Aleiah's Journal Entry

Scribe for March 2 2010

The first thing we did in class was go over some textbook questions. The first one was #28a.

Not sure if you could read that so here's the text version...

A small manufacturer makes air quality monitoring kits for home use. The revenue, in dollars, from the sale of n kits can be shown by -n^2 + 3600n. The cost, in dollars, to make n kits is represented by -3n^2 + 8600. The manufacturer makes a profit if the cost subtracted from the revenue is positive.

a) Write an expression to find the profit. Simplify your answer.

So basically here, you just have to subtract the cost to make the kits from the revenue (which I found out, actually means the company's income).

Then you simplify it.

After this, Mr. Backe talked about the rules of writing polynomials that have at least three terms.

The first thing to follow is that the terms are alphabetically ordered.

The second thing to follow is to order the like terms in an ascending or descending order. Usually, it's descending and the only time they ascend is if the terms are similar. eg. 3, 3x and 3x^2

So using these rules, we rearranged x^2y + x^3 + y^2. The math stuff is going to be really hard to read without the pictures so... yeah, if you can't read it, then sorry.

Then we rearranged a^3 + a^4b + a^5b^3c^2 +b^2c + a^4.

After that, we talked about #29.

29. Simplify (2x + 4x + 6x + 8x + ... + 2006x + 2008x) - (x + 3x + 5x +7 x + ... + 2005x + 2007x).

Here, the '...' means that it goes on until the next part.

So it's kind of troublesome to actually do all that so we did the smaller parts first.

2x + 4x - (x + 3x) = 2x.
2x + 4x + 6x - (x + 3x + 5x) = 3x.
2x + 4x + 6x + 8x - (x + 3x + 5x + 7x) = 4x.

Here, we looked for patterns and we found that the last term of the first phrase divided by two equals the answer.

2x + 4x - (x + 3x) = 2x.
2x + 4x + 6x - (x + 3x + 5x) = 3x.
2x + 4x + 6x + 8x - (x + 3x + 5x + 7x) = 4x.

Then the rest of the class was a work period for the stuff we have to work on (review, ch test etc.)

Next scribe is Shaneille.

Math Game-Teleporter Galaxy

Teleporter Galaxy

Instructions and Rules of Teleporter Galaxy:

1) 2 or 4 players can play this game. If 4 players are playing, split into two teams.

2) First player rolls the dice and goes forward.

3) Look at the colour you landed on and take a card from the same colour deck.

4) Answer the question without your teammate's help. You're allowed to use a calculator or do it on paper.

5) If you got it right, move one step forward. If not, stay.

6) Take turns doing this.

7) If you land on BONUS (the black triangle) take a card from the black deck. First team to answer correctly gets to switch spots with opposing team if the opposing team is ahead. If they aren't, move 3 spaces up.

8) If your teammate finishes first, they will be allowed to help you on the question.

9) First team to have both players around the star wins.

Mr. Backe

Hi Mr. Backe!

Like everyone else, we all miss you and hope you come back soon. You're an awesome teacher and everyone wishes you'd come back.

Haha, no seriously. You're the first teacher to actually praise us and keep praising us. You made us "The Class". I think other teachers thought we were bad students and they only think we're good students now because you said so. So come back soon!

Well for now, MERRY CHRISTMAS and HAPPY NEW YEAR! XD

Question 23

Write a subtraction statement involving two negative fractions or negative mixed fractions so that the difference is -4/3.

So basically, it's a - b= -4/3.

You can just inverse the statement and make it -4/3 + b = a. B and A have to both be negatives so for B, I just chose a random negative fraction like -2/5.

-4/3 + (-2/5) = a

When I did this, a came out as -26/15.
So it's -4/3 + (-2/5) = -26/15.

If you make it back to a - b = -4/3, it'd become -26/15 - (-2/5) = -4/3. I even checked it. It's right.

I wasn't sure if it might work with other negative fractions so I tried it with -6/7.

-4/3 + (-6/7) = a

It came out as -4/3 + (-6/7) = -46/21.

I made it back to a - b =-4/3 again. It became -46/21 -(-6/7) = -4/3. It also works.

I'd make pictures but my paint isn't being cooperative with me and neither are my cameras. I'll try again tomorrow though...

