Subitizing: Moving from Perceptual to Conceptual - Math Coach's Corner

# Subitizing: Moving from Perceptual to Conceptual

### Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

#### Math Games | Subitizing

Subitizing, a funny-sounding word, but a very important skill for developing number sense. Basically, we subitize when we instantly recognize a small group of objects as a number. For example, if I hold up five fingers and you instantly know it’s five without counting, you have subitized. This ability to move away from counting objects one-by-one is an important component of early numeracy. But did you realize that there are actually stages that students progress through as they develop subitizing skills?

### Perceptual Subitizing

Last year, when working with my Kinder babies, I noticed that most of them could recognize single groups of objects, such as the ones shown below.

These students were exhibiting the ability to engage in perceptual subitizing. They could subitize small groups of objects, typically up to 5,  and state the number. This is an important first step! If your kiddos struggle with perceptual subitizing, flashcards for them (like the ones above) showing different representations of small groupings to 5. Also, check out this blog post for an easy little game for subitizing the dot patterns on a number cube you can download for free.

### Conceptual Subitizing

When shown a card with two subgroups (example below), however, many of my students could only state the two subgroups (3 and 2), but not combine the subgroups to state the total shown (5). Which brings me to conceptual subitizing.

Conceptual subitizing involves not only recognizing the subgroups, but also combining them together to compose a whole. To help move my students toward being able to combine the subgroups, I began showing them cards with the subgroups plus just one more.  After they could state the total for the subgroup plus one more, I added in cards that showed the subgroup plus two more.

I created a deck of over 140 cards that can be used to gradually develop students’ subitizing skills. The cards show dice patterns, finger patterns, tally marks, ten-frames, and random dot patterns for sums up to 10 (5 and 5). Best of all? There’s now a digital version as well! I’m excited to hear how this gradual approach works for your students!

1. This article will be very helpful when making recommendations for math interventions especially in our K and 1 classes. Thank you for sharing!

• Thanks for giving the title or name to this activity/ activities.

2. This is informative, thank you. So what is the difference then between conceptual subitizing and composing/decomposing numbers? Is it just the fact that they can do it instantly?

• It is actually the same as composing and decomposing with images. Composing and decomposing can also be done without pictures, such as just knowing that 2 and 3 make 5.

3. So, I am so glad to read this. I bought your math bundle that contains the subitizing flashcards last week, but quickly realized that most of my kinders need to start a little slower. I will start this next week.