Ten frames and dot cards can be used to develop students’ subitizing
skills, the ability to “instantly see how many”. This skill plays a
fundamental role in the development of students’ understanding of
number. Two types of subitizing exist. Perceptual subitizing is
closest to the original definition of subitizing: recognizing a number
without using other mathematical processes. For example, a child as
young as two might “see 3” without using any learned mathematical
knowledge. Conceptual subitizing is being used when a person sees an
eight dot domino and “just knows” the total number. The number pattern
is recognized as a composite of parts and as a whole. The domino is seen
as being composed of two groups of four and as “one eight”.
Enlarged dot cards
can be used during mental math sessions to prompt mental images of
numbers and different mental strategies for manipulating these numbers.
Activities with enlarged ten frames
enable children to automatically think of numbers less than ten in
terms of their relationship to ten, and to build a sound knowledge of
the basic addition and subtraction facts for ten, which are an integral
part of mental calculation.
Listed below are some examples of ways that these materials can be used during mental math sessions to build number sense:
Flash a dot or ten frame card briefly and have students write the number on a whiteboard. Using whiteboards, rather than having students say the number, ensures that all children attempt to respond and allows the teacher to assess class progress. When the response is oral, not all student responses are audible. Encourage students to share the different strategies used to find the total number of dots for cards, “How did you see it?” This can be varied by asking students to write the number and draw the pattern they saw, or by having them build the number flashed on their own blank frame.
Flash: One More
Once students are familiar with the basic patterns, and know them automatically, flash a 10 frame or dot card and ask them to name the number that is one more than the number flashed.
Variation: ask students to give the number that is two more/one less/double/ten more than the number flashed
I Wish I Had 10
Flash a dot card or ten frame showing 9 or less and say, “I wish I had 10”. Students respond with the part that is needed to make ten. The game can focus on a single whole, or the “wish I had” number can change each time.
Variation: teacher flashes card and students write the complement of ten on individual whiteboards with dry erase markers.
I Wish I Had 12
As above but students respond with how many more are needed to make twelve. Students should be confident in facts of 10 before this is attempted. For example to go from 8 to 12, they should realize they need 2 more to get to 10, then 2 more to 12. 2 and 2 is 4.
Variation: students draw an empty number line on their whiteboards to show the two jumps used to get to the target number.
1 more/1 less/10 more/10 less
The following four prompts are written on the board:
The teacher flashes a dot or ten frame card as the ‘starting number’. The first student selects one prompt. For example, if the teacher flashes a card showing ‘5’ the first student might say, “one more than 5 is 6”, the second student might say, “ten more than 6 is 16”, and the third student might say, “one less than 16 is 15”. Continue until all students have had a turn.
Teen Frame Flash (11-20)
Once students are subitizing dot/ten frame patterns 0- 10, cards showing larger numbers (i.e. more than one ten frame) should be introduced. A large copy of dot cards 11-20 can be posted on the math bulletin board showing the numeral and numeral word and a smaller version, without numerals, used during mental math sessions with the following key questions: How many?; How many more than 10?
As students become familiar with the 'teen' patterns introduce further questions to develop number relationships.
Flash a dot or ten frame card and ask students to give you the product if the number you flash was multiplied by 2, 5 etc.