1. Welcome back to 2015
How much have you used your brain in the holidays?
Did you play 2048? Minecraft? Or did you actually get off screens and go outside?
Can you solve this number crunch?
 753
Time to get your brain thinking again…
TANGLE TABLES 1
(see hand out)

2. Welcome back to 2015 Take 5 min to make a title page Practical Issues:
Grid Books $2;
Calculators $22 pay at the office;
Text books - get the pdf from the Portal
It is a large file so we need to stagger the download.
Take 5 min to make a title page

3. Write the heading on a NEW PAGE!
ALGEBRAIC TECHNIQUES

4. Read through this as a class…

5. Complete the Pre-Test on p4 of the text book.
Write the HEADING, ALGEBRA PRE-TEST
Complete the Pre-Test on p4 of the text book.
Time allowed = 10 min

6. Write the Heading
Ask 4 volunteers to come out the front. Each one represents one of the expressions below! They are given an instruction and have to sort themselves in order from lowest to highest.

7. Revision from last year… Summarise the Theory/Notes with your teacher’s help.

8. Example 1 – Class discussion Example 2 – Class discussion
To do:
Exercise 1A Q1-3, 5, 6
Extension Q13-16.
Example 2 – Class discussion

9. Can anyone think of an algebraic rule for NRL or Rugby scores
Write the heading
Can anyone think of an algebraic rule for NRL or Rugby scores
Theory/Notes
In Algebra, you can replace pronumerals (variables) with numbers to evaluate an expression. This is called substitution or replacement.
Eg. Evaluate 4 + x if x = 3…

10. Q5-8 (ev 2nd part), Q9(all parts),
Example 1
To do:
Exercise 1B (p11) Q1-3 (all parts),
Q5-8 (ev 2nd part), Q9(all parts),
Q11
Extension Q14,17,18
Example 2

11. Algebra Like Terms TRAIN in the TUNNEL
Write the Heading
For this section, every student needs the Work Sheet found at the LINK:
Algebra Like Terms TRAIN in the TUNNEL
Click to go to the next slide to begin the Work Sheet.

12. TrAveLGEBRA
On a trip from Gosford to Sydney, a train breaks down whilst coming out of a tunnel. I can only see the front carriage and some of the second carriage. I know that there are 36 passengers per carriage. There is also a driver and an engineer in the front of the first carriage. If the number of carriages is x, how many people can the train hold?

13. If there is only 1 carriage, then there are 36 x 1 passengers
If there are 2 carriages, then there are 36 x 2 passengers
If there are 3 carriages, then there are 36 x 3 passengers
So if there are x carriages, then there are 36 x x passengers

14. So if there are x carriages, then there are 36 x x passengers
So if there are x carriages, then there are 36x passengers and 2 others (driver, eng)
36x passengers and 2 others (driver, eng)
36x people

15. Return Trip
On the trip back to Gosford, each carriage has the top deck closed, so that each carriage can only hold 18 passengers. How many people on the train for the return trip?

16. 18x + 2 people

17. Round Trip
How many people on the round trip? Show how you work it out.

18. Way there = 36x + 2 Way back = 18x + 2
Return Trip = (36x + 2) +(18x + 2)

19. 36x + 2 + 18x + 2 Final answer 54x + 4 2 and 2 make 4
Which terms can be put together?
36x and 18x make 54x
2 and 2 make 4
Final answer 54x + 4

20. You now hear there are 6 carriages
So x = 6
How many passengers on the round trip exactly, using 54x + 4

21. Substitute x=6 into the expression 54x + 4 54 × x + 4 = ? people

22. Substitute x=6 into the expression 54x + 4 54 × 6 + 4 = ??? people

23. Substitute x=6 into the expression 54x + 4 54 × 6 + 4 = 328 people

24. The shape must include the symbol IN FRONT of the term

26. 3a + 2a = 5w + 3w = 9d – 3d = 3h – h = Remember h is really 1h
Try These…
3a + 2a =
5w + 3w =
9d – 3d =
3h – h =
Remember h is really 1h

27. Like Terms Have EXACTLY the same pronumeral (letters) in them!
Which are the like terms to 3a?
2b , a2 , 4a , 5ab , -6a
Answer: 2b , a2 , 5ab are NOT like terms because they don’t have exactly “a” in them.
So 4a and -6a are the like terms to 3a !!!!

