible Rewrite: "Every quadrilateral with two pairs of congruent opposite sides is a parallelogram."

3.“For all real numbers x, x² > x.”

• Always true?  Sometimes true? Never true?
• Counter example?
• Rewrite?
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• Sometimes true.
• Counter example: 1² = 1
• Possible Rewrite: "For all real numbers x, x² ≥ to x."