Subitizing is the ability to quickly identify the number of items or dots in a small set without counting. Researchers have demonstrated the ability to subitize is a necessary early math skill. In addition, toddlers as young as 12 months have shown the ability to subitize. Sadly, this is a skill many of our students are not being exposed to. Why? Think about how we likely learned this skill 20, 30, or 40 years ago. We played lots of games that often involved a board and a pair of dice. Remember when you were a kid when you would roll the dice and could tell within a microsecond, without even thinking about it, how many places to move your game piece around the game board. Today, our kids play totally different games. Most games are in a digital format on some kind of screen. They almost never involve a pair of dice and rarely force the player to utilize any math skills at all. This is why, it is even more important we address this skill with direct and focused instruction in our math lessons. Here are some important things to keep in mind when teaching this important skill.
As teachers, we just love to dress things up and make them “cuter” and “prettier” in an attempt to make our boring material more engaging to our students. But, when it comes to subitizing it is critical to keep it simple and use only dots. Look at the two cards below:
I know I would have used the card with the butterflies when teaching my students to learn early counting skills. But, after taking some classes in math foundations, I learned it is better (and necessary) to use the the card with the dots. When learning this early skill of determining the number of images WITHOUT counting, you need to use the dots so the brain is minimally distracted. Once the skill is mastered, it is fine to introduce other images, but initially, the use of dots is critical.
2. Use standard placement
The dots on each side of a die is placed in a pattern that is consistent and strategic. The placement of the dots in this standard manner is another critical step to learning how to subitize. Take a look at the cards below:
Your brain can very quickly identify that there are 6 dots on the first card. However, it takes an extra second to determine the number of butterflies on the second card. Keeping the dot pattern consistent is critical when learning this early skill.
3. No counting allowed
What? Isn’t subitizing counting small sets of dots? Actually it is NOT. Subitizing is recognizing the number of dots without actually counting them. I found this to be the most difficult task of all to teach my students with special learning needs. When you ask “How many?” to a student with autism, he or she is automatically cued to begin counting. It is a strong learned response that has likely been drilled into them over and over again since kindergarten. That is why, if you are given the luxury, start teaching students students how to subitize BEFORE you teach them how to count. The way I found I could do this with the best results, was to play a subitizing game each morning. I would use either large flashcards or used my Smartboard to project images of dot patterns. The key was to only show the image for a couple of seconds. Do not leave the image visible long enough for the students to count. You simply want them to see the pattern. Of course, this required a lot of prompting to begin with; lots of prompting and lots and lots of trials.
4. Vary the presentation
So, we know you have to use standard dot patterns when teaching students to subitize, but we also know that students with special learning needs, especially autism, have a lot of difficulty with generalization. So, find different ways to practice this skill. This is part of the reason I used flash cards and projected images. Another great way is to play simple games that use dice. This has the added benefit of working on those important social skills as well that all of our students have on their IEPs. Again, when using dice do not give your students time to count the dots. I know it seems really mean to take the dice away before they have the chance to count the dots, but it is critical, even when playing a game, that you continue to train their brain to see the dots as an image that represents a quantity not individual objects that need to be counted.
5. So, now what….
Once your students are able to subitize, the next step is to connect that image to a quantity. Being able to match the dot patterns to sets of objects or numerals are also a critical skill. In addition, being able to order a set of dot cards from least to greatest, is another critical skill in building number sense. In older students, being able to add together sets of dots images will greatly help with skills such as doubles in addition. There are so many ways to utilize this mastered skill in your more advanced math lessons.
I learned about the importance of subitizing in my 8th year of teaching. It saddens me to think of all those students I had who missed out on learning this crucial early skill. In addition, there is NO doubt in my mind that those students (including my own son) who never learned how to subitize struggled in math for the rest of their school career. Consider adding this skill to your IEP goal bank. I promise you it is worth the effort!!
If you are looking for a resource that will truly help you become an amazing math teacher and successful at building really strong number sense in your students, I recommend the book below. It became my bible while teaching math during my last 2 years in the classroom, and then helping other teachers become better math teachers. (click on image below to go to the link on amazon.com)
Click on the image below for a FREE download of subitizing flashcards to use today!
To get my complete Subitizing Unit from my store on TPT click the image below to get a book, worksheets, and flashcards to practice this critical skill.