Welcome back to 2015 - PowerPoint Presentation

Slide1

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?100 25 8 5 3 2  753

Time to get your brain thinking again…TANGLE TABLES 1(see hand out)Slide2

Welcome back to 2015

Practical Issues: Grid Books $2; Calculators $22 pay at the office;

Text books - get the pdf from the PortalIt is a large file so we need to stagger the download.

Take 5 min to make a title pageSlide3

Write the heading on a NEW PAGE!

ALGEBRAIC TECHNIQUESSlide4

Read through this as a class…Slide5

Write the HEADING,

ALGEBRA PRE-TESTComplete the Pre-Test on p4 of the text book.Time allowed = 10 minSlide6

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. Slide7

Revision from last year… Summarise the Theory/Notes with your teacher’s help.Slide8

To do:Exercise 1A

Q1-3, 5, 6Extension Q13-16.

Example 2 – Class discussion

Example 1 – Class discussion Slide9

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…Slide10

Example 1

Example 2

To do:

Exercise 1B

(p11)

Q1-3 (all parts),

Q5-8 (ev 2

nd

part),

Q9(all parts),

Q

11

Extension Q14,17,18Slide11

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.Slide12

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? Slide13

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

passengersSlide14

So if there are

x carriages, then there are 36 x

x passengersSo if there are

x carriages, then there are 36x passengers and 2 others (driver, eng)

36

x

passengers

and 2

others (driver,

eng

)

36

x

+ 2

peopleSlide15

Return TripOn 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?Slide16

18x + 2 peopleSlide17

Round TripHow many people on the round trip?

Show how you work it out.Slide18

Way there = 36x + 2

Way back = 18x + 2

Return Trip = (36x + 2) +(18

x + 2)Slide19

36x + 2 + 18x

+ 2Which terms can be put together?36x and 18x make 54x2 and 2 make 4

Final answer 54x + 4Slide20

You now hear there are 6 carriages

So x = 6How many passengers on the round trip exactly, using 54x + 4Slide21

Substitute x=6 into the expression 54x + 4

54 × x + 4 = ? peopleSlide22

Substitute x=6 into the expression 54x + 4

54 × 6

+ 4 = ??? peopleSlide23

Substitute x=6 into the expression 54x + 4

54 × 6

+ 4 = 328 peopleSlide24

The shape must include the symbol IN FRONT of the termSlide25
Slide26

Try These…3a + 2a =5w + 3w =9d – 3d =3h – h =

Remember h is really 1hSlide27

Like Terms Have EXACTLY the same pronumeral (letters) in them!Which are the like terms to 3a?

2b , a2 , 4a , 5ab , -6aAnswer: 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 !!!!Slide28

You try:Which are the like terms to -4y? 3e, 7y , 14y2

, -8y, 7qy, 6yAnswer: 7y , -8y, 6yDid you get it right?Slide29

Only add LIKE TERMS!!!!!!!!!!!!!!!!!!!2d + 3d + 4a =

3e + 5y + 4e =8a + 2b – 2a + b =4a + 3b – 2a – b =

To do:

Exercise 1C

Q1-8

(left column)

Extension Q13-16.Slide30

Write the heading

THINK???

Does 5

 a  b  2 = a  2  b  5 = 10ab ????Slide31

Key Ideas/Theory

For example, Slide32

Example 1

Example 2

Example 3

Exercise 1D

(p20)

Q1-4,

Q5-9 (ev 2

nd

part),

Extension – Q14Slide33

The top class may choose to do the Extension Exercises 1E, 1F (Algebraic Fractions)Slide34

Write the heading

Investigation:

1

. 3(x + 2) =

…

= x + 2 + x + 2 + 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/TheorySlide35

Key Ideas/Theory

Eg

: 5 x 27 = ….

= 5 ( 20 + 7 )

= 5 x 20 + 5 x 7

= 100 + 35

= 135.

We use this rule without realising it when we multiply…Slide36

Example 1

Exercise 1G

(p35)

Q4, 5,

Q6-10 (ev 2

nd

part)

Q11, 12, 15.

Example 2

Example 3

Would the distributive law work on expressions with three terms?

Eg. Expand 3(

a

+

2

b –

4

c

)Slide37

Write the headingSlide38

Theory/Notes

Example 1Slide39

Example 2

3x + 6 = ___ ( x + 2 ) 2y - 8 = ___ ( y - 4 )x2 + 7x = ___ ( x + 7 )

2y + 10 = 2 ( ___ + ___ )4a - 8 = 4 ( ___ - ___ )3t + 9 = ___ ( ___ + ___ )8x - 16 = ___ ( ___ - ___ )

6x + 9 = ___ ( ___ + ___ ) 20a + 25 = 9m - 15 =

Harder Example 3

Exercise 1H

(p39)

Q3-9 (ev 2

nd

part)

Q11, 12, 15. Slide40

Write the headingSlide41

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.Slide42

Example 2

Example 3Slide43

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 centsCost of pears = 4  2k

cents

= 8

k

cents

Total cost = 6

k

+ 8

k

cents

=

14

k

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 Slide44

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?Slide45

Theory/NotesSlide46

Example 1

Example 2

Exercise 1J

(p48)

Q1-6 (all parts), Q7-9 (ev 2

nd

part), Q10, Q11.

Extension: Q12, 13, 15, 16Slide47

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