Rational Numbers
Rational Numbers
Items in this lesson
Rational Numbers
This lesson opens with the big idea that rational numbers are numbers that can be written as a fraction. Keep examples concrete and familiar: halves, negatives, and decimals such as 0.5.
Our learning goal
I can recognise and use rational numbers in fractions, decimals and integers.
This item has no instructions
What number words come to mind: fraction, decimal, integer?
Use this as a quick activation. Accept simple words or examples such as half, point five, whole, negative, zero.
What is a rational number?
A rational number is a number that can be written as a fraction.
It can be written as a/b where:
a and b are integers
b is not 0
Use simple spoken examples: 1/2, 3, -4, and 0.75. Stress that whole numbers are also rational because they can be written over 1.
Examples of rational numbers
These are all rational numbers:
1/3
-2/5
7
0.6
-1.25
Each one can be written as a fraction.
This item has no instructions
Integers are rational too
Any integer can be written as a fraction.
Examples:
5 = 5/1
-3 = -3/1
0 = 0/1
So integers are part of the rational numbers.
Students often think fractions and whole numbers are separate groups. Emphasise that rational numbers include both.
Rational numbers on a number line
Rational numbers can be:
positive
negative
zero
They fit on the number line between and beyond whole numbers.
Point out that 1/2 is between 0 and 1, and -1/2 is between -1 and 0. This helps students see rational numbers as part of one number system.
Fractions, decimals and integers
Rational numbers can look different, but they can name the same value.
Examples:
1/2 = 0.5
3/4 = 0.75
2 = 2/1
-1 = -1/1
This slide links the different forms named in the objective. Keep the focus on equivalence, not conversion methods in depth.
Which number is an integer and a rational number?
0.6
-3
1/2
2/5
Checks the idea from slides 2 to 6 that integers are also rational numbers because they can be written over 1.
Rational numbers can look different
A rational number can be written as a fraction. An integer is rational too, because 5 can be written as 5/1. On a number line, rational numbers can be positive, negative, or zero.
Echoes the key summary of the first subtopic: definition, integers as rational, and location on the number line.
Changing a fraction to a decimal
To change a fraction to a decimal, divide the top number by the bottom number.
Examples:
1 ÷ 2 = 0.5
3 ÷ 4 = 0.75
1 ÷ 5 = 0.2
Model the reading aloud: numerator divided by denominator. Avoid long division detail unless needed; the slide's beat is the idea of division.
Changing a decimal to a fraction
A decimal can be written as a fraction.
Examples:
0.5 = 5/10 = 1/2
0.2 = 2/10 = 1/5
0.75 = 75/100 = 3/4
If helpful, say that the place value tells the first fraction: tenths, hundredths, and so on. Then simplify.
Equivalent rational numbers
Some rational numbers look different but are equal.
Examples:
1/2 = 2/4 = 4/8
0.5 = 1/2
These are called equivalent numbers.
Connect this idea to why fractions and decimals can represent the same point on a number line.
Terminating decimals
Some rational numbers have decimals that stop.
Examples:
1/2 = 0.5
3/5 = 0.6
7/20 = 0.35
These are terminating decimals.
Use the word 'stop' alongside 'terminate' for accessibility.
Repeating decimals
Some rational numbers have decimals that repeat a pattern.
Examples:
1/3 = 0.333...
2/3 = 0.666...
1/11 = 0.090909...
These are repeating decimals.
Students may think the dots mean the answer is unfinished. Explain that the pattern goes on forever, and that still makes it rational.
How to spot rational numbers
A number is rational if it is:
an integer
a fraction
a terminating decimal
a repeating decimal
All of these can be written as a fraction.
This is the landing summary of the lesson's main classification rule.
How do you change 1/5 to a decimal?
Add 1 and 5
Divide 1 by 5
Multiply 1 by 5
Swap the numbers
Targets the rule on slide 7: top number divided by bottom number.
Fractions and decimals can match
A fraction can change to a decimal by dividing the top number by the bottom number. A decimal can change to a fraction. Some numbers look different but are equivalent. A decimal that stops is called terminating, and a decimal with a pattern is called repeating.
Covers the second subtopic from slides 7 to 12: conversion, equivalent values, and decimal types.
Name one rational number.
Look for one correct example from the lesson: an integer, a fraction, a terminating decimal, or a repeating decimal. Invite students to explain why if they can.
What is one thing you learned today?
Reflection only. Encourage short answers about one idea they learned, such as fractions, decimals, integers, or repeating decimals.
What helped you understand best?
Reflection only. Students may mention number lines, examples, changing fractions to decimals, or seeing matching values like 1/2 and 0.5.
What part felt hardest today?
Reflection only. Possible answers include repeating decimals, changing decimals to fractions, or telling integers and fractions apart.
Glossary
rational number - a number that can be written as a fraction
fraction - a number written as one integer over another integer
integer - a whole number, a negative whole number, or zero
decimal - a number written with a decimal point
equivalent - equal in value even if it looks different
terminating decimal - a decimal that stops
repeating decimal - a decimal with a pattern that goes on
This item has no instructions
