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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5 Comments

  1. Kim Barbaro
    Posted August 14, 2014 at 1:35 pm | Permalink

    Fawn,

    I am a huge fan btw! I can always count on you for insightful resources. As school starts in a week I am rabidly gathering bon mots I see on the web to use in my classroom. I teach 6th grade math and science in Winnetka, IL.

    I love this idea of ASN–I want to use it in my class for a beginning of year, see where kids are at the start of the year–kind of activity.

    I wondered when in the year you were using this and besides generating thoughtful discussions and giving kids practice in justifying their thinking, what was your objective in doing this in your class?

    Please advise and thanks!

    –Kim

    • Fawn
      Posted August 16, 2014 at 10:39 am | Permalink

      Hi Kim. Thank you so much for the kind words. Really happy that you’ve found something useful here. ASN can be used any time during the year, completely dependent on the statements that you put in front of them. A good source for these might actually be your textbook. (See, they are not just good for making ramps and propping doors open :) ) Just change the questions you find in the textbook into statements and use them for ASN. Out of the 8 math practices, MP1 and MP3 loom largest for me, and ASN is a great way to get to kids to engage in MP3. We want to be “generating thoughtful discussions and giving kids practice in justifying their thinking” every day of the year.

    • Claire Toland
      Posted November 8, 2016 at 6:52 am | Permalink

      Hi,
      Do you have an answer key for this activity?

      Thank you,

      Claire Toland

  2. Posted November 8, 2016 at 6:53 am | Permalink

    Do you have an answer key for this activity?

  3. Krizzle Dapito
    Posted January 25, 2017 at 3:52 am | Permalink

    Hi! Do you have some questionnaires for Algebra and Geometry that can be answered by Always, Sometimes and Never?

7 Trackbacks

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    […] want parents to observe their children do Taco Cart and Always, Sometimes, and Never. I want them to listen in on the kids’ math talks. I want them to walk in on a day when […]

  • […] did I hear about this strategy? I first saw this strategy on Fawn Nguyen’s blog. I strive to get as much mathematical thinking out of my 11th/12th graders as she gets out of her […]

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