Math and Science

Hey! Class FE7B has just finished off many units to end the holidays. Firstly, in math class, we have just finished our unit on geometry! I hope everybody studied for our test a couple of days ago! Also, we were all given two other assignments involving geometry-A tessellation and a floor plan of our "dream mansion". If you don't quite know what a tessellation is, I'll tell you. A tessellation is when you take a shape and apply transformations to it. The five transformations are rotation, reflection, translation, enlargement and combination.

Rotation: When you rotate a shape by a certain degree. In this case, The horizontal figure was rotated 90 degrees clockwise.

Reflection: When you reflect or "flip" a shaped off of a certain line. In this case, the figure to the left was reflected off of a vertical line.

Translation: When you move a shape without shifting or changing the way the shape is positioned. In this case, the rectangle on the left was moved down, then moved to the right.

Combination: When you combine multiple transformations to apply to a shape. In this case, the pink triangle was rotated 90 degrees clockwise, then translated to the right, then reflected off of a horizontal line.

For our "dream mansions" our class used many different shapes to make three floor plans for our dream mansion. We had to calculate the area of each room using our previous knowledge on shapes. For example: The formula of a Trapezoid: b1+ b2 x h divided by 2. The formula of a rectangle and parallelogram: b x h. The formula of a triangle: b x h divided by 2. Class FE7B had a great term in math!

As for science, class FE7B has just finished our science summative project by either building a bridge, tower crane, or trebuchet. Now, we are watching films on other structures such as an obelisk, Egyptian pyramid and the most fascinating Stone Henge. Nobody quite knows how stone henge was formed but there were many theories. For example: Many people believed that the workers on stone henge used pulley systems to place these large stones in the ground. Science is very exciting and let's see what we do next year!

Have a happy holiday!

My Last Post of 2008!

Last Science class in FE8B (Tuesday) we did an experiment. Everyone was split into groups of 2 and was given a piece of aluminum foil about 15cm x 15cm. Using the aluminum foil (and nothing else including tape or glue) we had to make a boat. We put these boats one at a time into a tank of water and tried to place in as many pennies as possible before it sank. The boat that held the most pennies won.
Most of the boats were along the same idea: they were shaped as bowls. You could make a fairly large bowl out of the aluminum foil, so the boat would have a large volume. Since density is mass divided by volume, the bigger the volume is the lower the average density would be. The lower the average density is, the more pennies the boat will hold.
Some other ideas in the class were to make a raft-like shape. The aluminum foil is just in a sheet, but the edges are rolled over to create air pockets. I heard in FE8A that one group did something along those lines with 2 or 3 air pockets in it, and their boat held significantly more pennies than all the others did. This would work the same way a cruise ship does, as the boat would have a large volume because of all the air it holds, but not a large mass seeing as air has an extremely small mass. This would result in a lower average density.

In Math, we have been constructing our dream mansions. We drew an orthographic drawing of our mansion, then Mr. Foster made them into a net using a computer program. Then he printed out the net and we had to use that to make our house. We also got to incorporate art into this project by colouring our house and gluing it to an 8 1/2 x 11" piece of paper and drawing what our whole dream lot would look like. This was a fun and interesting activity as we got to learn about geometric shapes in an exciting and different context.

That's all for now.
I hope everyone has a safe and happy holiday, and I will talk to you again in the new year!
Until then,
-K

Science and Math in FE8A

Today in science we looked at average density. This is, in case you weren't paying attention, or didn't take notes, something which we are all guilty of one time or another (but don't do anymore), is simply all the masses and all the volumes divided by each other.
In this diagram it shows the experiment that we did in class which illustrates average density.
1 to start this experiment we mixed baking soda and vinegar which caused us to end out with a bubbly liquid.
2 After we got our bubbly liquid we placed corn kernels in to the beaker causing the bubbles to form on to the kernels making them float.(lowering the average density)
3 Then when the kernels came to the top of the beaker the bubbles released into the air causing the average density to rise and the kernel sinks to the bottom. Then the process repeats over and over until there is no gas left to release.

Now to math.
In math recently we have been looking at angle proofs. tonight we had many angles to solve using all the rules. We will be having our unit test on Monday.
See you tomorrow
Eric

Buoyancy in FE8B

Hello everybody,

In FE8B Science, we have been learning about buoyancy just like Eric said in FE8A. The definition of buoyancy is the ability of a fluid to support an object that is in or on it. Buoyant force is the opposite force to gravity, so if there is more buoyancy than gravity on an object in a fluid, it floats. The opposite happens if there is more gravity than buoyancy (it sinks).

