Always Sometimes Never

I did Always-Sometimes-Never (ASN) questions with my 6th graders.  The kids were randomly paired up to work on placing 18 mathematical statements into appropriate columns: always true, sometimes true, and never true.

The students were really involved in the discussion and coming up with examples.  They had to translate some of the statements into equations or inequalities and defend their answers.  They learned to give counterexamples.ASN works for any math level (and could really be used in other subjects).  The kids are comfortable working and having that math conversation with just one other person initially, then they build up the confidence to share their reasoning with the whole group later.

I got this particular set of 18 from Swan and Ridgway.  Sixth Sense has a set also.

  1. Max gets a pay raise of 30%.  Jim gets a pay raise of 25%.  So Max gets the bigger pay raise.
  2. When you cut a piece off a shape, you reduce its area and perimeter.
  3. If you add the same number to the top and bottom of a fraction, the fraction gets bigger in value.
  4. In a sale, every price was reduced by 25%.  After the sale, every price was increased by 25%.  So the prices went back to where they started.
  5. (a+b)/2 ≥ (ab)1/2
  6. If you divide the top and bottom of a fraction by the same number, the fraction gets smaller in value.
  7. It doesn’t matter which way you multiply, you get the same answer, like a × b = b × a.
  8. If you add a number to 12, you get a number greater than 12.
  9. The square root of a number is less than the number.
  10. It doesn’t matter which way you divide, you get the same answer, like a ÷ b = b ÷ a.
  11. If you divide 12 by a number, the answer will be less than 12.
  12. The square of a number is greater than the number.
  13. p + 12 = s + 12
  14. (n + 5) is less than 20
  15. 2(x + 3) = 2x + 3
  16. 3 + 2y = 5y
  17. 4p is greater than 9 + p
  18. 2(3 + s) = 6 + 2s

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