Subitize comes from the Latin word “subit(us)”, which means “to appear suddenly.” In my last post, we talked about the Early Number Sense Trajectory that was created from the work of John Van de Walle, Doug Clements, and Julie Sarama. According to the trajectory, subitizing is the first mathematical stage a learner experiences. Students who can subitize are able to visually recognize a quantity of five or less. However, there are multiple levels of subitizing, and recognizing the difference between 1, 2, or 3 objects happens as early as within the first few months of infancy!

It’s important to note that when students call out these number names, they are only matching the number name to a visual pattern. In other words, students do not know what those number names mean as a quantity yet. For instance, suppose I show the following image to a young learner:

The learner yells “3!” Yes, the young mathematician knows the number name of the visual pattern but when asked to count how many, the learner may respond “1,3,5.” This is known as **perceptual subitizing**: the learner can state the number name of a visual pattern but cannot explain why. At this stage of learning, that is okay! We are working with learners who are beginning with perceptual subitizing.

The next stage is **conceptual subitizing**. This is a learner who can explain why a number name matches a visual pattern and recognizes subgroups that can be combined together to compose a whole. So for the image above, the student may explain that it’s 3 because 2 and 1 make 3.

With that said, there are many ways to support young learners at home during this stage of learning, and what better way to talk about math than through games! Below are three simple games you can play to practice the concept of subitizing. All you need is a deck of subitizing cards (find them for free down below)!

## Subitizing Game #1: How Many?

- Two players split the deck and take turns flashing the top card from their pile to their playing partner for 1-3 seconds.
- If the player correctly identifies the quantity on the card they keep the card as a point. Otherwise, it goes to the discard pile.
- The player with the most points/cards wins the game.

## Subitizing Game #2: Memory

- Place all the cards face down and players alternate flipping over 2 cards to find a match.
- If a player finds a match, they collect the cards as their points. The player with the most points/cards wins the game.

**Note:** You will have to make two copies of the subitizing cards to ensure that each card has a match. Mounting on colored paper or copying on cardstock may also be necessary so students can’t see through the paper.

## Subitizing Game #3: How Many? War

- All the cards are kept in a single pile and one card is flipped over.
- The first player to say the quantity on the card gets to keep the card as a point.
- The player with the most points/cards wins the game.

**Related: Subitizing for Multiplication: Building Number Sense and Multiplicative Reasoning**

## Differentiation

There are many ways to differentiate these games to meet your learner where he/she is at. If you have a young learner in Pre-K or Kindergarten, subitizing cards within 5, like five frame cards, would be more appropriate. For first and second graders, subitizing cards within 10 and 20, like ten frame and double ten frame cards, are a great fit!

Do you have any subitizing games that you love? Share in the comments below! I’ll be sharing some more games for the next stages in the Early Number Sense Trajectory, so stay tuned! Always remember, we are better together.

## Resources to Help

### Grab and Go

*Remember: Depending on what you are using the subitizing decks for, you may need to make multiple copies.*

K-2 Learning Trajectory Document

### Deep Dive

Learning and Teaching with Learning Trajectories- This website will provide a wealth of information on specific learning trajectories for learners of all ages!

Learning and Teaching Early Math: The Learning Trajectories Approach by Clements & Sarama