Subitizing meaning, plus free dot card games

What is subitizing?

Subitizing is recognizing and naming how many are in a group without counting (learningtrajectories.org (opens in a new tab)). Roll a die, and your learner says "five" before touching a single dot. That instant "I just see it" is subitizing. The word comes from a Latin word meaning "suddenly," which is exactly how it feels.

Where does the word subitizing come from?

The term was coined in 1949 by E. L. Kaufman, M. W. Lord, T. W. Reese and J. Volkmann in "The Discrimination of Visual Number," published in the American Journal of Psychology 62(4) (doi (opens in a new tab); U. Alberta Dictionary of Cognitive Science (opens in a new tab)). It comes from a Latin word meaning "suddenly" (Clements 1999, NCTM (opens in a new tab)). Their team described fast, confident, accurate reports of small groups (Mandler and Shebo 1982 (opens in a new tab)).

What is the difference between perceptual and conceptual subitizing?

Perceptual subitizing is instantly recognizing a small amount, up to about 4 or 5, without counting. Conceptual subitizing is seeing a few small groups and knowing the whole they make, like seeing 7 as 3 and 4 (IES REL module (opens in a new tab)). An eight-dot domino seen as two fours is conceptual subitizing (Clements 1999 (opens in a new tab)).

How many things can a child subitize?

Perceptual subitizing reaches about 4 or 5 (IES REL (opens in a new tab)). Stanford's DREME team notes many scientists see the basic ability as limited to about one to three, maybe four (DREME (opens in a new tab)). Bigger groups need a familiar pattern, like the dots on a die.

Why does subitizing matter for number sense?

Children who quickly recognize small numbers are better able to find how many, show the number and later add (learningtrajectories.org (opens in a new tab)). Conceptual subitizing is one important way to understand addition (DREME (opens in a new tab)). The IES practice guide calls recognizing small numbers a critical skill for counting larger sets and for adding and subtracting later (IES practice guide (opens in a new tab)).

Is subitizing the same as counting?

Both answer "how many," but subitizing does it without counting each item (DREME (opens in a new tab)). NAEYC notes that children who always count one by one can become less skilled at subitizing (NAEYC (opens in a new tab)). One homeschool parent put it this way: when counting gets pushed hard, subitizing can fade (r/homeschool (opens in a new tab)).

How do I practice subitizing at home?

Free games with household things:

1. Snack-time questions. "How many crackers?" and "Put on your two shoes" (IES for families (opens in a new tab)).
2. Flash a die. Show it, hide it, say the number (DREME (opens in a new tab)).
3. Match How Many. A dot card matching game. Ask "How did you see it?" (NAEYC (opens in a new tab)).
4. Ten frame on screen. Fill a ten frame in the free MLC Number Frames app (opens in a new tab) to see numbers in relation to 5 and 10.
5. Make the pattern. Flash a dot card for about 3 seconds; your learner rebuilds it with counters (Build Math Minds cards, PDF (opens in a new tab)).
6. Fingers, then two hands. Show numbers on fingers, then across both hands (Lucky Little Learners (opens in a new tab)).

Tips: Say "say the number," not "count" (WeAreTeachers (opens in a new tab)). Scattered and circle arrangements are harder than neat patterns (NAEYC (opens in a new tab)).

Free subitizing resources

• Math Learning Center Number Frames app (opens in a new tab): free, in a browser or on iPad.
• Polypad by Mathigon (opens in a new tab): free for parents per the Mathigon FAQ (opens in a new tab), with a ten-frame tile per its changelog (opens in a new tab).
• Build Math Minds dot pattern, ten frame and MathRack cards (PDF) (opens in a new tab)
• NAEYC dot card and finger games (opens in a new tab)
• IES Teaching Math to Young Children for families (opens in a new tab)

More free math: math deals and resources, free all year, the free placement pack. A parent notes Math with Confidence has a big focus on subitizing (thread (opens in a new tab)); see Math with Confidence sale dates.

Subitizing words to know

• Subitizing: naming how many are in a group without counting (learningtrajectories.org (opens in a new tab)).
• Perceptual subitizing: seeing a small amount, up to about 4 or 5, at once (IES REL (opens in a new tab)).
• Conceptual subitizing: seeing small groups and putting them together into the whole (IES REL (opens in a new tab)).
• Cardinality: the last number counted tells how many are in the set (IES practice guide (opens in a new tab)).
• One-to-one correspondence: matching one number word to each object (IES practice guide (opens in a new tab)).
• Ten frame: two rows of five boxes that show numbers in relation to 5 and 10 (MLC Number Frames (opens in a new tab)).
• Dot cards: cards with dot patterns, flashed briefly so the learner says how many (NAEYC (opens in a new tab)).
• Part-part-whole: two parts make a whole, like 7 is 5 and 2 (MLC family page (opens in a new tab)).
• Composing and decomposing numbers: putting numbers together and breaking them apart (Clements 1999 (opens in a new tab)).
• Number rack (rekenrek): two strings of 10 beads in groups of 5 (MLC family page (opens in a new tab)).
• Number sense: the ability to understand the meaning of numbers, define different relationships among numbers, recognize the relative size of numbers, and think flexibly with numbers (NCTM 1989 definition, as quoted by the Rhode Island Department of Education) (RIDE (opens in a new tab)).