Students who are not yet “fully operational” or able to reason using abstract concepts, can still learn form mathematical concepts with support. They typically need to develop these abstract representations of concepts in three stages, using: 1) concrete representations (like a geo-board) ; 2) semi-concrete representations (like a drawing); and 3) abstract representations (like a formula). While concrete “manipulatives,” like base-ten blocks, are widely used and effective in introducing concepts like place-value, evidence suggests that “virtual manipulatives” can be similarly effective.
Toytheater has an excellent selection of “virtual manipulatives” that students can use online, including a realistic version on fraction strips or fraction blocks. The image below will take you to their website (in a new tab) where you can explore their fraction strip app, along with other virtual manipulatives.
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