Key visualizations: Middle School Mathematics

As students begin to explore and learn about negative numbers, they benefit from building models that help them to look for and make use of structure within the system of rational numbers. The standards require that students understand integers as points on a number line. Students build on their prior understandings by extending number line diagrams. In so doing, students develop a deep understanding of opposites—as reflections across zero, as having the same distance from zero, and as having the same absolute value.

Connections to the TEKS []

This animation addresses the following Grade 6 TEKS for Mathematics:

(1)    Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(E)   create and use representations to organize, record, and communicate mathematical ideas;

(2)    Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:
(B)    identify a number, its opposite, and its absolute value;
(C)    locate, compare, and order integers and rational numbers using a number line;

About this animation []

This animation engages students in understanding how negative numbers are represented on the number line. Students begin with a standard number line and then reflect the positive part of the number line to create the negative part of the number line. In so doing, they begin to see new structure and balance in the number line as they are introduced to the key ideas of opposite and absolute value. This key visualization provides an engaging introduction and foundation for students’ work with integers.

How can Archibald find -5 on the number line?
If you place a mirror at zero, you can see the reflection of the number line.
Do you see the symmetry?
You don’t need a mirror to see the symmetry. You can use a piece of paper. Draw a line of symmetry through zero. Then create a reflection by folding the paper.
The numbers to the left of the zero are called negative numbers.
Archibald’s bank balance is negative five dollars, or $-5.
Negative five and positive five are reflections of each other.
Numbers that are the same distance from zero on the number line are called opposites. Archibald and his opposite are standing on two opposites, 5 and -5. Both are 5 units from 0 on the number line. What number is the opposite of zero?
Zero is the opposite of zero. In other words, zero is its own opposite.
The arrows for 5 and -5 have the same length, but go in different directions from 0. The integer 5 is five units to the right of 0. The integer -5 is five units to the left of 0. The distance from 0 is called the absolute value of the integer.