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Vertical Number Lines are Important, Too!

Katelyn Devine

Introduction

Concrete representations are used to develop an un derstanding of the mathematics involved in the world around us. The Virginia Standards of Learn ing (SOL) call for the use of multiple representa tions to develop number sense and computation concepts. However, when the use of number lines are called for, teachers too often rely on the hori zontal orientation. Exposing students to a balance of vertical and horizonal number lines builds spa tial reasoning and flexible thinking about numbers. Encouraging students to use a representation that makes sense to them is imperative to the develop ment of a positive mathematical identity. When comparing both absolute and relative num bers, results show a stronger desire to use a vertical number line compared to a horizontal number line (Winter & Matlock, 2013). People are more likely to use a vertical mapping when applications to real world context involve magnitude and are more likely to use a horizontal mapping for those that in volve distance (Simms, Muldoon, & Towse, 2013).

Figure 2: Ordering integers

When a context is not provided, allow students to choose between using a vertical or horizontal num ber line representation. Providing children with opportunities to explore another type of orienta tions, the vertical, can lead to a deeper understand ing of comparing and ordering numbers and solv ing single and multistep practical problems. Language plays a role in determining if the context is better situated for a horizontal or vertical orienta tion. Words such as above and below provide nat ural connotations for a vertical orientation whereas words like before and after relate to horizontal ori entations. Figure 1 shows five scenarios and how students in sixth grade typically sorted them when asked if they would use a vertical or a horizontal number line. When comparing and ordering integers, it is im portant to provide opportunities for students to see differing integer values in multiple representations including tiles, horizontal number lines, and verti cal number lines. Many times, teachers present contexts that are best suit for vertical number lines but only provide a horizonal number line. This limit student ’ s ability to think flexibly about num Connection to Language Comparing and Ordering Integers

Vertical

Horizontal

A fish was swimming 5 feet below sea level. A bird was flying 8 feet above sea lev el. If the sea turtle was swimming 7 feet below the fish, what was the distance between the sea turtle and the bird? At noon on a given day, it was 7 degrees below zero in Boston, 12 degrees above zero in Erie, 15 degrees above zero in Harrisonburg, and 13 degrees below zero in Minneapolis. Which city was the coldest at noon on that given day? You must be a minimum of 54 inches to ride the roller coaster. If Tommy is 42 inches tall, can he ride the roller coaster?

Sally, Jamiya, and Breyanna were running a race. After eight minutes, Sally was 8 feet before the finish line, Jamiya was 7 feet after the finish line, and Breyanna was 3 feet before the finish line. Assuming they all ran the race as a constant speed, arrange the runners from fastest to slowest. On the first play, the Jagu ars gained 4 yards. On the second play, they lost 6 yards. Where are they in relation to where they start ed?

Figure 1: Sorting solution from 6th grade class

Virginia Mathematics Teacher vol. 46, no. 2

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