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Saturday, April 20, 2013

Using dice to promote fluency with additive reasoning

I work with kids from kindergarten right up through grade 6 and there is one activity that I do with kids in all grades.  It is simple, fast and very effective.  It is a simple dice game where kids are rolling and adding or rolling and subtracting.  There is not record sheets to copy or materials to prep and the kids love it.  If you want kids to keep a record of their rolls, it is quick and easy to have them make their own record sheet.  Let me take you from K up through the grades to see how this rolls out.

Kindergarten and Early/Intervention Grade 1

I use dot dice or my large foam dice and have kids start with 2 and roll and add them.  We add more and more dice as the kids are ready for more challenging numbers.  In the beginning, kids count each dot one by one.  As the year progresses, they start counting on and even adding two together before counting on the rest. 

In this picture are my over sized foam dice.  VERY ENGAGING for small kids, especially kids  who need more movement.  In this example, kids could count all the dice, count on from one number or do some combination of counting and adding.  Using the dot dice puts the game at a reachable level for all K kids.

Grade 1/Advanced K/Intervention 2

The next step in this game is to use the 1-6 numeral dice.  Same rules and regulations apply.  Students start by rolling and adding the 2 dice.  When they show proficiency with this, I change the game in one of two ways.  I have them roll and add with more dice (grade 1 common core has students adding 3 addends up to 20) or I have them roll 2 dice and find the difference.  

Here is the 1-6 numeral dice with a 5-10 numeral dice thrown in to challenge students.

Here is an example of a time where I wanted first graders to create a  record sheet to go with their game.  They just record the sum they got and draw a line on a small white board.  When they get that number again, they write it beside the first one.  I have used this simple record sheet idea over and over again at all these different levels of this dice game.

Grade 2/Advanced 1/Intervention 3

I start the year in grade 2 with a lot of work on the 12 sided dice.  I give each pair 2 and they do a lot of practice with roll and add and roll and subtract.  As they show proficiency at this level, I give them additional dice until they are rolling a small handful.  This is when they really begin anchoring on 10 and spend a lot of time moving dice around and making tens.
An example of a student rolling 5 12 sided dice.  They might pull the 8 and 2 together to make a ten and then the other eight and the two fours together to make 16 and then add 16 + 10.  All of this is done mentally and it bridges nicely into the work second graders have to do with multi-digit addition in the common core
 Next we move into adding some small 2 digit numbers.  I have a few dice with 2 digit numbers but have purchased a bunch of blank dice and made my own.
The next step for second graders is adding small 2 digit numbers with other small 2 digit numbers.  You can see in this shot, one of the dice is one I chose the numbers for.  I highly recommend hat teachers have a few bags of blank dice at all times.  You can custom make games for your students so easily if you start with blank dice
Followed by adding in more dice

Having 3 addends brings out all kinds of strategies!

And more dice......

You can see this student is grouping some of his dice.  The 15 +5 is a nice chunk that makes 20 and the 28 + 2 makes 30.  I see kids doing this (making friendly 10's) a lot as I add more and more dice.  Being able to roll and add this many dice is my goal for the end of second grade.

Another important second grade skill is counting mixed coins.  Do you see how these dice can keep kids practicing counting mixed coins?

Third and Fourth Grade

We continue to refine strategies for adding multiple 2 digit numbers mentally.  We play this game as a quick warm-up at the start of math classes a few times a month.  Sometimes we will add in a dice with 3 digit numbers on it to keep things fresh.  (It really helps to have a big bag of blank dice so that you can customize your games as you go!)

How would you find the sum of these 8 dice?

Grades 5 and 6

This game keeps on coming with more practice with additive reasoning but the numbers have changed a great deal by this point.  In our school (and in the common core!) there is a lot of focus on fraction and decimal operations at fifth grade and by the end of grade 6, I want them to be very fluent with these ideas.  Being fluent with fraction operations is a very important cornerstone to kids developing proportional thinking in middle school and manipulating fractions becomes very important as kids delve into algebra. I love using fraction dice with kids this age because it is a fun way to promote fluency.

Fifth grade students playing a simple roll and add game with a self made record sheet. 

Sixth grade students rolling and adding a variety of fractions.  As more dice are added, kids think more and more about combinations that make one.  This time the kids are playing with no record sheet

Fifth and sixth grade students work on adding a combination of fractions and decimals.  This game is also easily adapted to roll and find the difference

Kids who have been working with percents fractions and decimals roll and add all three types of dice.  It is very interesting to watch this and see which students think in decimals and which think in fractions

These games make great warm-ups in fifth and sixth grade and would also benefit plenty of older students!  One more version of the game I use with sixth graders is with my integer dice.  The common core moves some of the emphasis on integer operations up to seventh grade, but I find this dice game a nice match for sixth graders as well.  Especially those sixth graders who are really proficient with fractions and ready to try something new.  So sometimes while some sixth graders are still playing these games with fraction or decimal dice, I give these integer dice to kids who are ready for the next step.

Integer dice roll and combine

Do you use dice in your classroom to promote fluency?  How else do you use dice in your classroom?

Looking for more ideas?  Check out this post about how I use a set of seven dice to work on double digit addition and subtraction.  


  1. Thanks! Such a great way to practice fact fluency (and so easy to differentiate for different levels!)

    Learning to the Core

  2. Hi Amanda
    Thanks for the comment! I hope you found some useful ideas!

  3. Great post! I'm featuring this on Bagels and Blogs tomorrow. :)

    Math Coach’s Corner

  4. May I ask where you got the dice that have fractions, percents, and decimals on the same die? I would LOVE to get some of those for when we are converting. Thank you for sharing these wonderful ideas!

    Eclectic Educating

    1. Hi Amy,
      The fraction, decimal and percent dice are from EAI Education. Here is a link to the product page
      EAI education has a nice selection of dice. MANY of the dice in this post are from there. Here is a link to their dice page
      Thanks for stopping by!

  5. I'm glad I can follow you now. The last time I visited, I didn't see an easy way to do that. I'm looking forward to reading your posts!
    ❀ Tammy
    Forever in First

  6. Hi Tammy,
    Thanks so much! I figured out how to make the follow me process easier this morning. All thanks to the help of other teacher blogs!

    I love your blog!

  7. Replies
    1. Hi Barbara!
      I am so excited to have you as a follower. I can talk all day about math!

      Love your blog design!

  8. Hi!!

    I found you in a roundabout way through the Manic Monday Linky - you commented on a post at Eclectic Educating right above me... Anyway, I have a real passion for math, and I'm your newest follower! :)

    Mrs. Beattie's Classroom

    1. Hi Erin!
      I am so glad you found me. I have a lot to say about math, that's for sure!


  9. Love this especially because I'm secretly obsessed with dice. :)
    I'm a new follower.

    1. I share your obsession. I have an entire shelf full of dice. They make me a better teacher


  10. your blog is really useful for many people I think. Because many times I have found the useful information which was really important for me. Reading this your post was good.

    Multiplication strategies

  11. What a wonderful blog post... this makes the student really enjoy learning math. Thanks for sharing! :-)