Numeracy is an essential life skill for communication, just like literacy. We use the alphabet to communicate words and place value notation to communicate numbers.
We encounter ideas related to fractions, decimals, ratios and percentages on a daily basis. These concepts are the key to everyday estimation and mental calculation, understanding scales on maps, interpreting probabilities and odds, analysis and planning.
Arithmetic, Population and Energy
Dr. Albert Bartlett, University of Colorado talking with a few slides.
It is the first of an 8 part series. If you would like to watch it all the playlist can be found here.
A surprisingly good explanation of the importance of understanding basic mathematics.
information about the topic
In this section you will revise the following:
Basic arithmetic is everywhere around us when shopping, working, building, cooking, travelling.
Examples
Whether you use a calculator, a spreadsheet or pencil and paper, it is still important to understand the basics of arithmetic.
Basic maths concepts are important across many aspects of business including accounting, budgeting, and financial statement preparation and analysis. For example, preparation of a profit and loss statement to demonstrate whether a business is profitable will require calculations involving mathematical concepts such as subtraction, addition, multiplication and division.
Profit and Loss Statement of Truss Pty Ltd
for the month ending 31 March
| Sales Revenue | 960 000 |
| Less Cost of Goods Sold | 460 000 |
| Gross Profit | 500 000 |
| Less Operating expenses | |
| Interest expense | 3 000 |
| Electricity | 39 000 |
| General Supplies | 30 000 |
| Telephone | 20 000 |
| Rent | 60 000 |
| Wages | 232 000 |
| Total other operating expenses | 384 000 |
| Net Profit | 116 000 |
Truss Pty Ltd has applied to the bank for a short term loan of $40 000. The business has been asked to prepare a Profit and Loss Statement (Income Statement) by the bank to demonstrate that the business is profitable and able to repay the loan.
In order to calculate the profit figure above the business had to first calculate the total amount of operating expenses. To do this the business had to sum each of the expenses (32 000 + 30 000+ 20 000 + 10 000 + 60 000 + 232 000) to obtain the total expenses of $384 000.
In order to calculate the interest expense on the company's existing long term loan that had to apply the concept of division, multiplication and addition. The amount owing on the loan is $72 000, the current interest rate is 15% and interest needed to be calculated for one month only. Applying basic mathematical concepts the interest was calculated as: (72 000 x 5/100)/12 = $300. To calculate the interest required knowledge of relationships between operations and order of operations also.
About This Lesson
Image: Wikipedia elementary arithmetic
These are the basic operations of arithmetic and underpin all mathematics Although a great deal of arithmetic is now done using calculators and computers, it is still important to be able to perform these basic skills without them.
Test Yourself
For a brief explanation, practice and self test, look at
CIMT - Four Operations Using Whole Numbers
CIMT - Four Operations Using Decimals
If you feel confident with the material in this lesson you can jump to lesson 2
Learn More
If you need more help with this these, the Khan Academy series contain video tutorials and self tests.
Khan Academy - Addition and Subtraction
Khan Academy - Multiplication and Division
Khan Academy - Decimals
Maths is Fun -Decimal Numbers Menu
When you have had some practice, try the interactive worksheets again
CIMT - Four Operations Using Whole Numbers
CIMT - Four Operations Using Decimals
About This Lesson
In this lesson we look at the Commutative and Associative properties of arithmetic operations
Source: Math is Fun
Addition is commutative, meaning that order does not matter
Example
a+b=b+a | (a+b)+c=a+(b+c) | (1+2)+3=3+3=6 |
Addition is also associative, meaning that when more than two numbers are added together, the order in which addition is performed does not matter
Not all operations are commutative or associative, so in expressions with other operations like subtraction, it is important to specify the order of operations.
Subtraction is not a commutative operation, order does matter
Example
c−b does not equal b–c
15–10 does not equal 10–15
Multiplication is commutative and associative, order does not matter
Source: Math is Fun
Example
3×5=15, and 5×3=15
6×5×7=5×7×6=5×6×7
The result of an operation is known as a product.
Division is not commutative, order does matter
Example
a ÷ b does not equal b ÷ a
10 ÷ 15 does not equal 15 ÷ 10
In the expression a ÷ b = c,
a is called the dividend or numerator,
b the divisor or denominator
and the result c is called the quotient.
a ÷ 0 is undefined as there is no number which, multiplied by 0, gives a
0 divided by any number = 0
Test Yourself
Maths is Fun Tutorial and Test - Commutative Associative and Distributive Laws
If you feel confident with the material in this lesson you can jump to the next lesson.
