Lesson 2

Points on the Number Line

Lesson Narrative

In this second lesson on signed numbers, students learn about opposites​.  First they revisit the context of temperature, represented on a vertical number line, extending previous work with interpreting equally spaced divisions to the negative part of the number line. The purpose of this activity is to reestablish the interpretation of distance on the number line in the context of negative numbers. They then create folded number lines to reason about opposites, which are numbers that are on opposite sides of 0 but the same distance from zero. Students will have more practice placing rational numbers of all kinds on the number line in future lessons. In this lesson, it is more important to focus on the concept of opposites than plotting different kinds of rational numbers.

Learning Goals

Teacher Facing

• Comprehend that two numbers are called “opposites” when they are the same distance from zero, but on different sides of the number line.
• Interpret a point on the number line that represents a positive or negative rational number.
• Plot a point on a number line to represent a positive or negative rational number.

Student Facing

Let’s plot positive and negative numbers on the number line.

Required Preparation

Each student needs access to a ruler marked with centimeters and at least 1 sheet of tracing paper. If the tracing paper is less than 20 cm wide, then students will need to construct their number lines in the “Folded Number Lines” activity to go from -7 to 7, or otherwise construct their number line on the diagonal of the tracing paper.

Student Facing

• I can determine or approximate the value of any point on a number line.
• I can represent negative numbers on a number line.
• I understand what it means for numbers to be opposites.

Building On

Building Towards

Glossary Entries

• negative number

A negative number is a number that is less than zero. On a horizontal number line, negative numbers are usually shown to the left of 0.

• opposite

Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.

For example, 4 is the opposite of -4, and -4 is the opposite of 4. They are both the same distance from 0. One is negative, and the other is positive.

• positive number

A positive number is a number that is greater than zero. On a horizontal number line, positive numbers are usually shown to the right of 0.

• rational number

A rational number is a fraction or the opposite of a fraction.

For example, 8 and -8 are rational numbers because they can be written as $$\frac81$$ and $$\text-\frac81$$.

Also, 0.75 and -0.75 are rational numbers because they can be written as $$\frac{75}{100}$$ and $$\text-\frac{75}{100}$$.