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Overview
Overview
Unitizing is the understanding that you can count a large group of items by decomposing or breaking it down into smaller equal groups of items, and then counting those. For example, a group of 12 counters could be unitized into groups of 3 (easy to perceptually subitize), and then skip counted, "3, 6, 9, 12". Unitizing can be thought of as many-to-one correspondence. We can think of unitizing the 12 counters from before as three-to-one correspondence, as we are counting 3 items in each group. Unitizing also connects to multiplication and ratios.
In our base-ten place value system, we unitize by grouping objects into tens once the count exceeds 9 (and into tens of tens when it exceeds 99). This grouping of objects is indicated by a 1 in the tens place of a number once the count exceeds 9 (and by a 1 in the hundreds place once the count exceeds 99).
While students are learning the counting principles, these principles, such as unitizing, are important foundational skills that must be consolidated into a strong understanding. You will find that many of the counting principles are interconnected. Once students have a solid understanding of the counting principles, many of them will become key ideas that support students as they develop addition/subtraction strategies for learning mathematics.
Supporting Students with Unitizing
Supporting Students with Unitizing
To support students learning to unitize, provide many opportunities to practice counting groups of objects (e.g., 1 group of 2, 2 groups of 2, 3 groups of 2, etc.). Allow students opportunities to sort objects into groups in ways that make sense to them (e.g., by colour). Initially, these groups can be any size, as the focus is on getting students to see a group as a single unit, but eventually, we want the groups to be equal amounts to support students in understanding the efficiency of counting by groups.
Games to Promote Unitizing
Games to Promote Unitizing
Bug Under the Rug
Bug Under the Rug
This game provides the opportunity for students to subitize in a variety of ways. Plates or paper image representations include numerals, die dot patterns, raised fingers and five-or ten-frames.
Bug Under the Rug game instructions (BLM) (English)
Unitizing - Concrete Materials Activity Cards
Unitizing - Concrete Materials Activity Cards
This activity can be completed by students using the Large Concrete Activity Cards and a concrete math material (e.g., unifix cube ten sticks) to deconstruct various 2-digit numbers, unitizing the tens and ones quantity shown.
Unitizing - Concrete Materials activity instructions (English)
Unitizing - Concrete Materials activity cards (BLM) (English)
Tens & Ones Place Value Chart (BLM) (English)
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