Term 3 Week 8

Apologies for the delay here - between year 8 and year 9 camps and some time off with the flu there has not been a lot of action on this blog.

The topic we are completing is Pythagoras.

Students will have covered this before, however it is very important to be able to use Pythagoras' theorem quickly and effectively.

As we all know Pythogoras was the first to prove the relationship between the lengths of the two short sides of a right angle triangle and the long side:

h² = a² + b²

Which literaly means that if you draw a square on each side of the triangle the two small squares add up to the size of the big square.

Very useful!

Using this formula we can calculate any side of the triangle if we know the other two sides. We only need to be careful to check whether we are finding the long side (hypotenuse) or a short side.

Pythagoras Assignment 1 is here

Term 2 Week 9

Due to Winter Festival commitments there is no Year 8 maths this week.

Congratulations to those who completed the Probability topic test last week, you have all done very well.

I will post next weeks assignment here shortly anyway...

Regards,

Josh

Term 2 Week 8

Due to the class play, and other delays the Probability Assignment 2 due date is extended to Thursday - at which time we will have an end of topic exam.

The next assignment will be set on Tuesday week 9 for the new topic and due Tuesday of Week 10.

Term 2 Week 7

We continue our study of probability by giving absolutely impossible and absolutely certain events a number value:

P(certain) = 1
P(impossible) = 0

We also note that probabilities are 'complementary', that is the probability of something happening added to the probability that it won't happen is always 1.

Eg The probability of rolling a '5' is 1/6 and the probability of not rolling a '5' is 5/6. Adding these together we get the probability of either rolling a '5' or not rolling a '5' is 1.

Knowing this we can calculate the probability of some events very simply:

Eg If we know the probability of winning a lottery is 1/1000000, then we can subract that number from 1 and work out that the probability of not winning the lottery is 999999/1000000.

The Probability Assignment 2 is here

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Term 2 Week 6

After a whistle stop tour of percentages we are now moving to probablility. This is a very hands on subject where we can explore how chance works, and have fun tossing coins and rolling dice.

We have all heard expressions like 'you have a 50-50 chance' but what does this mean?

It simply means that the likelyhood of something working out is 1 chance out of 2 - ie a 50% or 1/2 chance.

Much study has been done on understanding chance and probability - particularly when there is money to be made (or lost!)

To formalise the maths of chance we write the chance that something will happen as a ratio of what we want to happen over number of possible ways things could happen.

So the probablility of winning the toss in a football match is 1 chance of heads over 2 (heads or tails) or again a 50% or 1/2 chance.

We call the range of possible out comes the 'sample space' and put curly braces around it to make it look flash:

What is the sample space for a 6 sided dice? {1, 2, 3, 4, 5, 6}

So we can work out the probablility of getting a '2':

P('2') = 1 / 6
(ie 1 desired outcome ('2') out of a sampe space with 6 things in it: {1,2,3,4,5,6})

By calculating and comparing probabilities for things it is possible to make more informed choices about taking risks.

It is said that mathemeticians never gamble - because they can calculate the exact probability that they are going to lose their money!

Probability Assignment 1 is here

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Term 2 Week 5

some people take their 50% very seriously

Percentages roll on this week.

By now we have reaffirmed that fractions, decimals and percentages are all interchangeable, and all indicate how much of something we have.

eg 1/2 is the same as 0.5 which is the same as 50%

We know how to change from one to another:

To convert 1/2 to a percentage we multiply by 100%

1/2 x 100% = 100/2 = 50%

To convert 0.5 we also multiply by 100%

0.5 x 100% = 0.5 x 100 = 50%

Converting from a percentage to a fraction or a decimal is just the reverse:
To convert 50% to a fraction just divide by 100 and then simplify

50% = 50/100 = 5/10 = 1/2

To convert 50% to a decimal just divide by 100 with a calculator (can also be done mentally if you are careful)

50% = 50/100 = 0.5

We also need to be able to recognise common fractions and so be able to quickly convert them:

1/2 = 0.5 = 50%
1/3 = 0.33 = 33.33%
1/4 = 0.25 = 25%
1/5 = 0.2 = 20%
1/10 = 0.1 = 10%

The Percentages Assignment 2 is here
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Term 2 Week 4

We finish Geometry this week with a topic test.

