1. Computation With Integers
Vocabulary:
mental divide number line
problems order of operations written
add digit money
compare subtract equivalent
operations computation integers
place value grouping symbols multiply
directed number direction rational

2. Place Value
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3. Signpost p6 Q1-8

4. Ways of working with number:
Adding?
Subtracting
Multiplying
Dividing?
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7. Order of Operations
To avoid confusion, mathematicians developed a set of procedures to ensure that everyone obtained the same answer when they completed calculations; for example…
What is the answer to 10÷2(3+2)?
The accepted order is:
Work with grouping symbols and exponents first
2. Work out multiplications and divisions in order from
left to right
3. Work out additions and subtractions in order from left to right
e.g. 17 – 52 ÷ (2+3) =
In your book

9. A diagram to help you remember the order of operations.
Signpost p 56 Q1-8
Signpost p 58 Q1-5
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12. Puzzle!

13. Long Division…the ‘Easy’ way
Although you may have learned traditional long division in primary school, an easier, more understandable way is by using the preferred multiples method.
e.g )

16. Directed Numbers or Integers
Integers are whole numbers. They can be either positive or negative, or zero. An example of a negative integer is ‘The temperature is -4 degrees’. Think of a – sign as meaning the opposite to +
-3,-2,-1, 0, +1, +2, +3
Which of the following are integers?
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19. Using Directed Numbers
Seven degrees below Celsius _____
Going up four floors on the elevator ______
Owing $ ______
150 meters above sea level ______
Move back four spaces ______
Five shots under par ______
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20. In your book
Place these numbers on the number line below in their correct position:
Rearrange the numbers below into ascending order, i.e. from smallest to largest.

21. Ordering Directed Numbers
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22. Using a Number Line with Integers
e.g. 4 x -1 = =
(-6) ÷ (-2) =
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24. Operations With Integers
We can visualise a number line to help evaluate problems using directed numbers…or just use the one on the wall…
3 – 7 = ? – 2 – 5 = ?
= =
= =
= =
= =
= (6 + 4) =
In your book

26. In your book

33. In your book

34. Multiplying and Dividing Directed Numbers
Investigation:
3 x 3 = x 3 = -12
3 x 2 = x 2 = -8
3 x 1 = x 1 = -4
3 x 0 = x 0 = 0
3 x (-1)= x (-1) =
3 x (-2)= x (-2) =
3 x (-3)= x (-3) =
Simplify the following:
1. -2 x 3 = x (-5) =
2. -6 x -3 = 5. (-3) x 2 x (-4) =
3. (-3) x 2 = x (-2) x -2 =
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35. When multiplying: positive x positive = positive
Rule:
When multiplying: positive x positive = positive
positive x negative = negative negative x positive = negative
negative x negative = positive
The same rules apply to division.
In your book

42. Show -12 as the product of at least 3 integers
A number and its opposite are 24 units apart on a number line. What are the numbers?
Two numbers are 10 units apart on a number line. One is positive and one is negative. Give three pairs of numbers which would fit this description.
Give an example of:
Two numbers which give a product greater than their sum.
Two numbers which give a sum greater than their product.
Make up the most difficult question you can (and its answer) for the class to solve.