But if this is true, than why do small rocks sink in water while large ships float? This is where average density comes in. Average density is the total mass divided by the total volume. A rock has a large mass, as there is a lot of matter in a rock, but not as big a volume as it is not very big. This results in a large density. A ship doesn't have a very large mass as it has a hollow hull, but it has a very large volume so the average density of a ship is fairly small. The density of a ship is much less than that of water, so it floats. The density of a rock is more than that of water, so it sinks.

Another cool thing with buoyancy is how objects of larger area on the water float easier compared to those with the same mass but less area on the water. For example, when you just stand straight in water without moving your hands, you will sink. However, if you lie on your back without moving your hands, you float. You still have the same mass and gravity pulling you down as when you were straight up and down, but this time you float. This is because there are more water particles supporting you when you take up a larger area. More particles under you means that there is more buoyant force pushing you up than the gravity pulling you down, so you float. When you are straight up and down there aren't as many water particles underneath you. This results in less buoyant force than gravity which makes you sink.

That's all for now.
Until next Wednesday,
-K

Another Day, Another Lesson

First I will start with science. Today in science we looked at buoyancy and page 134.
On page 134 it states how a solid pushes particles out of its way to get through. The reason the solid doesn't do this is because it is made of a lattice structure. Also it is held together with the force of attraction which is like a magnetic force. In order to break the magnetic force you have to add kinetic energy, heat, which will get the particles moving and break the lattice.

In this picture it shows a finger and a piece of cheese (our fluid)
When we push our finger in, the fluid under our finger will compact.

Now let's say that there are more particles in the cheese (red dots). If you push on the fluid now that it is denser your finger will bounce back which is Buoyancy.(buoyancy defined by black arrows)
Next time
-Eric

What's Happening in FE8A

Here we come winter.
Another new unit of math. In math we are doing angle proofs, which is made up of of intersecting line rules and parallel line rules. These rules can be used to figure out a whole group of angles when only given.
For intersecting lines the rules are:
complementary (two or more angles that add up to 90*)
supplementary(two or more angles that add up two 180*)
opposite (two angles that are on the other side of the line are equal)
For the parallel lines rules there are:
F-rule(two angles are equal because the angle on the inside of the arms of the F)
Z-rule( two angles are equal because they are on the inside of the Z)
C-rule(two angles equal 180* because they are located in the inside of the C)

exterior alternate(two angles are equal but only if they are on the out side of the parallel lines)
That concludes the math overview.

Now on to science, in science we have learned about density and how it can be calculated. To do so you will need to know 2 of the 3 properties of one sub stance: Mass, Volume, or Density. to find mass you can use a Triple Beam Balance. To find volume place object in to a container filled to the top with water and the water that spills out is the volume (Thanks to you Archimedes). To find density you use this triangle of usefulness:
The reason there is a X in between the D and the V is because you have to multiply Density by Volume to get Mass. Same thing for the 2 division signs under M because you have to divide Mass by Density or Volume to find Density or Volume.
That concludes my post for today.
See you soon
Eric

So in FE8B Math we have been continuing with our angle proofs unit. We have learned new rules for a set of parallel lines with a transversal line. A transversal line is a straight line that goes though both the parallel lines. There is the F-rule that states the the two angles on the inside of the F are equal. Here is a diagram:

The green lines are the F, and the two red angles are equal.

The next rule is the Z rule which states that the two angles in the Z are equal. These are called alternate angles.

The green lines are the Z and the two red angles are equal.

The third rule is the C rule which shows that the two angles in the C equal 180 degrees. These are called corresponding angles.

The green lines are the C, and the two red angles equal 180 degrees.

The final rule is the exterior alternate rule which means that the two angles on the outside opposite each other are equal.

In this diagram, the two red angles are equal.

In Science we are learning about fluids. We have been talking about density of fluids, viscosity of fluids, and the properties of the different states of matter (solid, liquid, gas).

We have also learned about how states of matter change from one to the other. The transitions are as follows:

When a solid is heated, it becomes a liquid. This is called melting. An example of this is when you eat ice cream in the summer and it melts in your cone when you don't eat it fast enough.

When a liquid is cooled, it becomes a solid. This is called freezing. An example of this is when you leave a water bottle in your car over a winter night and the next day it has become ice.

When a liquid is heated, it becomes a gas. This is called vaporization. An example of this is when you boil water and vapour comes of, as the water has become a gas.

When a gas is cooled, it becomes a liquid. This is called condensation. An example of this is if you put a lid on the boiling water, the vapour cools as it hits the cold metal and turns back into water again.

When a solid becomes a gas or a gas becomes a solid WITHOUT going through a liquid stage it is called sublimation. An example of this is "dry ice" (solid carbon dioxide) that is used for special effects in concerts, movies, etc.

Until Next Wednesday,

-K