“Number visualization occurs when students create mental representations of numbers.”1 Students use concrete, pictorial, and symbolic representations to explore strategies and communicate their mathematical thinking. When students use a concrete or pictorial model, that model is a tool that students use to make their thinking visible.

“In order to develop every student’s mathematical proficiency, leaders and teachers must systematically integrate the use of concrete and virtual manipulatives into classroom instruction at all grade levels.”2 

Visuals that are familiar to students can also connect a new concept to prior learning. For example, number lines are a visual of number order that students use when working with whole numbers. When fractions or decimals are introduced that same number line, which is now familiar, can be used to build an understanding of how decimals and fractions can fall between whole numbers.

There are many different ways to represent numbers and representations can be used to focus student thinking on different concepts found within number sense.

1Ministry of Education, S. (2007). Retrieved 20 June 2020, from p. 13.

2Improving Student Achievement in Mathematics by Using Manipulatives with Classroom Instruction., 2013. NCSM Position Paper. [online] Available at: <> [Accessed 19 August 2021].