Counting

Functional Skills Maths

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.

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.

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.

Counting

• Try counting the following number of buttons

Counting

• Try counting the following number of buttons

• There are 6 buttons

Counting

• Try counting the following number of buttons

Counting

• Try counting the following number of buttons

• There are 10 buttons

Counting

• Try counting the following number of buttons

Counting

• Try counting the following number of buttons

• There are 68 buttons.

• Even simply counting can be quite difficult.

Counting• Try counting the following number of buttons

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.

Counting

• Try completing the following sequences:

• 2, 4, 6, 8, 10, 12, …

• 3, 6, 9, 12, 15, …

• 4, 5, 6, 7, 8, …

• 10, 20, 30, 40, 50, …

• 5, 7, 9, 11, 13, …

• 32, 30, 28, 26, 24, …

• 1.3, 2.5, 3.7, 4.9, 6.1, …

Counting

• Try completing the following sequences:

• 2, 4, 6, 8, 10, 12, …

• 3, 6, 9, 12, 15, …

• 4, 5, 6, 7, 8, …

• 10, 20, 30, 40, 50, …

• 5, 7, 9, 11, 13, …

• 32, 30, 28, 26, 24, …

• 1.3, 2.5, 3.7, 4.9, 6.1, …

• 14

• 18

• 9

• 60

• 15

• 22

• 7.3

Counting

• Write down all the numbers up to and including one hundred.

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?

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?

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

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

x 1 2 3 4 5 6 7 8 9

f(x) = 2x 2 4 6 8 10 12 14 16

x 1 2 3 4 5 6 7 8 9

f(x) = 2x 2 4 6 8 10 12 14

x 1 2 3 4 5 6 7 8 9

f(x) = 2x 2 4 6 8 10 12

x 1 2 3 4 5 6 7 8 9

f(x) = 2x 2 4 6 8 10

x 1 2 3 4 5 6 7 8 9

f(x) = 2x 2 4 6 8

x 1 2 3 4 5 6 7 8 9

f(x) = 2x 2 4 6

x 1 2 3 4 5 6 7 8 9

f(x) = 2x 2 4

x 1 2 3 4 5 6 7 8 9

f(x) = 2x 2

x 1 2 3 4 5 6 7 8 9

f(x) = 2x

x 1 2 3 4 5 6 7 8 9

f(x) = 2x +1 3 5 7 9 11 13 15 17

x 1 2 3 4 5 6 7 8 9

f(x) = 2x +1 3 5 7 9 11 13 15

x 1 2 3 4 5 6 7 8 9

f(x) = 2x +1 3 5 7 9 11 13

x 1 2 3 4 5 6 7 8 9

f(x) = 2x +1 3 5 7 9 11

x 1 2 3 4 5 6 7 8 9

f(x) = 2x +1 3 5 7 9

x 1 2 3 4 5 6 7 8 9

f(x) = 2x +1 3 5 7

x 1 2 3 4 5 6 7 8 9

f(x) = 2x +1 3 5

x 1 2 3 4 5 6 7 8 9

f(x) = 2x +1 3

x 1 2 3 4 5 6 7 8 9

f(x) = 2x +1

x 1 2 3 4 5 6 7 8 9

f(x) = 2(x + 1) 4 6 8 10 12 14 16 18

x 1 2 3 4 5 6 7 8 9

f(x) = 2(x + 1) 4 6 8 10 12 14 16

x 1 2 3 4 5 6 7 8 9

f(x) = 2(x + 1) 4 6 8 10 12 14

x 1 2 3 4 5 6 7 8 9

f(x) = 2(x + 1) 4 6 8 10 12

x 1 2 3 4 5 6 7 8 9

f(x) = 2(x + 1) 4 6 8 10

x 1 2 3 4 5 6 7 8 9

f(x) = 2(x + 1) 4 6 8

x 1 2 3 4 5 6 7 8 9

f(x) = 2(x + 1) 4 6

x 1 2 3 4 5 6 7 8 9

f(x) = 2(x + 1) 4

x 1 2 3 4 5 6 7 8 9

f(x) = 2(x + 1)

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

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

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.

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.

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.