Using Dot Cards to Build Number Sense - Math Coach's Corner
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# Using Dot Cards to Build Number Sense

### Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.
##### Freebies | Grades K-2 | Number Sense

“…that ability to ‘just see it’ without counting is called subitizing.” (Van de Walle)

There’s no doubt about it…subitizing is all the rage!  It’s not a new concept, though.  According to Wikipedia the phrase was first used in 1949.  So why are we just hearing about it now?  My theory is that the popularity of subitizing is directly related to the implementation of the Common Core State Standards for Mathematics, which stress conceptual understanding and number sense over rote memorization of mathematical procedures and facts.

Not surprisingly, John Van de Walle’s books have featured activities related to subitizing for many years.  I enlarged some of Van de Walle’s cards (shown below) so they would be easier to use, and you can grab them here.

You can also easily make dot cards using large index cards and colored labels.  Van de Walle suggests using paper plates, but I find index cards or cardstock cut in half are easier to store and use.  I hole punch them and put them on an O-ring.  Make multiple configurations of each number.  In the picture below, you see four different cards showing the number 3.  Using different colors of dots helps students see how smaller numbers combine to make larger ones.

So, now that you’ve made your dot cards, how exactly do you use them?  First off, you want to develop routines for using your dot cards.  You don’t want to flash a card and just have students shout out the number.  Start out, obviously, with smaller numbers.  Even if you are subitizing in 1st or 2nd grade, if your kiddos haven’t subitized before, you need to start with smaller numbers.  I like to have kiddos seated on the floor in front of me.  I use a strategy I saw on the DVD that accompanies Sherry Parrish’s book, Number Talks: Helping Children Build Mental Math and Computation Strategies.  Flash a card briefly.  When a child thinks they know the number shown on the card, they put a thumbs-up against their chest.  Totally silent!  You want to be able to look for those kiddos who are counting the dots one-by-one and also see how quickly each student determines the number.  Call on “thumbs” one by one and ask what number they saw.  Don’t be surprised if you get different responses!  Avoid the temptation to comment on responses.  Use a good poker face and just accept all answers.  Next, show the card again and call on several students to tell you how they knew what number was on the card.  There is no “right” answer.  Looking at the cards above, you might have kids say:

• I saw 2 and 1 more and 2 plus 1 equals 3
• I just saw 3
• I counted…1, 2, 3
• There’s 1 blue dot and 2 red dots and that makes 3

Notice how each of those responses tells you something very important about the child’s understanding of numbers.  Repeat for different cards.  This is a quick, whole-class daily routine that has a huge payout!  You also want to use the dot cards, however, in small group instruction to differentiate your instruction.  For example, the first kiddo in the example above is probably ready to work with larger numbers and combinations while the third kiddo is not subitizing at all.

5- and 10-frames are powerful tools for building those all-important benchmarks of 5 and 10, and they should also be part of your subitizing routines.  They can be used in much the same way as random-pattern dot cards.  A great resource for using 10-frames in your classroom is It Makes Sense!: Using Ten-Frames to Build Number Sense.  Click here to download blank ten-frames (3 to a page) to make your dot cards.

Go forth and subitize!!

You might also want to check out these posts on DIY rekenreks and number bracelets.

1. Thank you. I needed more ideas about what to do.

2. I’m very much inspired when I’ve visited your blog. Your blog is really informative. Hope you will continue with new article.

3. Hi Donna, I love the dot cards and have incorporated them into my daily number sense! Thank you for sharing. I have created my math structure based on a program called BUILD! Have you heard of it? Basically, my kids are composing and decomposing numbers daily to increase number sense. Check out my blog – I highly suggest it for your teachers! 🙂

http://buildingkindergartennumbersense.blogspot.com/

Angelica

• Thanks for sharing, Angelica. I’m a big believer in a workshop approach! Yes, I’ve heard of BUILD–it’s very similar to the GUIDE structure Laney Sammons uses in her Guided Math books.

4. Thank you for the cards! I’m confused where you said “the third kiddo is not subitizing at all.” At the very beginning of the post you quoted, “…that ability to ‘just see it’ without counting is called subitizing.” (Van de Walle) So are they supposed to see an equation in order to be “subitizing”?

• Hey, Whitney! No, they don’t need to see an equation, but they can’t count. Notice that the third student said he “counted…1,2,3.” In other words, he had to count the individual dots to know there were three instead of just seeing a group of three. Does that make sense?

5. You might be interested in this study on subitizing http://www.optomlab.com/pubs/sub_arit.htm My take aways are that children who struggle in math struggle with subitizing, the ability to subitize improves with practice, basic arithmetic skills improve when the ability to subitize improves. Thanks for the enlarged dot cards.

6. I love the using 10 frames to build number sense book. It is full of ideas and routines if you are just getting started or if you have been using 10 frames for a long time. It is a resource that all primary teachers should have access to. It makes a great discussion book for professional learning committees as well.

Tara
The Math Maniac

• Me, too, Tara!

• Thanks Donna! Can’t wait to see it!

Tara
The Math Maniac

• I absolutely agree about the book, Tara. I also love their hundred chart book, and a little birdie tells me that there’s a number line book in the works. 🙂

7. I love your blog! You always give me great ideas and they are usually very easy to implement. Thanks!

• Thanks, Kelly!! It’s totally my pleasure to share math ideas, and it’s always nice to hear that my blog is useful to teachers. 🙂

8. Thanks for the great thoughts! I want to implement this in a third grade classroom. Should I still start with smaller numbers, and build as I see students progressing? Should I/could I tie our subitizing to multiplication?

-Mary Kate
Windy City Learning

• Yes, Mary Kate, if your kiddos have not subitized in the past, I think it’s totally appropriate in 3rd grade. They will likely catch on and move to larger number fairly quickly. You will likely have kiddos who make the multiplication connect, for example describing a card showing two groups of 5 as 5 x 2. Just be sure to let them make that connection on their own. Much more powerful.

9. I love the Number Talks book! It is helpful for planning a progression through the different dot cards and five and ten frames. I have mine on 1/2 sheets of card stock filed by number. I have wondered if I should mix the numbers up more, but the Number Talks book has them grouped by number. Thoughts?
-Carol
Mrs. Cobb’s Kindersprouts