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Wednesday, December 11, 2013

Fluency with Double Digit Addition

I spend so much time in grade 2 working with kids on thinking strategies for double digit addition. First, I make sure they are comfortable adding and subtracting 10 from any 2 digit number we do many problem strings and spend time sharing strategies and ideas.  By the end of grade 2, I expect that kids will fluently be able any two double digit numbers in their heads.  I NEVER introduce the standard algorithm for addition of 2 digit numbers because it makes kids stop thinking about the math and just do it and because I really don't believe anyone should need the traditional algorithm to add two double digit numbers.  Everyone should develop the skill of doing it in their head.

Why is it so important that kids are fluent with this by the end of grade 2?


In grade 3 we get into strategies for multiplication facts and MANY of these strategies only work if students can quickly and easily add double digit numbers.

Example 1: 4x9= ?

The student decides to double the 9 to get 18.  They then have to do 18+18.  If this is easy and effortless and does not require paper it helps kids learn multiplication facts much quicker.  If they have to write 18+18 down and do the traditional algorithm or if they do not have an efficient and reliable method to figure out the answer, they are stuck.  They don't learn their multiplication facts as quickly as their peers and that will hurt them for years to come.

Example 2: 6x8=?

The student sees six groups of 8.  They know 2 groups of 8 is 16.  16+16 will give them 4 groups of 8.  32+16 will give them six groups of 8.  They just had to do 2 double digit addition problems.  See why fluency with this is important?

So how do I get them there?  Here are a few quick, easy and low to no prep ways I have kids practice this skill at the end of grade 2.  I do these after a lot of whole group instruction around strategies for adding two double digit number.  I also pull these out just as we are about to head into our multiplication fact unit in grade 3 and add them to math stations to make sure ALL KIDS are fluent with this.  If I have to, I do a small group intervention with third graders to get them solid on this skill.  Since I started assuring kids could fluently add double digit numbers before introducing multiplication facts, kids have learned their multiplication facts faster and with less frustration.

Flip and Add

This is one of the first ways I have kids practice independently or with a partner.  They just flip 2 cards from my place value to 120 deck.  The visual image of the  base 10 pieces supports kids who still need it.  I sometimes have them flip and add alone and sometimes with a partner.  I also sometimes have them make a simple record sheet like the one shown below.  I also use these cards as exit tickets.  I pass out 2 to each kid and they can line up when they know the answer.  I stand by the line and each kid tells me the answer as they line up.  

Rolling Dice

20 Sided Dice (level 1)

I have a huge bucket of 20 sided dice and I like to use them for a quick, easy and no prep addition fluency game.  Students simply roll 2 dice and add the numbers.  They can do this alone or with partners.

This student is adding 12 and 6.  See how having this skill will help support them when they learn 3X6?

These students rolled 17 + 19.  They have to think about regrouping.  These kids ended up doing 17 + 20 = 37 and then subtracted 1 since they were only supposed to add 19.  37 - 1 = 36.  

The Infamous 7 dice (level 2) 

Earlier this week, I posted about how I use the same set of  7 dice in classrooms from grades K-6.  I like to get 2 of these dice out once kids are fluent with adding the 20 sided dice and do the same thing.  The numbers are mostly in the 20's and many require thinking about regrouping. I often don't use record sheets for these games but occasionally do, especially if I have a large class or am unsure about how accurate they are.  
With this roll, kids can just add the 10's and add the 1's.  Straightforward but important to make sure kids have fluency at this level.
This pair brings up a lot of good ideas about thinking strategies and what parts to add first.  

Bringing out the big dice (level 3)

Once kids have shown me fluency using the last set of dice, I like to give them even larger double digit numbers to work with.  These will include some where the sum is over 100.  I have a set that I made out of card stock that I like to use to introduce this part to the whole group because they are REALLY BIG.  I also make my own double digit number cubes with higher numbers using blank dice.

I made an origami cubes following these directions.  I have also made these cubes with students.  I find some second graders are successful but third grade and up is the best choice if you are making these with students.

Students love rolling and adding with these big dice and it gives them the extra practice they need to achieve fluency.  
What do you do to make sure your kids are fluent with double digit addition?  Please respond in the comments below!


  1. I, too, do not teach my students algorithms for two-digit addition. I think it's so much more useful and efficient for them to learn to do math mentally. It takes so much more thought and demonstrates so much more understanding.
    I struggle, though for two reasons...
    1. Without fail, when parents see it on homework, they teach the child the algorithm.
    2. The third grade teachers expect the students to know how to use the algorithm.
    Any suggestions?

    1. No ideas but I'm curious about this too!

    2. I address these two issues in a few different ways. First I never send multi digit addition or subtraction for homework in second grade. It just isn't worth it because parents teaching kids "how to do it" undoes the work I do around conceptual understanding and flexible thinking.

      Second, I have the advantage of also being in the third grade classroom. It took some years of convincing but now the third grade teachers I work with have seen how much better it is when kids think about math rather than doing it. You also have the common core on your side. It specifies that students need to show mastery of a standard algorithm for addition and subtraction by grade 4. That is a long way off from second grade. I would also invite the third grade teachers into your classroom when your kids are doing some of this great conceptual development. Keep having the conversation in your building and keep sending them links to blog posts about other ways to think. I have written about this issue multiple times and there are other bloggers out there writing about it as well. Good luck!

    3. I thought of one more thing. Talk with the third grade teachers about how their students learn multiplication facts. If they are using the distributive property and building up, do the watchers want kids to have to write out and solve double digit addition problems with the standard algorithm or do they want them to be able to do it mentally? I have never met a third grade teacher who wants to add extra steps to the processor learning multiplication facts.

    4. I teach both and leave the option to the students. With a dual curriculum we have very little time and it is very VERY hard to explain to second grade kids the mental math concepts.

    5. It definitely takes more time to teach kids to think about math rather than just do it. I find the initial time invested up front saves me time in the long run when kids "forget" the algorithm and have to be re-taught it in third grade, and fourth grade and fifth grade.