Below in italics are the outcomes for this unit. Please do not edit them. Use them as the headings for lessons. You can then add a couple of sentences to explain how to do the maths, you may add a picture or a link to a relevant site.

Know these terms:
ascending - increasing, from smallest to largest
descending - decreasing, from largest to smallest
integer - a positive or negative whole number or zero
debit - money taken out of an account such as fees or withdrawals
credit - money put into an account such as interest or deposits



Lesson 1

recognise the direction and magnitude of an integer

Numbers have a size (magnitude) and a direction . For example, 5 degrees hotter or 5 degrees colder have identical magnitudes (5 degrees) but opposite directions. In terms of mathematics, hotter would be a +, and colder would be a -.

Another example would be this iceberg.
Iceberg2.jpg
You can see there is a section of the iceberg above sea level (positive value) and a large section below sea level (negative value).

Lesson 2

placing directed numbers on a number line
Picture_1.png
There are some key features of a number line that you have to remember:
  • There are ALWAYS arrows on both ends which indicate that the number line stretches on to infinity.
  • Zero is often (but not always) included, and is referred to as the origin.
  • Integers to the right of the origin are positive.
  • Integers to the left of the origin are negative.
  • Each of the markings on the line are exactly the same distance apart.
  • As shown below, not every marking has to be labelled.
  • Each mark on the line represents a 'step' or 'distance' of 1 (as above) OR 2 (as below) OR 3, OR 4, etc, but for every number line each marking represents the same step.


Lesson 3

ordering directed numbers

Once you have placed all directed numbers on the number line, the number furthest to the right is the largest and the number furthest to the left is the smallest. This pdf file will help explain this.


Lesson 4

adding and subtracting directed numbers

There are different ways of adding and subtracting integers, but I strongly suggest using a number line to do this.
Example: -6 + 7
  1. Draw a number line.
  2. Start with your finger/pencil at the first number (in this case, -6)
  3. Determine the direction to move (adding does to the right, subtracting goes to the left)
  4. Check the sign of the second integer. If it is negative, reverse the direction from step 3.
  5. Move the number of steps determined by the second number (in this case, 7)
  6. Where your finger/pencil stops is the answer.

This clip will show the above example.
adding integers.mov

These movies show how to add and subtract integers using a number line.
adding negative numbers.mov
subtracting integers.mov

Here's an activity which uses the number line to add and subtract.

...Another method
This video shows another method of how to add and subtract directed numbers. This activity will help reinforce the idea.


Lesson 5

interpreting different meanings (direction or operation) for the + and – signs depending on the context

Of course, once you become comfortable with adding and subtracting integers, you'll find a quicker way of doing it. Below are three examples of how by understanding the effect of + and - signs, complex operations can be made simple.

integers_eg.png


Lesson 6

multiplying and dividing directed numbers

Firstly, multiplying and dividing is the same for directed numbers as it is for normal numbers, except you have to consider the signs of the numbers involved.
  • If both numbers have the same sign (both + or both -), the answer will positive.
eg1. 6 x 4 = 24
eg2. (-6) x (-4) = 24
  • If the numbers have opposite signs (1 + and 1 -), the answer will be negative.
eg3. (-6) x 4 = -24
eg4. 6 x (-4) = -24

This video shows yet another method to add and subtract integers and also how to multiply and divide integers .

Lesson 7

using grouping symbols as an operator

As you get better at maths, you will be faced with ever more complex sums. The trick with any complex problem is knowing where to start. With maths, all you need to do is start with any brackets (or parentheses). After that comes multiplication and division (if any), and finally addition and subtraction.

Eg. 4 x [5 - 2] + 7divided_by.png (-3 + 2) (looks rather complicated, start with brackets and parentheses)
= 4 x [3] + 7divided_by.png (-1) (we don't really need the brackets any more, so we can write...)
= 4 x 3 + 7 divided_by.png -1 (now we deal with any multiplication or division)
= 12 + -7 (finally do any subtraction or addition)
= 5

Lesson 8

applying order of operations to simplify expressions

This is a very good web site which will cover all of the order of operations you will need. There are also 5 questions at the end you can use to test your knowledge.