Patterns and Relationships

Mathematical Literacy 2Future Managers 1

Patterns and relationships• Patterns for different relationships

• Using information to solve problems

• Translate between different representations of relationships

Mathematical Literacy 2Future Managers 2

Patterns for different relationships

• Investigate and understand numerical and geometric patterns

• Describe patterns in words and/or through formulae

• Use formulae with confidence

• Generate patterns from their descriptions

Mathematical Literacy 2Future Managers 3

Background to patterns

• Arithmetic patterns– Show a constant difference– e.g. 2; 4; 6; 8; 10

• Geometric patterns– Show a constant ratio– e.g. 2; 4; 8; 16; 32

Mathematical Literacy 2Future Managers 4

Interest rates• Interest rates form patterns• The original amount represents 100% or 1.00• The rate of interest is expressed as a decimal (e.g.

10% = 0.1) and is added to the 1.00• We then take the original amount and multiply it

by this number (e.g.. 500 x 1.1)• For each year, we multiply it by 1.1 each time

Mathematical Literacy 2

An interest rate of 10% means you double your money every 7 ¼ years

Future Managers 5

Direct and indirect relationships

• Direct relationship– An increase in one variable leads to an increase in the

other e.g. petrol and range

• Indirect relationship– An increase in one variable leads to a decrease in the

other e.g. price of petrol and litres that can be bought with R100

Mathematical Literacy 2Future Managers 6

Putting patterns into words• Input and output values

– The value that you put into the formula is called the input value (x-value)

– The value that you get out of the formula is called the output value (y-value)

• e.g. multiply the number by 4 and add 5

y = 4x + 5• This information can be plotted on a graph

Mathematical Literacy 2Future Managers 7

Mathematical Literacy 2

x -value

y - value

-4 -11

-3 -7

-2 -3

-1 1

0 5

1 9

2 13

3 17

4 21

-15

-10

-5

0

5

10

15

20

25

-4 -3 -2 -1 0 1 2 3 4

y = 4x + 5

Future Managers 8

Using information to solve patterns

• At the end of this outcome, you will be able to:– Identify and select information from different

representations of relationships to solve problems

Mathematical Literacy 2Future Managers 9

Translate between different representations of

relationships

• At the end of this outcome, you will be able to:– Convert representations of relationships from one

form to another to solve problems– Select and developed representations of relationships

to solve problems and to communicate or illustrate a result

Mathematical Literacy 2Future Managers 10

Translate between different representations of

relationships• Converting patterns

• Selection of presentations

Mathematical Literacy 2Future Managers 11