Learn More
If you need extra help to understand this, look at the following series of tutorials:
Khan Academy - Commutative Law of Addition
Khan Academy - Commutative Law of Multiplication
Khan Academy - Associative Law of Addition
Khan Academy - Associative Law of Multiplication
Then try this test again
Maths is Fun Tutorial and Test - Commutative Associative and Distributive Laws
About This Lesson
The order in which the basic operations are carried must be done according to an agreed set of rules. Otherwise two people could interpret a series of arithmetical operations differently and obtain different results.
The order of operations is as follows:
Image: Acronyms and Slang
Brackets - evaluate any operations in brackets first
Indices - simplify any part of the expression which has powers or roots
Multiplication and Division - have the same priority and are done in order from left to right
Addition and Subtraction - have the same priority and are done in order from left to right
Test Yourself
For some examples and an interactive self test try
CIMT - Order of Operations
If you feel confident with the material in this lesson you can jump to the next lesson.
Learn More
If you need more help to understand this topic go to:
Maths is Fun - Order of Operations - BODMAS
Khan Academy - Detailed video tutorials on Order of Operations
Try this self test
Khan Academy - Order of Operations
There is a short self test at the end of
Maths is Fun - Order of Operations - BODMAS
About This Lesson
...
Test Yourself
Needs work
If you feel confident with the material in this lesson you can jump to the Measurement Lessons
Learn More
Needs work
Test Yourself Again
In this section you will revise the following:
Lesson 1 - Place value and the use of zero
Lesson 2 - Measurement and the Metric System
I would suggest putting something really grabbing/funny to capture the students interest in this space about each topic
Measurement can be used to work out length and distance, capacity, weight, times & dates, money, temperature and calories. Some everyday business contexts for measurement include:
The concepts of measurement including place value and the use of zero and application of the measurement system are used for financial report preparation and business analysis. For example to allocate rent expense across business departments in order to calculate the profit figure for each department;
Truss Ltd is a clothing store and for management and control purposes the business is divided into 3 departments. For the month of March the following information has been collected to determine the best way to allocate rent expense to each department.
| Evening wear | Day wear | Shoes | Total |
|
|
|
|
|
Sales | $480 000 | $288 000 | $192 000 | $960 000 |
Floor area occupied (m2) | 200 | 300 | 100 | 600 |
Profit before rent allocation | $96 000 | $42 000 | $38 000 | $176 000 |
The business needs to allocate the overhead expense rent across each of the three departments in some way. To do this the manager has measured the amount of floor space used by each department and they want to calculate the amount of rent expense for each department based on the percentage of floor space they use.
| Evening wear | Day wear | Shoes |
Allocation on basis of floor area | 60 000 X (200/600) = $20 000 | 60 x (300m/600) = $30 000 | 60 x (100/600) = $10 000 |
Profit after rent allocation | $76 000 | $12 000 | $28 000 |
Calculating how to allocate rent expense requires knowledge of measurement. The floor would need to be measured and the metres squared figure calculated for each department. The calculation to allocate rent expense requires knowledge of the mathematical concepts of measurement, addition and multiplication.
About this Lesson
We use the base 10 system where numbers are represented using the digits 0,1,2,3,4,5,6,7,8,9.
The value of a number is determined by the digits used and their place value.
Example
Hundreds - Tens - Units . Tenths - Hundredths - Thousandths
Units could also be called Ones
756 means 7 Hundreds + 5 Tens +6 Units
67.56 means 6 Tens + 7 Units + 5 tenths + 6 hundredths
Test Yourself
Try this quick quiz
That Quiz - Place Value
Note: when using That Quiz you can create your own quizzes on a range of topics and vary the questions by changing the parameters down the left side of the screen.
There is an interactive tutorial and self assessment worksheet on place value at the Centre for Innovation in Mathematics Teaching (CIMT)
CMIT - Decimals and Place Value
If you feel confident with the material in this lesson you can jump to the next lesson
Learn More
If you need extra practice with place value use the following resources
Work carefully through the interactive tutorial again using the built in help.
About this Lesson
Measurement involves the comparison of something with an agreed unit of measurement.
