These *Geometric Subitizing Cards* have been in beta the past two years.

I asked our buddy Joe Schwartz to take them for a test drive last spring and he reported back. Joe’s all in.

How do they work? Let’s play…

Last week I took them for another spin in some kindergarten classes. Here’s two examples of how it went and we’re only 2 months into the school year.

Last year I captured me playing cards with my girls. Here’s me playing with my kindergartner.

Here’s me playing with my 3rd grader.

Your turn.

Take these cards and give them a try. If you need some ideas how to use them you might want to check out this task card. I plan to share my thoughts about Geometric Subitizing in a future post but for now I just want you to go and play. The only thing I ask is that you report back and offer feedback.

- How did it go?
- How can we make them better?
- Any other ways we could use them?
- What am I missing?

Great task for students in kindergarten. Muscle memory at it finest!

I love how you have applied the concept to geometry! Different learning objectives are covered all at once – geometric attributes, multiplication or repeated addition, logical reasoning. Brilliant!

I put the cards into a PowerPoint presentation so that I could show them on my whiteboard. Flashed one card and asked the children to write their own questions. asked could they predict my question I had written on a card. The first go at this lead to simple questions, after a couple of days ( I did 3 slides a day- I like to work in threes), the children’s question had a lot more depth and they enjoyed comparing and trying to out do each other.

This was a great beginner number talk for my high school Geometry class!

These have so many applications! I am creating a TK/K center that has students place the subitizing cards to match & represent a number on the number line. I will mix these in with other number representations such as subitizing dot pictures, standard form numbers, word form and ten frames, etc. that range from 0 – 20. I am hoping to teach students how to do this independently in a math center after pre-teaching/practicing whole class. Wish me luck!

Good luck Susie and please report back and let us know how it goes.

Super excited to use these to reinforce comparison problems (how many more/how many fewer) in conjunction with defining attributes in first grade!

I can’t get these to print correctly. They are printing a portion of the cards. I am not real tech savvy so I hope it is a simple correction I can make.

Just tried it with a kinder class near the end of the year. Great discussion about corners vs. sides and counting the sides on the cards that included circles. They also liked showing off their shape knowledge. Thanks for the resource!

Great internet sitewebsite! It looks extremely good! Keep up the excellent job!

I used them today with my kindergarteners. They liked them a lot! I started with the cards with just 1 shape and we talked about the shapes and how we knew what shapes they were (sides, corners, etc.). Then, we did a few with just how many shapes do you see and talked about how they saw the amount. Some used familiar combinations, such as I saw 2 and 2 and I knew that was 4, but some saw it as 3 triangles and 1 rectangle making 4. It helped the students to again see amounts in different arrangements building flexibility with numbers.

We also did a couple where I covered up 1 shape (I used the cards with 2 shapes on them). I gave them a clue like the total number of corners or sides, and then they thought about what shape could be hidden and why they thought that.

I thought it was a fun way to continue to build fluency and flexibility with numbers and to do some more shape recognition. It added a different context to our number talks.

Thanks for the cards! If you have other ideas for using them, I’d love to hear them!

Graham, What I really like about these in addition to building some great geometry sense is that these are a really nice transition from dot image number talks to number talks involving computation! These are really great! Thank you for sharing!

Your generosity and fabulous ideas are why when someone mentions math, you name instantly pops up. Thank You!

I am trying this next week and I’ll let you know how it goes. This is a home run idea.

Love this! I’m printing them now to try out in a couple of classrooms!

Thank You! These are cards I can use with ALL my students! Plus for my older students it helps review the attributes of different geometric shapes â these are so useful in so many different ways.

Pattie Perry

NILD Inside

Cognitive Therapist/Curriculum & Instruction Director

[CCA_LOGO_hi-res]

My head just exploded. I’ll be trying these with my first grader and will even share them with some middle school teachers I support. I love the varying degree of mathematics behind these cards. Lots of algebraic thinking here, too!

Cheers bud! Love to know how it goes if you giver’ a whirl with the middle school folks.

Love these cards, and honored to have received one of the first sets. I’ve used them as I would quick-look or dot cards, and also as a way to generate equations. Perfect mash-up promoting geometric and multiplicative thinking. As for Michael’s comment above, I’ve never understood subitizing to be confined to randomly arranged shapes. For example subitizing 6 from the 2 by 3 dot arrangement on a die.

Joe, you could well be right. My impression from the reading I’d done in the ’90s was that subitizing entailed instant recognition of a random group of objects, not of a regular (and familiar) arrangement. Of course, in working with young children, there could well be reasons to want to help them gain facility with just the opposite: recognizing patterns of objects and learning to group a number of objects into smaller subgroups to reduce reliance on counting.

