“…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.
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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.