## Saturday, April 21, 2012

### Subitizing - Making Sense of Numbers

I'm in love.

With subitizing. Rhymes with oobitizing. (I always thought it rhymed with rub-itizing.)

Know what it is? If you're teaching, it's a great tool to add to your toolbox!

Ever since I read about it in Teaching Children Mathematics, I've been on a mission to learn more. Basically, it's the ability to instantly recognize a quantity. An example that frequently comes up: dice. Most adults see a number on a die and immediately recognize the number, without counting. We define two different types of subitizing:

Perceptual Subitizing - a number is instantly recognized, usually with quantities of 5 or less.

Conceptual Subitizing - recognizing small quantities within a number and combining to find a total. For example, you might see 7 dots as a combination of 3 dots and 4 dots.

You can see how the ability to subitize leads to all kinds of math skills. If you can instantly recognize a quantity, you can count faster, add/subtract/multiply/divide more easily and efficiently...the list goes on. It's a no-brainer that we want our kids to master this.

So I've been trying.

I started by placing objects on a peg board, showing a quick glance, and having the child replicate it on his own board. I also tried flashing quantities on a DIY counting rope.

More recently, I've been flashing quantities on a five frame. We used ducks after our lesson with Little Quack's Hide and Seek.

I've only done subitizing a handful of times (probably less than 5) this year. My little student showed a good grasp of numbers up to 5, but anything beyond that was pushing it. I thought. Shows how much I know.

Yesterday, I printed off some subitizing cards. (Went to a TON of effort. Smirk.) Googled "subitizing cards" and printed out cards from the first Google link. (Apparently, they go to a private school site, but I found the same ones linked here titled "subitizingcards.pdf.") They are FANTASTIC. Mostly because I didn't have to make them. But also because they fit neatly into a cardboard flap. I literally grabbed a piece of cardboard out of the recycling box and had a flap made in seconds. You'll see how it allows you to flash the dot pattern and then reveal the number after the child states an answer.

I apologize that the child's volume isn't more clear. I need to invest in an external mic. Listen carefully, however, and you'll hear the reasoning that went into his answers. You might think about when he used conceptual subitizing...or when he was able to instantly see smaller quantities within the number and add them together to get a total.

Although you certainly don't need to ask a child how he arrived at an answer, I found it very helpful to help assess my student's abilities. I was surprised that he knew so many number combinations. Formal addition is going to be an easy next step.

Now...go subitize! Here are some more links/resources to assist you:

Math Four
A terrific blog entry, Why Learning to Subitize is Important. (Thanks, to Tricia for the suggestion!)

Staff development with 1st grade teachers
In this YouTube Video, the facilitator guides teachers through steps that children might take in gaining number sense. It's 20 minutes but really gives you an education.

Math Coach's Corner
Donna has several posts about subitizing. She writes that subitizing is "foundational to the development of number sense." She links blacklines from John VanDeWalle's book with lots of subitizing cards. I'm printing these next. Also read her post describing different ways that kindergarten students saw a dot pattern.

Dr. Nicki's Guided Math Blog
Love Dr. Nicki's resources. She has several posts on using subitizing in the guided math setting.

Freebie! - Number Rack
Read about Math Learning Center's new free app, Number Rack. It could be easily used for subitizing, both online and on an iPad/iTouch. The entry also links you to a free activity/lesson book.

PDFs - Use with Subitizing
This site has a whole list of pdfs to print for subitizing with kids.

1. I love subtizing! I had no idea I was saying the wrong. This is what helped K do mental math quickly in her head. Surprisingly, it has helped me as well as I've been trained to rely on paper and pencil computation during my schooling years. I will be tutoring another child this summer and I hope to do a combination of subtizing and Montessori Math. Love your video and all the resources. I also found this site which has free printouts.

2. I found another one but for some reason I am unable to copy and paste using my phone. I'll get back to you when I get on the computer.

3. http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf

2. I have always done this with my kids, but I didn't know there was a name for it! Now I know.

1. Phyllis, I'm constantly amazed at what you do with your kiddos!!! It's like all this stuff comes naturally to you. Wish I was so lucky! :) Your kids are so fortunate to have you as their teacher!!! :)

3. Last year my daughter played a lot on Dreambox site which I believe is based on this principle. It really helped her to instantly recognize qualntities and manipulate within 20, which is really a step to manipulating anything. Thanks for sharing your links!

1. You're welcome! I like the Dreambox subitizing activities too.

4. Found you from TBA...I am your newest follower! I would love if you would stop by and visit me...

learnplayandhavefun.blogspot.com

1. Coming over for a visit! Thanks for stopping by!

I've been pronouncing "subitizing" wrong, too, since I picked up the word from reading online and never heard it pronounced. Now that you've told us the right way, it sounds weird to my mental ears.

1. Denise...me, too. Funny how something gets ingrained. I have to keep saying Soo, soo, soo.... Actually found that online too. By watching YouTube videos. ;)

6. Subitizing is a big part of my instruction on number sense. It's so important.
I really like this blog post at Math is not a FOUR letter word.
http://mathfour.com/sets-and-counting/why-learning-to-subitize-is-important

1. Tricia, I LOVE your resources! THANK YOU SO MUCH!!!

7. Wow! What a wonderful post! I finally learned what subitizing means. I have been hearing it for awhile now but since I am not in the formal classroom, I sometimes feel out of the loop with new terminology (this is new right? LOL) I have been out of the classroom for 15 years! Thanks for filling me in Cindy!

8. Tamara, how kind of you to say so! (Means a lot!) It's caught my attention because it means SO MUCH SENSE! And this year I've watched some little students really take off with number sense with only a few sessions. Your kids will love it. :)

9. Subitising is a big part of our Kinder maths program in Australia! It is nice to see a post about it - sometimes I feel like people don't know what I am talking about!

1. Melanie, I'm convinced that Australia is waaaayyy ahead of the game. Wish we had some of the resources you do!!! Thanks for writing. :)