Answering Mr. Backe's question, I think it will work everytime because it's a - b = -3/4, right? A and B have to be negatives. So when you inverse the statement to -3/4 + b = a, it should work because A has to be a negative and a negative plus a negative equals a negative.

Question 21

21. Andrew drove his car 234 km from Dawson to Mayo in Yukon Territory in 3h. Brian drove his truck along the same route at an average speed of 5km/h greater than Andrew's average speed. How much less time did Brian take, to the nearest minute?

First you need to find out Andrew's average speed to find out Brian's average speed.

Andrew took 3 hours to drive 234 km. This would look like 234 km/3h. The average speed is always per hour, right? So you'd need to divide 234 km by 3.

So Andrew's average speed is 78 km/h. Brian is driving 5 km/h greater than Andrew. So 78 plus 5 would be 83. Therefore, Brian is driving at 83 km/h.

We need to find out how much less time Brian took, right? To do that we actually need to know how much time Brian took to get to Mayo.

So Brian's driving 83 km/h and the distance from Dawson to Mayo is 234 km so we need to divide 234 km by 83.

It took him 2.819277108 hours. Of course that's kind of ridiculous so we need to find out how much time that would be in simpler terms.

There are 60 minutes in an hour, right? I think it might be easier to find out the answer if you convert it into minutes. So he takes 2.819277108 hours to get there. 2.819277108 multiplied by 60 is...

It's 169.1566265. Just round that off to 169 minutes. So now we know Brian takes 169 minutes to get from Dawson to Mayo.

To make things easier, I'll just tell you that Andrew took 180 minutes to get from Dawson to Mayo. (3 multiplied by 60)

Now all you need to do is find the difference in their times.

So this means that Brian took 11 minutes less time to go to Mayo from Dawson than Andrew.

Scribe Post for Oct 5, 2009

Today, everyone was handed a rectangular prism. Afer that, we were asked what the formula for a rectangular prism's surface area was. We were also asked about the dimensions which are length, width and height or length, width and depth.

Anyways, you know how there's like a plane of symmetry through the dimensions because of the identical faces opposite of each other? We talked about that for a bit. There's the pair of faces with height and length (hl). There's height and width (hw) and there's also length and width (lw).

(That's really hard to see but the first one shows height and length, the second shows height and width and the third shows length and width)

So that covers all the faces of the rectangular prism, right? Since there's 2 of each face, that makes the formula for the surface area of the rectangular prism:

2(hl)+2(hw)+2(lw)

Well after that, we took out the nets for our rectangular prism, talked about which is the face, edge and vertex, coloured the faces that are the same and labeled each face its dimensions (hl, hw or lw).

We also got our tests back. Don't forget to get the parent signature.

After, we were asked to draw the net for a cylinder with a height of 6 and a circumference of 10 and cut it out without the circles on top which by the way is just a 6 by 10 rectangle since there are no circles. This is because the circumference is the length of the rectangle on the net (you know, if you unrolled the circle onto the length, it'd be the same).

So that was class. Here's the homework:

-Stick the nets in your journal and explain how to get the formula. I'm not sure if you're supposed to label them so can someone clarify that?
-Find the surface area of the cylinder with the height of 6 and circumference of 10
-How did you get the area of the circles on the top and bottom of the cylinder?
-Where is the symmetry on a cylinder and I think, how many planes of symmetry does a cylinder have?
-There's something on the grade 9 homepage to look at, I think.
-Journal


I pick Zerlina for the next scribe.

Why 360?

Did you notice how a circle has 360 degrees and not 100? If you haven't, then wow...

Well, now that you for sure noticed, I'll tell you. The people to blame for having 360 degrees in a circle are the Babylonians.

See, a long time ago, the Babylonians used a number system with a base of 60. It's called a sexagesimal system. Big word, I know. Our base is 10, by the way.

The point is that the Babylonians had 360 days in their calendar. They thought that the Earth took 360 days to rotate around the Sun in a circle. (I just gave you a really big hint just now.) Therefore, when they decided how many degrees a circle should have, they chose 360.

Also, 360 has a lot of factors. They're 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360 . Trust me, the last thing you want to do is be told to measure out 1/3 of a circle and have to look for 33.333333 and so on degrees from your 100 degree protractor.