The document discusses the importance and applications of counting in mathematics and daily life. It provides examples of how counting is used in basic arithmetic operations like addition and multiplication. It also explains how counting is applied in business for inventory management and logistics. The key points are that counting is fundamental to verifying mathematical operations, it can be done in various units of measurement, and accuracy in counting is important for accounting of physical goods.
2. Counting
• All mathematics is based on the very basic
principle that one and one are equal to two.
That two and one are equal to three.
• Counting in itself is quite a monotonous task.
• Many people find counting to be quite
tedious as a result.
• Counting is very important as it is the only
way any other mathematics can be verified.
3. Counting
• Counting doesn’t have to involve counting
individual units – you can count in groups
of units, fractions of units or in larger
denominations such as tens or millions.
• Counting does involve measuring in
predefined fixed amounts.
• Where a sequence is predefined but not
fixed then this is a function.
4. Counting
1 2 3 4 5 6 7 8 9 10
2 4 6 8 10 12 14 16 18 20
3 6 9 12 15 18 21 24 27 30
4 8 12 16 20 24 28 32 36 40
5 10 15 20 25 30 35 40 45 50
6 12 18 24 30 36 42 48 54 60
7 14 21 28 35 42 49 56 63 70
8 16 24 32 40 48 56 64 72 80
9 18 27 36 45 54 63 72 81 90
10 20 30 40 50 60 70 80 90 100
11 22 33 44 55 66 77 88 99 110
12 24 36 48 60 72 84 96 108 120
• All multiplication
tables are based
on counting.
• Counting is a
form of addition.
• The number of
times you count a
number equal the
amount you have
to multiply it by
to get that result.
12. Counting
• Try counting the following number of buttons
• I estimated that
there were around
800 buttons.
• I counted two 1cm
by 1cm squares and
used this as the basis
of my estimate.
15. Counting
• Write down all the numbers up to and
including one hundred.
16. Counting
• Write down all the numbers up to and
including one hundred.
• Pass the paper to the person next to you and
ask them to highlight any mistakes you
made.
• Did you find the results surprising?
• Did you use a method of laying out the
numbers to help prevent you from making
errors?
17. Counting
• A lot of people think counting is easy but
could you count quickly in an alternative
number base?
• For example computers these days often
use a hexadecimal or binary code.
• What are the hexadecimal and binary
equivalents of the number 16 in the
decimal sequence?
18. Sequences
• If you run across a series of numbers that appear to
have a natural order but that don’t change by a fixed
amount then it is likely that there is a function
controlling the sequence.
• Functions are typically notated as f(x).
• An example might be that f(x) = x2.
x 1 2 3 4 5 6 7 8 9
f(x) 1 4 9 16 25 36 49 64 81
19. Sequences
• Given the functions see if you can
complete the following sequences:
x 1 2 3 4 5 6 7 8 9
f(x) = 2x
2
4
6
8
10
12
14
16
18
x 1 2 3 4 5 6 7 8 9
f(x) = 2x +1
3
5
7
9
11
13
15
17
19
x 1 2 3 4 5 6 7 8 9
f(x) = 2(x + 1)
4
6
8
10
12
14
16
18
20
20. Sequences
• Given the functions see if you can
complete the following sequences:
x 1 2 3 4 5 6 7 8 9
f(x) = 2x 2 4 6 8 10 12 14 16 18
x 1 2 3 4 5 6 7 8 9
f(x) = 2x +1 3 5 7 9 11 13 15 17 19
x 1 2 3 4 5 6 7 8 9
f(x) = 2(x + 1) 4 6 8 10 12 14 16 18 20
21. Sequences
• You can see that the amount you count by
each time is equal to the sum of any
multiplications in the function.
• Where you begin counting is equal to the
sum of any additions in the function.
• Two of the most common functions are:
– f(x) = x2; also known as square numbers
– f(x) = (x(x + 1)) ÷ 2; also known as triangular
numbers
22. Counting
• Counting is a very important part of all
industries.
• Most companies that deal in physical
goods will have a number of teams which
deal in counting goods.
• Normally there will be a goods in
department, a despatch team and a stock
control department.
23. Counting
• For these sorts of job role counting is so important
that often the counts will be checked and double
checked and then compared to data on the
system.
• For example, when goods go out whoever picks
the goods counts how many they’ve picked. A
checker will then check the goods once they’re in
the bay. The loader will then count the goods on
to the vehicle picking up the delivery and the
driver will verify the count.
24. Counting
• When your calculator or computer
performs any type of action it uses
counting to reach an outcome.
• Like most activities the more you practice
the better you get. Easy ways to practice
might be to count reps when exercising or
to count how many times you beat a
friend in a competition.