Types of measurement include:
Units of measurement - metric
Image source: wikiHow
In Australia and most parts of the world the metric system for measurement is used. The following chart shows the measuring units used for length, mass and volume, and their abbreviations.
Length | Mass | Volume |
|---|---|---|
millimetre (mm) | milligram (mg) | millilitre (mL) |
centimetre (cm) | gram (g) | litre (L) |
metre (m) | kilogram (kg) | kilolitre (kL) |
kilometre (km) | tonne (t) |
These metric units are based on multiples of 10, as can be seen in the following table:
Length | Mass | Volume |
|---|---|---|
10 mm = 1 cm | 1000 mg = 1 g | 1000 mL = 1 L |
100 cm = 1 m | 1000 g = 1 kg | 1000 L = 1 kL |
1000 mm = 1 m | 1000 kg = 1 t | |
1000 m = 1 km |
Convert between units of measurement
The information in the table above can be used to convert from one unit to another, for
example:
Measurement Calculations
Test Yourself
The following CIMT interactive worksheets and self tests will help you check your understanding of metric units and calculations.
CIMT - Estimating Metric Units (Note that this is from the UK so Football means Soccer)
CIMT - Conversion Between Metric Units
If you feel confident with the material in this lesson you can jump to the next lesson
Learn More
If you need to learn more on this topic, the interactive worksheets above contain built in help and examples, work through them carefully and then check your score.
Lesson 1 - Fractions and Percentages
Lesson 2 - Maximum, Minimum, Range and Averages
Fractions and Percentages
The concepts of practions decimals and percentages are very important in business. The concepts of maximum, minimum range and average will be particularly important in the area of business analysis.
Example
Profit and Loss Statement of Truss Pty Ltd for the month ending 31 March | |
| Sales Revenue | 960 000 |
| Less Cost of Goods Sold | 460 000 |
| Gross Profit | 500 000 |
| Less Operating expenses | |
| Interest expense | 3 000 |
| Electricity | 39 000 |
| General Supplies | 30 000 |
| Telephone | 20 000 |
| Rent | 60 000 |
| Wages | 232 000 |
| Total other operating expenses | 384 000 |
| Net Profit | 116 000 |
Truss Pty Ltd have an existing long term of $72 000, for which they pay an interest rate of 15%. To calculate the interest expense for the month will require applying basic mathematical concepts percentage and fractions. Interest can be calculated as: (72 000 x 5/100)/12 = $300. To calculate the interest required knowledge of relationships between operations and order of operations also. To calculate interest expense the accountant need to understand the relationship between percentages and fractions. They needed to know that the percentage figure of 5% equals the fraction 5/100, and they could express the percentage in this way in order to calculate the interest owing.
The bank has also requested that a projected financial statement be prepared for the next month, April 2014 to demonstrate the range different levels of income that the company might expect to earn. The business is confident that the businesses expenses will remain steady over the following months but they have identified that the sales could be a minimum of $2 500 for the month or they could reach as high as $4 500.
Projected Profit and Loss Statement of Truss Pty Ltd for the month ended 30 April 2014 | April | May |
| Sales Revenue | 1 200 000 | 1 500 000 |
| Less Cost of Goods Sold | 560 000 | 500 000 |
| Gross Profit | 640 000 | 1 000 000 |
| Less Operating expenses | ||
| Interest expense | 3 000 | 3 000 |
| Electricity | 39 000 | 42 000 |
| General Supplies | 30 000 | 28 000 |
| Telephone | 20 000 | 20 000 |
| Rent | 60 000 | 60 000 |
| Wages | 232 000 | 260 000 |
| Total other operating expenses | 384 000 | 413 000 |
| Net Profit | $256 000 | $587 000 |
The bank has asked the business to calculate the minimum amount of income they feel the business might earn over the next two months, the maximum income and the average. The accountant has worked out that the minimum monthly income would be $640 000 to be earned in April, the maximum monthly income would be $1 000 000 in May. The average income over the two months would be (640 000 + 1 000 000)/2 = $820 000 per month. The income will range from $640 000 to $1 000 000 therefore having a range of $1 000 000 – $640 000 = $360 000.
About This Lesson
Fractions and percentages are ways of expressing parts of a number.
Image: 4Freephotos
Example
Half a pizza is enough for me.
