Math songs
Below are the math songs we sang in class, hope you get to sing them to someone else!
June 15, 2007
More logic problems
You can see some more logic problems (with a ranking for difficulty) by following the link below.
http://www.geocities.com/Heartland/Plains/4484/logic.htm#xpls
Another Java applet
Try this applet out instead if you want:
Java applets for Platonic solids
June 11, 2007
Online compass built in Flash
If you need to brush up on your ability to read a compass, check out the link below. It's a compass built in Flash.
June 10, 2007
Class Summary for 6 June 2007
Aim: Sets
A set is an unordered list of objects (which are known as elements). Here is an example of two sets:
{2,3,5,9,1,0}= A
{1,2,4,8,16}= B
The elements of the list do not have to be in any paticular order.
{1,2,3}={3,1,2}
So you could, for example, reorder them from smallest to largest if it helps you.
There are many things we can determine with these sets, such as their intersection (written as n): which means the list of elements that appear in both of those two sets. For example, the elements that appear both in set A and set B, are 1 and 2. This is written as:
AnB={1,2}
There are times where there are no elements which appear in both sets. For example, if:
A= {odd numbers}
B= {even numbers}
In this case AnB is written as:
AnB=empty set OR AnB={}
We can also determine the union of these sets (written as u), which means list all the elements of the two sets. The duplicates are only listed once. So the union of set A and set B would be written as:
AuB={1,2,3,4,5,8,9,16,0}
A universal set is the largest set required to do a problem. At our level, the universal set will always be defined for us.
A complement U, means list all the elements in a universal set (U) and not in set A. It is written as:
or 
So for example, if:
U={0,1,2,3,4,5,6,7,8}
A={1,3,5,7}
={0,2,4,6,8}
So, these rules, are always true:
An={}
Au=U
Sets are commonly shown in venn diagrams:
For example, AnB can be shown as:
The shaded part is the elements in set A that overlaps the elements in set B. In other words, the elements that are both in set A and B
Here is a more complicated example:
^1)
can be shown as:
The shaded parts are the elements that do NOT appear in all of the three sets, A, B and C.
That's all on sets!
We spent the rest of the lesson revising some maths terms that we have not looked at in a while. Here are some reminders.
Largest Common factor: the largest number that divides into two numbers.
Least Common multiple: The smallest number that the two numbers divide into.
Natural Number: Counting numbers, positive whole numbers. Ex)1,2,3,4
Integers: All whole numbers including negatives.
Rationals: All numbers that can be written as a ratio of integers.
Real numbers: All numbers including irrationals.
The next presenter is.. whoever hasn't gone yet! =)
A set is an unordered list of objects (which are known as elements). Here is an example of two sets:
{2,3,5,9,1,0}= A
{1,2,4,8,16}= B
The elements of the list do not have to be in any paticular order.
{1,2,3}={3,1,2}
So you could, for example, reorder them from smallest to largest if it helps you.
There are many things we can determine with these sets, such as their intersection (written as n): which means the list of elements that appear in both of those two sets. For example, the elements that appear both in set A and set B, are 1 and 2. This is written as:
AnB={1,2}
There are times where there are no elements which appear in both sets. For example, if:
A= {odd numbers}
B= {even numbers}
In this case AnB is written as:
AnB=empty set OR AnB={}
We can also determine the union of these sets (written as u), which means list all the elements of the two sets. The duplicates are only listed once. So the union of set A and set B would be written as:
AuB={1,2,3,4,5,8,9,16,0}
A universal set is the largest set required to do a problem. At our level, the universal set will always be defined for us.
A complement U, means list all the elements in a universal set (U) and not in set A. It is written as:
So for example, if:
U={0,1,2,3,4,5,6,7,8}
A={1,3,5,7}
So, these rules, are always true:
An
Au
Sets are commonly shown in venn diagrams:
For example, AnB can be shown as:
The shaded part is the elements in set A that overlaps the elements in set B. In other words, the elements that are both in set A and B
Here is a more complicated example:
The shaded parts are the elements that do NOT appear in all of the three sets, A, B and C.
That's all on sets!
We spent the rest of the lesson revising some maths terms that we have not looked at in a while. Here are some reminders.
Largest Common factor: the largest number that divides into two numbers.
Least Common multiple: The smallest number that the two numbers divide into.
Natural Number: Counting numbers, positive whole numbers. Ex)1,2,3,4
Integers: All whole numbers including negatives.
Rationals: All numbers that can be written as a ratio of integers.
Real numbers: All numbers including irrationals.
The next presenter is.. whoever hasn't gone yet! =)
June 5, 2007
Class Summary for Thursday May 31, 2007
Aim: What are Radians?
A Radian is the length of an arc measured out by an angle on the unit circle. Basically, a Radian is another way of calculating the length of an arc without expressing the final result in degree form. This is important because it is much easier to express answers in numbers. Radians usually contain pi in the answer and should we need to convey mathematical methods and answers to a different life form we would be able to use radians instead of degrees.
Some Important Radians to Remember for Grade 11 and the Future are:
 \times\2\pi\ = \frac{\pi}{6})
 \times\2\pi\ = \pi\div\4)
 \times\2\pi\ = \pi\div\3)
 \times\2\pi\ = \pi\div\2)
 \times\2\pi\ = \pi\)
 \times\2\pi\ = 2\pi\)
The left side of the equation is in degrees mode, the middle of the equations is the conversion from degrees to radians and the result, on the right side of the equation is the same number of degrees in Radian mode. the above cases are for when the radius of the unit circle is 1, which it always is. The generic formula for the conversion from degrees to radians is:
Radians are just a different form of calculating the lengths of arcs using the Unit Circle.
Thanks,
Matein
The Next Presenter has been told.
A Radian is the length of an arc measured out by an angle on the unit circle. Basically, a Radian is another way of calculating the length of an arc without expressing the final result in degree form. This is important because it is much easier to express answers in numbers. Radians usually contain pi in the answer and should we need to convey mathematical methods and answers to a different life form we would be able to use radians instead of degrees.
Some Important Radians to Remember for Grade 11 and the Future are:
The left side of the equation is in degrees mode, the middle of the equations is the conversion from degrees to radians and the result, on the right side of the equation is the same number of degrees in Radian mode. the above cases are for when the radius of the unit circle is 1, which it always is. The generic formula for the conversion from degrees to radians is:
Radians are just a different form of calculating the lengths of arcs using the Unit Circle.
Thanks,
Matein
The Next Presenter has been told.
This is the blog for Mr. Wees' classes. Here we will be able to include images, flash files, mathematical discussions, or whatever else is relevant to our discussions.
We can also include mathematical equations in our posts, like
.
You can also see a tutorial on how to include mathematical equations here