September 26, 2022

# Why is the use of the number line a relevant strategy to teaching number operations?_ Felix Agboyi *What is a Number Line?*

A Number Line is a graduated straight line that graphically represents real numbers. And every point on a number line is assumed to correspond to a real number, and every real number to a point, where positive numbers always lie on the right side of zero, negative numbers always lie on the left side of zero, and arrowheads on both ends of the line is meant to suggest that the line continues indefinitely in the positive and negative directions.

The integers (whole numbers, when understood to include zero and negative numbers) are often shown as specially-marked points evenly spaced on the line.

The diagram below, characteristically, is a number line. As indicated earlier, and although it only shows the integers from –5 to 5, the line includes all real numbers, continuing forever in each direction, and also numbers that are between the integers. It is often used as an aid in teaching simple comparisons, orderings, addition, subtraction, multiplication and division, especially involving negative numbers.

<—+—+—+—+—+—+—+—+—+—+—+—>
-5 -4 -3 -2 -1 0 1 2 3 4 5

Besides, if a particular number is farther to the right on the number line than is another number, then the first number is greater than the second (equivalently, the second is less than the first). As such, and per the number line above, we can vividly say that 0 is greater than -1, and 1 is greater than 0.

Why is the use of the number line a relevant strategy to teaching number operations?

A strong foundation in early number concepts is critical for students’ future success in Mathematics. Research suggests that visual representations, like a number line, support students’ development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction to transition from concrete to visual to abstract representations of Mathematics concepts supports students’ conceptual understanding (Woods et al., 2018).

Irrespective, most teachers wrongly assume that learners know or should know basic number operations at a particular level, and that they (teachers) just have to spell out the several rules and formulas of performing basic operations to be at par with time. And this makes such teachers become guilty of giving faulty instructions. Why?

For instance, telling your learners that two negatives make a positive (“nege. nege. po.” as it is usually sounded) without an activity aimed at proving the rule would seem as a rule forced on them. And when it happens so, learners, mostly the struggling ones, start to ask within themselves “how and why it is so.” This simply means the learners need a “plan” on how to figure out the answer independently, and this is why the number line activity is an invaluable resource!

Apart from the number line being a versatile and powerful visual tool to help students learn numbers, using it in a motivating and accessible way even makes learners do perfectly well without using books or pencil/paper work to figure out answers to given operations.

Number lines in effect help learners to count forward and backwards with less effort since it presents numbers in real life primarily because they enable negative numbers to be represented in a way that makes sense.

_*When and how is the number line used to teach number operations?*_

The number line can be used as an introductory activity,a reinforcement or build up or as an assessment tool.

A. *The use of the number line as an introductory activity:*

For lower grades, a ray (a definite extending line in one direction from zero (0) )can be introduced, where learners are asked to complete the count sequence or identify missing numbers. E.g.

<—+—+—+—+—+—+—+—+—+—+—+—>
0 1 2 4 5 6 7 9 10

For upper grades, first be sure to point out to learners that apart from the usual counting numbers (positives which could be interpreted as assets) we use daily, there is also a group of numbers that are less than zero(0) called negative numbers which could be interpreted as dept. And that both groups of numbers could be visually represented as a number line. Further discuss the concept that the more you move to the right, the higher the number, and the more you move to the left, the lesser the number.

B. *The use of the number line as a reinforcement (in the course of the lesson):*

The number line can be incorporated in the course of number operation lessons as an activity to prove basic mathematics facts. For example, simple logic may prove 2-6 to be -4, yet it cannot prove that 2-(-4)= 2+4= 1. But a number line activity can perfectly do so. And as more illustrative number operation examples are solved with the number line, with the aim of creating a pattern, learners become the discoverers of the rule, and not the other way round.

C. *The use of the number line as an assessment tool:*

Assessment embodies reflection on experiences, and the number line can positively serve this purpose since it has a bearing on real life. And knowing that learners will be required in the near or far future to understand symmetry, where mathematics will be geometrically portrayed as the Cartesian Plane to knowing when and where their next turn will be when driving on a road, gives a substantial motivation for providing them with a kinesthetic number line activity at their early stages.

*To make it more a learning by doing activity, the number line could be drawn on the floor and learners tasked to perform given operations using their feet to do the moves, skips or hops.*

In summary, teaching basic maths facts should have a connection to real life, for it is expected that learners are taught well the foundational concepts of maths to enable them thrive in a world that requires a substantial knowledge of Mathematics more than ever. And learning by doing is the only strategy that can bridge this gab.

References:
_Number Line_. Wikipedia. https://en.m.wikipedia.org/wiki/Number_line

_Adding and Subtracting Positive and Negative Numbers using the Number Line_. ChiliMath.com. https://www.chilimath.com/lessons/introductory-algebra/add-and-subtract-numbers-using-the-number-line/

_Real World Examples For Teaching Fractions On a Number Line_. Beyond Traditional Maths. https://www.google.com/amp/s/beyondtraditionalmath.wordpress.com/2017/04/10/real-world-examples-for-teaching-fractions-on-a-number-line/amp/

✍️ Felix Agboyi_ Lead Educator_ Informed Teachers Network