Concept Byte: Always, Sometimes, or Never

Use With Lesson 1-5

ACTIVITY

A statement can be always, sometimes, or never true. For each activity, work with a group of 4 students. Take turns predicting each answer. If the predictor gives a correct answer, he or she scores 1 point. Otherwise, the person who proves the predictor incorrect scores 1 point. Whoever has the most points at the end of an activity wins.

Activity 1

Is each description always, sometimes, or never true about the members of your group?

1. takes an algebra class
2. lives in your state
3. plays a musical instrument
4. is less than 25 years old
5. speaks more than one language
6. is taller than 5 m

Activity 2

Suppose each member of your group takes one of the four cards below. Will a group member chosen at random always, sometimes, or never have a number that fits each description?

7. greater than 2
8. greater than 25
9. even
10. irrational number
11. prime number
12. rational number

Activity 3

Each member of your group substitutes any integer for x in each statement. Will a group member chosen at random always, sometimes, or never have a true statement?

13. x − 2 x minus 2  is greater than x.
14. | x | absolute value of x ,  is less than x.
15. 7 + x = x + 7
16. 13 − x = x − 13 13 minus x equals x minus 13
17. x + 0 = x
18. − 4 + ( 3 + x ) = x + ( − 4 + 3 ) negative 4 plus open 3 plus x close equals x plus open negative 4 plus 3 close
19. x ÷ 5 x divides 5  is less than x.
20. x · 0 = 0 x middle dot 0 equals 0
21. x + 9 is less than x.
22. | x | absolute value of x ,  is greater than x.

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