The next topic is Percentages. See pages 109 - 137 of the text.

Percentage Trivia: The symbol for percent (%) evolved from a symbol abbreviating the Italian per cento.

Being able to convert things to percentages allows us to compare 'apples' with 'apples'.

For example if one person scores 10 goals out of 20 attempts, whereas another scores 9 goals out of 15 attempts we can work out who is the higher scoring player by converting their score to a percentage. In this case player 1 has a 50% score rate, whereas player 2 has a 60% score rate and is probably a better goal shooter.

Fractions and decimal values also allow us to compare things.

The purpose of this unit is to increase students capability to convert things to and from percentages, and compare them. This is very applied mathematics as we know that percentages and proportions come up quite frequently in every day life.

The Hammer Percentages Assignment 1 is here.
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Term 2 Week 3

geometry in art

This week we continue with triangles, and then quadrilaterals.

We note that for any triangle at all if we measure the angles inside it they always add up to 180 degrees. Similarly for any shape with four sides (Quadrilateral) the angles always add up to 360 degrees.

Click here for Geometrical Figures Assignment 3
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Term 2 Week 2

Knowing Geometry is critical to many forms of construction

This week we continue exploring Geometrical figures - we have looked at parallel lines, and the angles made by a third line crossing them, now we move on to defining and understanding triangles.

The various options all have mathematical names:

If all three sides are different lengths, it is a 'Scalene'
If two sides are the same length it is 'Isosceles'
If all three sides are the same it is 'Equilateral'
If all angles are <> 90 (blunt looking) then it is 'Obtuse-angled'
If one angle is = 90 then it is a 'Right-angled' triangle

Students also should discover that the angles inside ALL triangles always add up to 180 degrees.

Students should be able to identify the different types and solve problems based on the properties of each type. For example if a triangle has two sides the same, and the angle between those sides is 40 degrees, then from the knowledge of Isosceles triangles students should be able to work out that the other two angles are the same, and that they are equal to 70 degrees.

This weeks Hammer assignment is here.
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Term 2 Week 1

15th century (made up) depiction of Euclid

Welcome back to maths in term 2!

Geometrical Figures is our new topic.

Over the next week students should be able to name different types of angles, and solve geometric puzzles by using the properties of angles, triangles and parallel lines.

Much of this was put together by the Greek mathemtician Euclid about 2300 years ago. Euclid's approach was to work from a small number of foundational 'facts' (called 'axioms') and solve problems by using logic and reason to build answers by combining the axioms.

This weeks hammer assignment is here.

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Week 10

Class 8 have completed their Algebra revision, and have now all done the Algebra topic test. The test results should be available this Thursday. This ends our work with Algebra for this year in middle lessons. The topic will be revisited in more detail in Term 1 2008.

The next topic is Geometrical figures - angles, parallel lines, triangles, quadrilaterals and polygons. This will build on last years geometry main lesson.

This being the last week of term, there is no assignment! Enjoy the holidays, and we will continue the maths next term!

Week 9

triaxially woven spheres

This is our final week of Algebra, and we will conclude with an end of topic test. The date for the test will be set in the next few days. Some students may move to other classes based on their needs and preferences, and their work in assignments and the test.

Over the last 4 weeks we have covered how to do arithmetic with 'variable' numbers (algebra) in these areas:

• Adding and subtracting 'Like' terms
• Multiplying and dividing
  
• Fractions
• Expanding
• Factorising

Over the next couple of lessons we will be tidying up loose ends and doing revision.

The (Hammer) group are covering the use of variables in fractions (text p44-45), and then revising.

This weeks (Hammer) assignment is here and is due on Tuesday April 3rd.

Week 8

This week we are covering the 'power' or 'index' laws in Al-Jabr.

We all know that:

2 x 2 = 2²

The same power notation is also good for variables:

a x a = a²

When doing calculations where numbers are squared, cubed or multiplied by themselves a lot there are some good 'short cuts' that can be used:

a² x a³ = a x a x a x a x a = a⁵ - we notice that we can add up the powers so
a² x a³ = a^{2 + 3} = a⁵

If you are unsure about this try using a 'normal' number like 2 instead of 'a'.