28. You try:
Which are the like terms to -4y?
3e, 7y , 14y2 , -8y, 7qy, 6y
Answer: 7y , -8y, 6y
Did you get it right?

29. Only add LIKE TERMS!!!!!!!!!!!!!!!!!!! 2d + 3d + 4a = 3e + 5y + 4e =
8a + 2b – 2a + b =
4a + 3b – 2a – b =
To do:
Exercise 1C Q1
Extension Q13-16.

30. THINK??? Does 5  a  b  2 = a  2  b  5 = 10ab ????
Write the heading
THINK???
Does 5  a  b  2 = a  2  b  5 = 10ab ????

31. Key Ideas/Theory
For example,

32. Exercise 1D (p20) Q1-4, Q5-9 (ev 2nd part),
Example 1
Example 2
Exercise 1D (p20) Q1-4, Q5-9 (ev 2nd part),
Extension – Q14
Example 3

33. The top class may choose to do the Extension Exercises 1E, 1F (Algebraic Fractions)

34. Write the Investigation questions
Write the heading
Investigation:
1. 3(x + 2) = …
= x x x + 2
= 3x + 6
2. 4(a  1)= …
= a  1 + a  1+ a  1 + a  1
= 4a  4
Write the Investigation questions
THINK – Can you see a quicker way or a short cut to work out each answer???
Key Ideas/Theory

35. We use this rule without realising it when we multiply…
Key Ideas/Theory
We use this rule without realising it when we multiply…
Eg: 5 x 27 = ….
= 5 ( )
= 5 x x 7 =
= 135.

36. Would the distributive law work on expressions with three terms?
Example 1
Example 2
Example 3
Would the distributive law work on expressions with three terms?
Eg. Expand 3(a + 2b – 4c)
Exercise 1G (p35)
Q4, 5, Q6-10 (ev 2nd part)
Q11, 12, 15.

37. Write the heading

38. Theory/Notes
Example 1

39. Example 2 3x + 6 = ___ ( x + 2 ) 2y - 8 = ___ ( y - 4 )
x2 + 7x = ___ ( x + 7 )
2y = 2 ( ___ + ___ )
4a - 8 = 4 ( ___ - ___ )
3t + 9 = ___ ( ___ + ___ )
8x - 16 = ___ ( ___ - ___ )
6x + 9 = ___ ( ___ + ___ )
20a + 25 =
9m =
Exercise 1H (p39)
Q3-9 (ev 2nd part)
Q11, 12, 15.
Harder Example 3

40. Write the heading

41. Example 1
At an ‘ALL YOU CAN EAT’ restaurant, the price is $1.90 times your age.
How much would it cost for a 13 year old?
(b) How much would it cost for a 4 year old?
(c) How much would it cost for a 50 year old? Is this realistic?
Think – What would be a good age to ‘cap’ the prices at?
ANSWER:
$1.90  13 = $24.70
(b) $1.90  4 = $7.60
(c) $1.90  50 = $95. This is NOT realistic.

42. Example 2
Example 3

43. What is the cost of the fruit if k = 20?
Example 4
If I bought 6 apples which cost k cents each and 4 pears which cost 2k cents each, find an expression for the total cost of the fruit.
What is the cost of the fruit if k = 20?
Answer:
Cost of apples = 6  k cents
= 6k cents
Cost of pears = 4  2k cents
= 8k cents
Total cost = 6k + 8k cents
= 14k cents
If k = 20, then total cost = 14  20 = 280 cents (i.e. $2.80)
Exercise 1I (p43)
Q1-9,
Extension: Q9, 11, 13, 15

44. Can you think of a short cut to save on working out?
Write the heading
Can you think of a short cut to save on working out?
Can you think of another short cut to save on working out?

45. Theory/Notes

46. Q1-6 (all parts), Q7-9 (ev 2nd part), Q10, Q11.
Example 1
Example 2
Exercise 1J (p48)
Q1-6 (all parts), Q7-9 (ev 2nd part), Q10, Q11.
Extension: Q12, 13, 15, 16

47. TEXT