6th Grade Integers and Rational Numbers on the Number Line Lesson (Free PDF)

6th Grade math lesson: Integers and Rational Numbers on the Number Line – Maths PDF

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This integers rationals lesson for 6th Grade covers integers and rational numbers on the number line (Common Core 6.NS.C.5, 6.NS.C.6a, 6.NS.C.6c), with a free PDF to print.

Positive and negative numbers describe opposite directions from zero, such as above and below sea level. Opposites are the same distance from 0 on the other side, so the opposite of 3 is -3. Integers are whole numbers and their opposites, and rational numbers add fractions and decimals. All can be placed on a number line.

Grade 6 · Common Core State Standards: 6.NS.C.5, 6.NS.C.6a, 6.NS.C.6c

Key facts in this integers rationals lesson

Key facts

Positive numbers are above zero or to the right; negative numbers are below zero or to the left.
Opposites are the same distance from 0 on opposite sides.
The opposite of the opposite of a number is the number itself.
Integers are whole numbers and their opposites; rational numbers include fractions and decimals.
A vertical number line, like a thermometer, puts positive numbers on top.

What are positive and negative numbers?

Positive numbers describe amounts above zero, like 20 degrees on a warm day. Negative numbers describe amounts below zero, like a diver 25 feet below sea level or a bank balance that is overdrawn. Zero is neither positive nor negative.

Integers and rational numbers

The integers are the whole numbers and their opposites: -3, -2, -1, 0, 1, 2, 3 and so on. The rational numbers are all numbers that can be written as a fraction, such as $-\frac{1}{2}$, $2.5$, and $-7$.

A thermometer is a vertical number line.

How do you use integers to describe real situations?

Choose zero to mean “no change,” then use a positive number for one direction and a negative number for the other. A deposit of $60 is $+60$, and a payment of $40 is $-40$.

Positive and negative integers describe opposite changes.

What are opposites?

Two numbers are opposites if they are the same distance from 0 on opposite sides. The opposite of 3 is $-3$, and the opposite of $-3$ is 3. The opposite of 0 is 0. Writing $-(-3) = 3$ means the opposite of the opposite is the original number.

The opposites -3 and 3 are the same distance from 0.

How do you graph rational numbers on a number line?

Draw a line, mark 0, and choose a scale.
Mark equal intervals; positive numbers go to the right, negative to the left.
For a fraction or decimal, split each unit into equal parts.
Place a point and label it.

Rational numbers include fractions and decimals.

Rational numbers describe many real measurements: a temperature of $-2.5$ degrees, an elevation of $-\frac{3}{4}$ mile in a canyon, or a golf score below par. Always read the sign first, then the size. The sign tells the direction from zero, and the size tells the distance from zero.

The number $-2.5$ lies halfway between $-3$ and $-2$. A vertical number line, such as a thermometer, works the same way, with positive numbers going up.

Integers rationals lesson: questions and answers

What is an integer?

An integer is a whole number or the opposite of a whole number, like -5, 0, or 12. Integers have no fraction or decimal part.

What is the opposite of a number?

The opposite of a number is the number the same distance from 0 on the other side. The opposite of 7 is -7 and the opposite of -7 is 7.

What does zero mean in real-world situations?

Zero marks the starting point, such as sea level, 0 degrees, or a balance of $0. It means no gain and no loss.

How do you plot a negative fraction on a number line?

Split each unit into equal parts and count left from 0. The point for -1/2 is halfway between 0 and -1.

What is a rational number?

A rational number can be written as a fraction of two integers, with a nonzero denominator. Examples are 3/4, -2.5, and 6.

How to use this integers rationals lesson

Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.

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