## 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 reasonings with the whole group later.

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

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 reasonings with the whole group later.

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

- Max gets a pay raise of 30%. Jim gets a pay raise of 25%. So Max gets the bigger pay raise.
- When you cut a piece off a shape, you reduce its area and perimeter.
- If you add the same number to the top and bottom of a fraction, the fraction gets bigger in value.
- 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.
- (
*a*+*b*)/2 ≥ (*ab*)^{1/2} - If you divide the top and bottom of a fraction by the same number, the fraction gets smaller in value.
- It doesn't matter which way you multiply, you get the same answer, like
*a × b*=*b × a*. - If you add a number to 12, you get a number greater than 12.
- The square root of a number is less than the number.
- It doesn't matter which way you divide, you get the same answer, like
*a ÷ b*=*b ÷ a*. - If you divide 12 by a number, the answer will be less than 12.
- The square of a number is greater than the number.
*p*+ 12 =*s*+ 12*(n*+ 5) is less than 20- 2(
*x*+ 3) = 2*x*+ 3 - 3 + 2
*y*= 5*y* - 4
*p*is greater than 9 +*p* - 2(3 +
*s*) = 6 + 2*s*

Wow, what a simple but wonderful idea for engaging students in real math. Thanks for sharing this, Fawn - I'll definitely use it with my students.

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It works quite well, Peter, and the kids really have to think about it. I was actually "happy" to see how poorly my 8th graders did because it showed me they made a lot of assumptions, and if I didn't do this activity, then it all goes unchecked. And these ASN statements are perfect for the geometry students too -- I wish I could record and playback their conversations! Thanks for dropping by, Peter.

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What I love is that the students can't answer without thinking, or without really delving into the math in each statement. There are no routines that can be dredged from one's memory to answer. Yet at the same time with the right questions, they are quite achievable for students.

Love it!

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This is a seriously cool idea. I think I can use it in my College level course when we do a bit of remedial algebra.

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Thank you for stopping by, Dr. Nic. It's better than True/False questions because you have to think about it a little more

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Please tell me where the answers to this are listed (the always, sometimes, never) and are their explanations?

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Hi Karen,

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Did you write all these problems yourself? I want to do this activity with my middle school students, but I am terrible at writing my own problems.

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Hi Karen. I provided a link above to say where I got them. You can also look for True/False questions in the textbook for ideas. My geometry textbook also has a bunch of these Always/Sometimes/Never.

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It's a very good idea to engage students with activity oriented learning. Thanks!

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