I do know that the root of the word means “sudden” in Latin. Whether psychologists are measuring instant recognition of, say, nine randomly placed objects or nine pips on a playing card with the numbers removed, I’m not sure. Clearly, these cards are not offering random arrangements. I hadn’t thought about the notion of training young children to recognize patterns instantly, not having worked in pre-K or primary grades and being a very long way from the age when I didn’t know the patterns on dice or cards. 🙂

Hi Michael,

If you have access to Doug Clements book Learning Trajectories he has a whole chapter on subitizing. There are actually two kinds, perceptual and conceptual subitizing. Both are instant recognition of quantities. The first (perceptual) is instant recognition of quantities that you just see. Most kids come being able to subitize up to 3 without any practise. Once they get good at this they develop into a conceptual subitizer which means they are applying a strategy while subitizing but this is also happening very quickly. Once they start subitizing over 5 most start doing this. An example is: say you have 9 dots on the card. The student may perceptual subitize 5 and the 4 separately then combine them using a addition strategy like counting on. This all happens very fast, that is one reason why subitizing is so important for developing operations fluency. In Clements book he also lists how the dots should be introduced. Kids see dots in lines easiest, then rectangular formations and finally abstract formations. He suggests that they be introduced this order. Dice formations can fit in either category but are mentioned separately because many students have them memorized from playing board games. Clements book is all based on research and is developmental based on age, hence the trajectories name in the title. It is an amazing resource. There is more info on subitizing in his book, I have only summed it up quickly. In my board we have been doing a lot of work with this. I work with many teachers in my role as an Instructional leader and they have seen their students really take off in their understanding of quantity and early operations. This is the full name of Clements book: Learning and Teaching Early Math: The Learning Trajectories Approach. Hope this helps.

What Graham has posted here takes it to a different level, they are not only subitizing numbers, using operations but also learning geometry attributes etc. Excellent activity.

Oh I am so excited to try these! How late in the year did you record these videos? I am unsure of the expectation for Kinders to add up sides that quickly. Is this after winter break or before? Thank you for sharing these for free!

Thank you for being so creative with number talks. May be you can call it shape talks.

Not clear on the subitizing aspect. Maybe I am being dense or I’ve missed earlier posts on these cards. If the latter, just point me there. But I’m interested in what you want kids to get out of the “here’s a brief look at something: what did you see?” experiences. Is there a theory you’re testing? I’ve read in a few places that the average person (not sure about how this has been tested across age bands) can “subitize” 7 +/- 2 randomly arranged shapes. Your cards don’t have the shapes randomly arranged, so I would imagine you’re not trying to measure that ability or train it.

I’m intrigued that kids are able to notice the total number of shapes, what shapes, and how many of each shape. But again, I’m not sure what you’re going for (other than fun, which seems to be there in the group lessons). The “what’s the missing shape” activity seems engaging as long as kids accurately can do all the correct noticing of what they saw. You didn’t show any cases of kids “failing,” but I would think that has to happen. How does that play out in practice?

Not trying to be a pain. Just hoping to understand and learn more about what you’re doing and, I hope, put some useful questions out there.

What I’ve learned about subitizing’s purpose is to encourage kids to see groups of numbers instead of counting them one at a time. Kindergarteners start counting objects one at a time but as they move on to larger numbers later in Kinder and then in 1st, I want my students to see a group of 3 and a group of 5 automatically so that adding will be more efficient. Instead of starting to count the 5 as, “1, 2, 3, 4, 5” and counting on “6, 7, 8”, I want to hear kids say “5” and count on “6, 7, 8”. Eventually moving on to knowing 5 and 3 are 8 automatically. But it all starts with subitizing and “How many did you see? How did you see it?”

Thoughts?

@Carrie DeNote: Definitely in favor of helping students move from recounting everything to counting-on, though I never worked in K-2 or with teachers in those grades, so the subitizing issue never arose for me. I can see your point, now that I’ve broadened my perspective on the notion of subitizing itself. Makes sense.

Right on Carrie and thanks for jumping in here to help out.

You’re never “a pain” Micheal. You always bring a different perspective which makes us elementary peeps flesh out our own understanding. What I truly appreciate is that we continue to cross-pollinate (k-12) in an effort build our own knowledge and a common understanding. Cheers!

Love, love, love these and can’t wait to try! Having the videos gives me some ideas. I bet they could even be great for transition times and getting the group to pull together, focus, and listen. Getting a bit more math in our day! Thank you for sharing!

Thanks Debbie. Love to know how it goes so please report back.

We have our geometry unit in the winter this year. I’ll add these to my plan and report back!

Awesome and thanks Andrew! Can’t wait to hear how it goes.