The document provides information about different types of numbers: - Integers are whole numbers that can be positive, negative, or zero. Prime numbers only divide by 1 and themselves. - Rational numbers can be written as fractions or recurring decimals. Irrational numbers are never-ending, non-repeating decimals like π. - Positive numbers are greater than 0, negative numbers are less than 0. A number line can help visualize positive and negative numbers and find differences between them. - Place value refers to the value of each digit in a number depending on its position - the further left, the greater the value. Large numbers can be written with commas separating groups of three digits.

1. FUNCTIONAL
SKILLS MATH

2. Starter: Introduction
Tutorial: All about
numbers, place value
 practice questions
Extension activity –
worksheets
Today!

3. Types of Numbers
Integers
An integer is another name for a whole number. They can be positive, negative or
zero.
Examples:
Integers: -99, 123, -6, 1234, 0
Non integers: 0.5, -2.987, π, √7
Prime Numbers
Prime numbers are special integers that only divide by themselves and 1. This
means that they cannot be divided by any other number. They are: 2, 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, 37, 41, 43, 47…….

4. Whole Numbers
Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, ... (and so on)
No Fractions!
Examples: 0, 7, 212 and 1023 are all whole numbers
(But numbers like ½, 1.1 and −5 are not whole
numbers.)

5. All numbers are either rational or irrational. A rational number is a number that can be
written as a fraction. They come in 3 different forms:
Integers – e.g. 4, -12, 9
Fractions – a/b where a and b are non-zero integers e.g. ¼, ½, 7/4,
Recurring decimals – e.g. 1/3 is 0.333333333333333……….
Irrational numbers cannot be written as a fraction. They are never ending non-repeating
decimals. For example the famous π (pi) is 3.14159265359….. and carries on and on with
no repeating units.
Square roots can be either rational or irrational. For example √2 is irrational as it equals
1.414213562….. but √4 isn’t as it equals 2.
Rational and Irrational

6. Activity
1. Sort these numbers into either rational or irrational.
9.0, 7.543, -2.4, √7, √23, √25, 0.143143143143…

7. Positive and Negative Numbers
Numbers can either be positive, if they are greater than 0, or negative, if they are less
than 0.
Number lines can help you visualise certain number problems, for instance they are
really helpful in allowing you to grasp the concept of negative numbers. They can
also be useful to find the difference between two numbers.
The further right you go on the number line, the larger the numbers become, e.g. 3 is
larger than -1 and −1 which is larger than −2

9. Example 2: Positive and Negative Numbers
Which number is larger, -3 or -8?
Because both of these numbers are negative, so the number which is larger is the one
with a smaller number after the minus (−) sign, which is −3
Example 3: Number Line
The temperature at night was −3°C, and then the temperature in the daytime was 11°C.
Work out the difference between the temperature at night and in the daytime.
First draw a number line that includes both −3 and 11.
Then count on from −3 to 11.
As shown on the number line above, there are 14 steps, so the difference is 14°C

12. Scales
Scales are just number lines that are often used in real life scenarios, for
example a thermometer.
Sometimes they don’t always show every number and just increase
in intervals.
The ruler below is an example of a scale, used to measure lengths.

13. Place Value
The value of each digit decreases, going from left to right. Each digit in the number has a different value,
e.g. the 5 means 50,000. The value for each digit added together makes the number.
To read or write a large number, break up the number into groups of three digits starting from the right,
using commas if we wish.
We then have a millions group, a thousands group and the rest. Therefore, this number can be spoken in
words as
18 million, 852 thousand, 5 hundred and 34
or
eighteen million, eight hundred and fifty-two thousand, five hundred and thirty-four

14. Example 1: State the place value of the 6 in 5609.
Counting from right to left, we can see that the 6 is in the third column
along – the hundreds column.
Therefore, the value of the ‘6 digit’ in this number is 600.
Example 2: Write the number five million, one hundred and two
thousand and forty-five in figures.
Draw a place-value table and fill in the digits, from the right.

15. What is the value of the 5 in 527023?