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.
.

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.