Subitizing is a hot topic in Math education circles. Subitizing means “instantly seeing how many.” Math educators have discovered that the ability to see numbers in patterns is the foundation of strong number sense. The ability to visualize and understand numbers and numeration will lead to operational fluency, the ability to add and subtract mentally, to see relationships between numbers, and the ability to see patterns.

### Two Forms of Subitizing

Subitizing comes in two forms: Perceptual subitizing and Conceptual subitizing. The first is the simplest, and even animals are able to do it. The second is a more advanced skill, built on the first.

**Perceptual Subitizing** is a skill that even small children have: the ability to see perhaps two or three objects and know the number. In order to transfer this skill, a child needs to be able to “unitize” the set and pair it with a number name. Still, this skill is often is exhibited in children who recognize the number in dice, such as five, or four. To build perceptual subitizing, you want to give students lots of exposure to visual stimuli, such as patterns for three, four and five, or ten frames, to recognize numbers as 5 and whatever.

**Conceptual Subitizing** is the pairing the ability to see sets of numbers with larger sets, such as seeing two fours in the eight of a domino. It may also be recognizing such strategies such as counting on or counting down (as in subtraction.) Children may only be able to subitize small numbers, but they may be able, with time, to apply their understanding to constructing more elaborate patterns.

### Activities to Build Subitizing Skills

**Pattern Cards:**Make cards with different patterns of dots and show them to your students. You might try an “around the world” drill sometimes (pair up students and give it to the one who answers first.) You might try domino or die patterns, and then pair them, like the five and a two so your students see the seven.**Quick Image Arrays**Give students a number of manipulatives and then have them arrange them in numbers and compare patterns: diamonds for fours, boxes for six, etc.**Concentration Games**Have students match numbers that are the same but in different patterns, or create a number of cards which are the same number but different patterns, and one that is different. Ask students to identify the one that doesn’t belong.- Give each child an set of cards one to ten in different patterns and have them spread them on their desks. Call out a number and see who can find the number on their desk the most quickly.
- Challenge students to name a number one more than that on the dots on the card or one less. As they build skills, make the number two more.

- Use the cards as part of learning centers.

### Ten Frames and Conceptualizing Addition

Ten frames are rectangles made of two rows of five boxes. Numbers less than ten are shown as rows of dots in the boxes: 8 is a row of five and three (leaving two empty boxes). These can help students create visual ways of learning and picturing sums larger than 10 (i.e. 8 plus 4 is 8 + 2 (10) + 2, or 12.) These can be done as images, or done as in Addison Wesley-Scott Foresman’s Envision Math, in a printed frame, where your students can draw the circles.

### Resources

- Conklin, M. (2010) It Makes Sense: Using Ten Frames to Build Number Sense. (Math Solutions: Sausalito, CA.
- Parrish, S (2010) Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5,(Math Solutions: Sausalito, CA.)