# National 4 Applications of Mathematics

This course is spread across three units :

Managing Finance and Statistics (F&S), Geometry & Measures (G&M) and Numeracy (Num)

# Managing Finance and Statistics (F&S)

F&S 1.1 :Interpreting a situation involving finance and identifying an appropriate strategy.
F&S 1.2 :Using appropriate mathematical processes and/or calculations to determine a solution.
F&S 1.3 :Explaining a solution in relation to the context.

F&S 2.1 : Interpreting a situation involving data and identifying an appropriate strategy.
F&S 2.2 :Representing data appropriately.
F&S 2.3 : Interpreting and/or comparing data to draw conclusions.

## Finance

Key subskills:
Determining a financial position, given budget information.
Investigating factors affecting income.
Determining the best deal, given two pieces of information.
Converting between currencies.
Investigating the impact of interest rates for savings and borrowing in a basic situation.

F&S 1.1 Interpreting a situation involving finance and identifying an appropriate strategy. F&S 1.2 Using appropriate mathematical processes and/or calculations to determine a solution. F&S 1.3 Explaining a solution in relation to the context.

## Statistics

Key subskills:
Using statistics to investigate risk.
Using and presenting statistical information in diagrams.
Using diagrams to illustrate data.
Comparing data sets, using mean and range.
Constructing a frequency table.
Constructing a scattergraph.
Drawing a best fitting straight line on a scattergraph.

F&S 2.1 Interpreting a situation involving data and identifying an appropriate strategy. F&S 2.2 :Representing data appropriately. F&S 2.3 Interpreting and/or comparing data to draw conclusions. Num 2.1 Extracting and interpretation data from at least two different straightforward graphical forms. Num 2.2 Making and explaining decisions based on the interpretation of data. Num 2.3 Making and explaining decisions based on probability.

# Geometry & Measures (G&M)

G&M 1.1 : Analysing a situation involving measurement and identifying an appropriate strategy.
G&M 1.2 : Using appropriate mathematical processes and/or calculations to determine a solution.
G&M 1.3 : Justifying a solution in relation to the context.

G&M 2.1 :Analysing a situation involving geometry and identifying a valid strategy.
G&M 2.2 : Using appropriate mathematical processes and/or calculations to determine a solution.
G&M 2.3 : Justifying a solution in relation to the context.

## Geometry

Key subskills:
Determining the gradient of a slope.
Investigating a situation involving perimeter.
Investigating a situation involving area.
Investigating a situation involving volume.
Solving a problem involving the use of Pythagoras’ theorem.
Using a scale factor on the dimensions of a shape.

G&M 2.1 Analysing a situation involving geometry and identifying a valid strategy. G&M 2.2 Using appropriate mathematical processes and/or calculations to determine a solution. G&M 2.3 Justifying a solution in relation to the context.

## Measures

Key subskills:
Solving a basic problem in time management.
Calculating a quantity based on a related measurement.
Constructing a scale drawing with a given scale.
Carrying out container packing, using a first-fit algorithm.
Investigating the need for tolerance in a measurement.

G&M 1.1 Analysing a situation involving measurement and identifying an appropriate strategy. G&M 1.2 Using appropriate mathematical processes and/or calculations to determine a solution. G&M 1.3 Justifying a solution in relation to the context.

# Numeracy (Num)

Num 1.1 : Selecting and using appropriate numerical notation and units.
Num 1.2: Selecting and carrying out calculations.
Num 1.3 : Reading measurements using a straightforward scale on an instrument.
Num 1.4 : Interpreting the measurements and the results of calculations to make decisions.
Num 1.5 :Justifying decisions using the results of measurements or calculations.

Num 2.1: Extracting and interpretation data from at least two different straightforward graphical forms.
Num 2.2: Making and explaining decisions based on the interpretation of data.
Num 2.3: Making and explaining decisions based on probability.

## Calculations and Rounding

Key subskills:
Add and subtract whole numbers including negative numbers.
Multiply whole numbers of any size, with up to four-digit whole numbers.
Divide whole numbers of any size, by a single digit whole number or by 10 or 100.
Round answers to the nearest significant figure or two decimal places .
Use appropriate checking methods, eg check sums and estimation.
Interpret results of measurements involving time, length, weight, volume and temperature.
Give reasons for decisions based on the results of measurements or calculations.

Num 1.1 Selecting and using appropriate numerical notation and units.Num 1.2 Selecting and carrying out calculations.Num 1.4 Interpreting the measurements and the results of calculations to make decisions.Num 1.5 Explaining decisions based on the results of measurements or calculations.

## Fractions, Percentages, Ratio

Key subskills:
Find simple percentages and fractions of shapes and quantities.
Calculate percentage increase and decrease.
Convert equivalences between common fractions, decimal fractions and percentages.
Calculate rate: eg miles per hour or number of texts per month.
Calculate ratio and direct proportion.
Give reasons for decisions based on the results of measurements or calculations.

Num 1.1 Selecting and using appropriate numerical notation and units.Num 1.2 Selecting and carrying out calculations.Num 1.4 Interpreting the measurements and the results of calculations to make decisions.Num 1.5 Explaining decisions based on the results of measurements or calculations.

## Distance, Speed and Time

Key subskills:

Calculate distance given speed and time.
Calculate time intervals using the 12- and 24-hour clock.

Num 1.1 Selecting and using appropriate numerical notation and units.Num 1.2 Selecting and carrying out calculations.Num 1.4 Interpreting the measurements and the results of calculations to make decisions.Num 1.5 Explaining decisions based on the results of measurements or calculations.

## Measurements, Perimeter, Area and Volume

Key subskills:
Use measuring instruments with straightforward scales to measure length, weight, volume and temperature.
Read scales to the nearest marked, unnumbered division with a functional degree of accuracy.
Calculate volume (cube and cuboid), area (rectangle and square) and perimeter (shapes with straight lines).
Recognise the inter-relationship between units in the same family, eg mm→cm, cm→m, g→kg, and ml→l
Use vocabulary associated with measurement to make comparisons for length, weight, volume and temperature.
Give reasons for decisions based on the results of measurements or calculations.

Num 1.1 Selecting and using appropriate numerical notation and units.Num 1.2 Selecting and carrying out calculations.Num 1.3 Reading measurements using a straightforward scale on an instrument..Num 1.4 Interpreting the measurements and the results of calculations to make decisions.Num 1.5 Explaining decisions based on the results of measurements or calculations.

# Books

### Printed resources available at Amazon

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