This can be extended to these general rules:

a^m x aⁿ = a^m+n
a^m / aⁿ = a^{m - n}
(a^m)ⁿ = a^mn

For example (2²)³ = (2 x 2) x (2 x 2) x (2 x 2) = 2^{2 x 3 =} 2⁶

As usual, if it does not make sense - ask for help. Also with maths it sometime helps to try a whole lot of similar questions, and then the meaning of it starts to dawn.

The next (Hammer) maths assignment is here - due Tue 27th of March.
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Week 7

the 800 year old Arabic book from which Algebra gets its name 'Maqalah fi al-jabr wa-al muqabalah'

Al - Jabr continues with more work on expanding and factorising algebraic expressions. It is very important to practice this work, as familiarity will bring confidence.

To expand an expression simply multiply everything inside the brackets by what is outside:

3(a + b) = 3 x a + 3 x b = 3a + 3b

- each part inside the brackets ('a' and 'b') gets multiplied by what is outside ('3').

Factorising is the reverse - we pick out the Highest Common Factor (HCF) in each part of an expression and remove that to the outside of some new brackets:

3a + 3b = 3(a + b)

- looking at '3a' and '3b' we work out that the only thing that goes into both of them evenly is '3', so we can create a new set of brackets and put the three outside.


Justin and Josh are back from Nimboida, so it is full power ahead for all class 8 maths lessons.

Click here for the next (Hammer) maths assignment which is due on Tuesday March 20th.

Week 6

With class 8 back fresh from Nimboyda it is time for more Algebra! This week we move on from substituting values into algebra expressions, to finding 'like' terms so we can add them up. The method for multiplying and dividing with variables will also be covered.

Justin and Josh the Hammer will be away this week with class 9 at Nimboyda, but lessons will be as usual with substitute teachers.

Click here for this weeks (Hammer Maths) Algebra assignment - due Tue March 13th.

Week 4

All of class 8 have now completed their initial test with most students doing very well.

The classes have now been divided into four. Justin's group are in the class9 room, John's group are in class 8FionaGillian, Josh the Hammer's group are in class 8 TonRoch, and Karen's group are in her space.

All of class 8 will now be studying Algebra for the next 3 - 4 weeks (not including Nimboyda). Most of the students will have already covered some algebra in class 7, so these lessons will build on that basis, and ensure that all students have a chance to catch up. At the end of this Algebra period there will be another test, and some students may be required to move to different classes to suit their needs.

c8 'Hammer' maths have there first assignment here. Because Class 8 Is going to Nimboyda on Tuesday, this assignment is now due on Monday morning - please hand in to your class guardian at the start of school.

Week 2

The dust is starting to settle as the term gets under way, and our maths brains are starting to warm up!

We are planning to divide the class into 4 groups to provide the best educational opportunities for the students with different needs. Initially this division will be based on a test that students will complete in week 3. This test will be on the revision that we are doing now. Movement between classes will be possible at any time through the year as we get to know where individual students are at. Class sizes for mathematics in class 8 will be between 10 and 18.

The 4 groups will cover the same subjects throughout the year so that everyone will be on the same footing for year nine.

This week we are continuing the revision in chapter 1 of New Century Maths 8.

C8 Rochelle/Tony:
On Tuesday Josh is doing work with negative numbers and the number line, as well as the order of operations. Students in C8 Rochelle/Tony will have homework to complete Ex 1.03 1,2 and 3 (p9-10) and Ex 1.05 1 and 2 (p12-13) which will be due on Thursday. For this particular homework students are expected to write the answers including working in their pink grid book, and then to mark their own work using the answers at the back of the book. Don't forget to email Josh/Justin if you have any questions/comments!

Welcome to Class 8 Maths Middles in 2007

Click here for course information

contact justin: justini AT shearwater DOT nsw DOT edu DOT au
contact john: johnb AT shearwater DOT nsw DOT edu DOT au
contact karen: karend AT shearwater DOT nsw DOT edu DOT au
contact josh: joshs AT shearwater DOT nsw DOT edu DOT au

Click here for the Shearwater website