Subitizing and Why It’s Important

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.

  1.  Use dots

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:

dots and butterflies

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:

dots and butterflies2

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

learning trajectory book

Click  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.

subitizing unit

Do You Hug Your Students?

Do You Hug

As a previous elementary teacher in an autism classroom, I often got asked why I was not more affectionate with my students.  Don’t get me wrong, I did the occasional hugs, but in general I was not a big one for physical affection with my students.  This was sometimes mistaken as aloofness or coldness, but that was certainly not the case.  I simply had first hand experience of what showing a lot affection to young students in an autism classroom setting could lead to… lots of problems and behavior to un-learn.

My son is now almost 19 years old and has severe autism.  I am lucky because he has never shied away from giving me physical affection.  He loves his hugs.  However, somewhere along the line, he also started displaying very inappropriate ways of showing others (even strangers) physical affection. He used to want to kiss and smell everyone’s knees.  It is still by far his favorite body part.  I think it was partly due to the huge amount of time we spent at swimming pools when he was younger.  Everyone thought it was kind of cute when this 4-5 year old, who was just over knee high to many adults, would come up and kiss their knee.  Most knew he had autism, so they would just ruffle his hair and say “How sweet.”  Not the same response however when he was in high school.  With a lot of hard work from teachers and therapists, we were able to shape that behavior to kissing and smelling the top of a person’s arm.  Still kind of weird, I know, but it seemed the best we could do.  I look back now, and wish I had simply stopped that behavior at the pool all those years ago.  If I had just told people, that is going to be a big problem down the road, so let’s not encourage him.  Ah, hind sight…

So as I entered the classroom, I was already armed with this knowledge.  I knew how I interacted with my young students and how I allowed them to interact with each other would create a strong impression upon them that could last for years.  So, I emphasized to the other adults and peers who worked with my students, that hugging was probably not the best idea.  We did a lot of high fives and fist bumps.  I know it may have seemed cold to some of the people and parents I worked with, but I hope the middle and high school teachers who later had my students would appreciate the expectation we had set.

Showing affection can be a very difficult topic to address in special education settings, but setting clear expectations and models for appropriate behavior can be quite powerful tools.  In my store on teacherspayteachers, I have several resources you may find helpful.  I have a social story on showing affection that you can purchase alone or as part of my Valentine’s Day unit.

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Finally, as a thank you to all of you who take the time out of your busy day to read my blog, here is a FREEBIE for you!!


Circle Maps in Special Ed

Circle maps are a type of graphic organizer or thinking map.  It is a wonderful tool for helping students visualize what they know about a particular topic.  Below is a short video of how these can be used in a typical classroom setting.

video clip

So, how and why should you use circle maps in your special education setting?  I found circle maps to be an invaluable tool with my students, even for those who were more severely affected.  Circle maps provide a visual representation of the subject matter which the student can easily refer back to.  Here are some tips if you decide to use circle maps as part of your lesson plan:

  1.  Match the student’s learning level.

We all know that in a special education class, there are many different learning levels.  For my students on the symbol level, I would often use symbols from Boardmaker.  Some of my students were readers,  and I would use either words alone or words paired with symbols.  If my students where on the picture level, I would look for realistic pictures from either magazines or google searches for realistic images related to the content.  Finally, I always had at least one student on an object learning level.  So, I would try to find some actual objects that the student could manipulate and place inside a real circle map most often using a hula hoop.

2.  Keep it consistent.

Once you identify the learning level of your student, use the same symbols, pictures, words or objects in the circle map that you will also use for the assessment.  This will help reinforce the content during this early learning phase and make evaluating the results of the assessment more valid.

3.  Don’t forget to generalize.

We know students with disabilities, especially autism often have a hard time generalizing content.  Once they see a penguin, it will forever be that black and white bird they saw in the movie, March of the Penguins.  But, penguins can look very different and are still considered penguins.  That is why, it is important to introduce variations on the pictures or symbols you are using in various additional activities.  This can also be done with a separate circle map that contains all different kinds of penguins.

This concept also works very well when building number sense in your math lessons.  Creating a circle map for each number and displaying all the different ways you can represent that number can be quite powerful.

  • Tally marks
  • Sets of objects
  • Number word
  • Number of fingers
  • Various fonts and colors
  • Dots

Click on the button below to download this FREE circle map of the number two.