52% of the population is male
3/4 of our profit comes from coffee sales
Your score in the test was 75%
Fractions and percentages are used in many areas of business including calculating discounts, predicting sales, analysing markets and reporting on profits.
A thorough understanding of these topics is essential so if you have any difficulties with this you may need to spend a long time on this.
Practice your understanding by using this calculator to convert a percentage to a fraction and decimal.
Image: Calculator Soup
Test Yourself
CIMT - Introduction to Fractions
There is more work on fractions in Section 10 on the CIMT page
CIMT - Decimals and Fractions
CIMT - Fractions and Decimals
CIMT - Percentages
CIMT - Decimals, Fractions and Percentages
If you feel confident with the material in this lesson you can jump to the next lesson.
Learn More
You will find lots of basic help at the Maths is Fun Numbers Index
For detailed tutorials on all the areas above look at
Khan Academy - Khan Academy - Fractions
About This Lesson
"Someone who is lying with their head in the oven and their feet in the freezer will be, on average, comfortable."
Image: Money Marketing
If you are studying a large set of data such as the daily sales in a large number of branches of a shopping chain or the age distribution of a potential market, it is useful to have ways of describing and summarising the data especially if it contains many items of data.
If you are studying a large set of data such as the daily sales in a large number of branches of a shopping chain or the age distribution of a potential market, it is useful to have ways of describing and summarising the data especially if it contains many items of data.
This is an introduction to the topic, there will be more on this in a later module.
The main concepts to understand as an introduction to statistics are:
Maximum | The highest value in a set of data. |
|---|---|
Minimum | The lowest value in a set of data. |
Range | The difference between the maximum and minimum. |
Averages | There are three kinds of average, the mean, the median and the mode. |
Mean | The result of adding up all the data items and dividing by the number of items (also called The Average or Arithmetic Mean). |
Median | The middle value when all the data items are arranged in ascending order. If there are an even number of data items, it is the mean of the middle two. |
Mode | The most commonly occurring data item. |
It is possible for a set of data to have no mode if no item occurs any more frequently than any other or to have more than one mode if there is more than one item that is equally common.
There will be much more on this later. For now focus on understanding these terms and trying some simple exercise using the resources below:
Test Yourself
CIMT - Maximum, Minimum and Range of Data
CIMT - Mean, Median, Mode and Range
If you feel confident with the materials in this module, you can take the module Quiz.
Learn More
Maths is Fun - Data Probability and Statistics
Khan Academy Series - Measures of Central Tendancy
When you have a better understanding of this topic try the CIMT worksheets again.
In this topic you will revise the following
Triangles
About this Lesson
In this lesson you will revise the properties of a triangle and the vocabulary associated with triangles, review the special properties of right angled triangles and look at pairs of triangles called similar triangles.
Properties of Triangles
This Triangle Explorer from Math Open Reference will help you to revise the vocabulary and properties.
Image: Math Open Reference
Right Angled Triangles
This interactive resource from Math Open Reference will help you revise right angle triangles.
Image: Math Open Reference
Similar Triangles
This interactive resource from Math Open Reference will help you revise similar triangles
Image: Math Open Reference
About This Lesson
In this lesson you will revise Pythagoras' Theorem which tells us about the special relationship between the lengths of the sides of a right angled triangle.
Test Yourself
This interactive worksheet and self-test will help to check your skills and fill in any gaps.
Learn More
Click the following link from Math Open Reference to learn more.
Image: Math Open Reference
About This Lesson
The word Trigonometry comes from the Greek for Three Angle Measure.
In this lesson you will revise the main concepts of Trigonometry, the trigonometric functions Sine, Cosine and Tangent, how to graph these functions and how to solve problems involving them. Click on the link below for an introduction to Trigonometry from Math Open Reference.
Image: Math Open Reference
Learn More
This interactive explorer shows you how to graph the sine function. Click on the link below from Math Open Reference to learn about graphing a sine function.
Solving Trigonometric Problems
Problems involving finding sides
In some situations, you will know some information about a triangle but will need to use trigonometry to find a missing side.
Problems involving finding angles
In some situations, you will know some information about a triangle but will need to use trigonometry to find a missing angle.
Unit Circle Identities
Image: Math Open Reference
This provides a different way of dealing with trigonometric functions which you can explore at the link below from Math Open Reference
For more information on the topics included in this module refer to these reference sites:
