There are two forms of subtilizing, perceptual and conceptual.
Perceptual is the ability to see several small objects and instantly recognize how many. Children who can instantly recognize the dot patterns on a dice are demonstrating their ability to perceptually subitize.
Conceptual subitizing is the ability to recognize small groups of numbers and add them together, such as seeing two dice one having 4 dots and the other having 3 and knowing that together they equal 7.
Why is subtilizing important? Subitizing is the first critical phase to understanding addition and subtraction. It is important for children to be able to recognize qualities in a variety of configurations rather than just memorizing facts. Children who are able to subitize, posses the ability to visualize and understand numbers and numeration. This firm foundation will lead to operational fluency, the ability to add and subtract mentally, to see the relationships between numbers and have the ability to see patterns within numbers.
Activities to Build Subitizing Skills
Many researchers believe that subitizing is a skill that cannot be taught, but it can be fostered. Pattern cards, image arrays and concentration games can all help children develop their skills to subitize. Playing games that involve dice or dominos is another way for students to build subitizing skills. At first they will need to count the dots each time rather than just recognizing that they have rolled a 3 and a 5. As their visual recognition of the dot patterns build, so will their ability to recognize that 3 and 5 equal 8.
Below is a concentration game my students played matching the dot patterns to the numbers.
The first time I saw ten frames in our adopted math series, I wasn't really sure what to think about it. I didn't understand the reasoning behind the use of ten frames at first. As I began to teach the lessons from the teachers edition, I quickly realized the important role ten frames had on my young mathematicians. Ten frames enable children to see the relationship between numbers zero through ten. Using ten frames helps students develop visual images for each number. As students become familiar with the visual patterns on a ten frame, they begin to associate those patterns with specific numbers in terms of their relationship to ten. This begins to set the foundation for knowing the basic addition and subtraction facts for ten. Having sound knowledge of these basic facts are an integral part of mental calculations.
How Do I Foster the Skill of Subitizing?
In my classroom we begin early on using ten frames, dice and dominous. During my daily calendar routine I have a set of ten frame cards that hang on the calendar wall. In the beginning of the school year the only thing we are doing is counting the number of dots and saying the number. As time progresses I will ask the question "How many more dots do we need to make ten?" Soon the children learn to count the white boxes. We then begin to make the connections that 6 and 4 equal ten.
During our daily calendar routines throughout the year I introduce other actives that involve dice or dominoes. At first we just roll the dice, draw the dot patterns, count and write. We eventually work our way up to using two dice then using dominoes.
Below is another center or whole group actives using ten frames. I give a number and the students build the model.
This activity used erasers form the Target Dollar spot.
It was quick to make and prep and fun for the kids.
I hope I've given you some ideas on how to introduce subitizing into your classroom and why using dice, dominos and ten frame cards are so valuable in building a child's understanding of number sense.