Aviary Photo_130970021143777249

4.  Use as a study guide

Circle maps make great study guides. Students can take them home to review the content with parents and even use them while taking the assessment.  Many of our students with autism are visual learners, and being able to organize the content in this format makes it easier for them to organize the information in their minds and recall at a later date.  The circle map below is part of my Penguin Science unit that you can download from my store on teacherspayteachers by clicking on the image below.

Aviary Photo_130970029122581400

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5.  Consider adding distractors.

If your students are at the appropriate learning level, you can also add incorrect answers or distractors into your picture selection as well.  Most of my products do not include these distractors, as my students were often not at that level.  I was mainly focused on errorless teaching for the majority of my lesson, so it was easier for me not to include them.  However, they would be a nice addition to your higher level learners.

I hope this has encouraged you to consider adding circle maps to your teaching tool box especially if you teach students with special learning needs.  They are an engaging activity that can bring a lot of value to the content you are presenting.


Learning a New Year

Even for most of us it is always a challenge to remember to write the correct year after January 1.  Our brain and finger muscles have had 365 days to practice writing 2018.  Now, all of a sudden, we need to remember to write 2019.  That may take us a while…

Now imagine if you have a significant learning disability.  It may have taken you 300 of those 365 days to finally be able to “write” or “say” 2018 on your own.  Now, for no reason you can comprehend, you must forget that, and learn a new number to designate the year.  Very frustrating.

Admittedly, for many of the students I taught, knowing what year it was currently, probably was not high on the list of important facts to learn or be able to recite.  After all, many of my kids did not write or even speak.  But, there were always 1 or 2 that were at the high end of that curve who would go out for some time in the regular education setting and would be expected to write the CORRECT date on their papers.  In addition, there was always that one parent who felt their child should be able to parrot back the year when asked, just like their current age.  (Full disclaimer, I was one of those parents eons ago.  I so wanted my son to appear “normal” and be able to know what other kids his age knew.  It took a long time for me to be okay with the fact that at almost 21 years old now, he still does not know the current year or even how old he is.  But who really cares anyway?  Not him that’s for sure.)

So, how to go about teaching our students with disabilities that 2018 is over and now it is 2019?  Here are (what I think) some important things to consider.

  1.  Use ERRORLESS teaching

If they already know what year it is, we KNOW they will answer “2018” when asked “What year is it?”  So, you need to provide full prompting right away.  Stop letting them practice saying or writing the wrong year.  If you are asking your student verbally, then immediately follow your question with the correct answer and then allow your student to repeat you.  For some students you may need to give the full verbal prompt several times before fading.  For example:

Step 1= Teacher:  “What year is it?”

Step 2= Teacher: “2019”

Step 3= Teacher: “What year is it?”

Step 4= Student: “2019”

If your student is still saying 2018 after step 3, then repeat steps 1-2 several times before fading the full verbal prompt.  **Remember, there is a lot of research that shows that fading to partial verbal prompt is  NOT effective.  Just go from full verbal prompt to no verbal prompt.  If this is still not working and your student can read numbers, try using a cue card with the year written on it.  Pair that card with your full verbal prompt at first, then as you fade the verbal prompt keep the card.  Eventually fade the card.

If your students are writing the year on their papers, have then trace the correct year on their work for a while.  This will take some extra prepping on your part.  Beforehand, write the correct date in pencil and have them trace it.  Also put the correct date on the board or on an index card on their desk.  That way, you can fade the tracing to a visual prompt.  The index card is nice because it can go with them to various classroom settings if needed.

2.  Practice, Practice Practice

Set up lots of time and ways to practice writing or saying the new year. The more frequently it is practiced the quicker the muscle memory will build for either saying or writing the correct year.  Take every authentic opportunity to have students tell you or write 2019.

3.  Vary the stimuli

Remember, students with disabilities, especially Autism, have difficulty generalizing what they learn.  So, they may be able to put the date on their paper in your classroom, but not in Ms. Smith’s inclusion setting.  Taking visual prompts to new locations will help, as will practicing the skill in different environments with different people.  One way to practice is to try a cut and paste activity which you can download for FREE by clicking on the button below.  This is a great way for students to visualize the new year and manipulate the numbers.  I would try printing it on different colored paper each day for a while (repetition with variation).  In addition, don’t forget you can add color coding for your students who need more visual structure.

So if you are teaching your students it is now 2019, I wish you the best of luck!!  I am hoping to simply remember that myself this year.

***If you are looking for a unit to go with this activity, grab this New Year Unit in my store, over 40 pages for only $3.00.  Includes a story, circle maps, and cut and paste activities all designed for students with special needs, especially autism.  

Just click here!