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Always Sometimes Never Dice Activity for Real Number System

I created this always sometimes never dice activity for classifying numbers according to the real number system. We completed this after sorting numbers using our Real Number System Nesting Boxes.

photograph of colorful dice with text "always? sometimes? never? real number system dice activity."

I always hated Always, Sometimes, Never questions when I did them as a geometry student in high school. But, I decided to give it a go with my students.  So glad I did!

Always, Sometimes, or Never activities can be used with a wide variety of math topics.

Each student got an Always, Sometimes, or Never sheet to glue in their interactive notebooks.

Always Sometimes Never Dice Activity for Real Number System

On the board, I wrote the numbers 1-6.  I asked them to list different types of numbers.  They quickly came up with 5: natural, whole, integers, rational, and irrational.  It took a few more moments before someone remembered that those are all types of real numbers.

I handed out one jumbo foam die to each table group.  The other math teacher I work with gave me these last year, and my students and I have had so much fun with them!

Always Sometimes Never Dice Activity for Real Number System

This picture shows me using two foam dice, but I just did that to show how I got each box filled in for my #Teach180 tweet.  I had my students just roll one die two times.  This meant they had to write the number subsets in a certain order instead of being able to choose which subset went in which slot.

I did an example of how the activity worked on the board for students to see.  Then, I set them loose to do 5 as a group.  I went around and stamped them after I checked them.

Look at these cute stamps I picked up at Dollar General!  They were 5 for a dollar.  I’m not sure how long they’ll last, but the kids were definitely amused with them for this activity!


It was great to just be able to walk around and eavesdrop on their conversations.  When I noticed students were struggling, I brought over the nesting boxes for them to use.  One group had rolled this sentence: An integer is a natural number.  Half the group thought it was always true.  The other half of the group thought it was sometimes true.  So, I held up the integer box for them.  You have a number in this box.  Is it always in the natural number box or is it sometimes in the natural number box?  Looking at it this way, the answer seemed obvious to them.  Soon, I had groups fighting over who got to keep the nesting boxes sitting at their desks.  They informed me that I needed to make a set of boxes for reach group because they really helped.

I tried explaining that this was the same as the graphic organizer I had given them, but they weren’t buying it.  I think rolling the die to make the problems was the real selling point of this activity.  I’ve found that anytime I pull out the dice that my kids get excited.  There’s just something special about when the dice decide your problem instead of the teacher!  I found this was the case last year when working with point slope form!

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    1. I took cardboard boxes, cut off the flaps, and covered them in colored paper. I've seen others use aluminum cans, as well.

  1. I love this idea as well! I know sometimes the graphic organizer doesn't always click with students. I didn't have enough boxes to recycle, so I went to the dollar store, and bought various sizes of the aluminum baking pans. I was playing around with different sizes in the store to make sure they would stack how I wanted, and I was able to make it work. I'm not going to cover them entirely, yet, but I will color coordinate them and write on them to use this week. Thanks!

  2. I just want you to know that I heard about you on NPR before I graduated College, and I looked you up, and I am so impressed with your ideas and your enthusiasm. I just started my first year teaching at a small school, and I teach calc, pre-calc, algebra II, and Applied math. I am so excited to find so many hands on activities and great ways of explaining math on your website. Thank you for being an awesome teacher!

    1. Thanks Alexis! Hope your first year is going well! Let me know if there is ever anything I can help you with.

  3. I used your "Always, Sometimes, Never" assignment today with my Algebra 1 students. I heard some really interesting conversation and some good arguing (gotta love a good math argument!). Thanks!!

    I took to heart what you said about the students wanting to use the Real Number diagram. So I went to my local Dollar Tree and bought a bunch of different sized bowls. Then, students used post-it notes to label them. That way I could just buy 6 sets of bowls (for each group) and save some money. Here's a link to some pictures:

    I also did a card sort where they put different numbers into different sections. I think the model really helped them!

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