Many teachers play flash games using paper plates with circle stickers or dots created by bingo dabbers. They show a dot arrangement very briefly and ask students if they recognize it. Although some arrangments are more commonly used than others, some teachers use a variety of representations often enough that students begin to recognize them right away. Teachers might sometimes ask students to verbalize how they recognized the number they did, particularly numbers greater than five, although that is not necessary every time.”¹ 

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Numbers are just symbols until the have a referent. Referents are the visual images we store in our minds that help us to estimate.

For example, using non-standard units to measure length helps learners to construct a mental image based on a referent (e.g. two pencils long). When they explore using other non-standard units, learners build and compare measurement data and work toward refining their reasoning about measurement in different contexts – length (distance and time), area, perimeter, capacity, and mass.