Here is the Project Assignment if you have misplaced it: http://dl.dropbox.com/u/39411274/Math%20Foundations%2020%20Project.docx
I have decided that giving you the Holiday Break to finish your projects may be better than having them due before the break. Presentations will be on Wednesday, January 4 and Thursday, January 5. If you would prefer to present before the break, speak to me and we will arrange that.
The presentations will be as follows:
Wednesday, January 4
Michelle
Aaron
Alex
Kelsey
Jeff
Nina
Brydon
Emily
Colby
Joel
Thursday, January 5
Sarah
Amy
Koralyn
Allysa
Tanner
Cody
Taryn
Miranda
You should email your presentation and other files to be displayed on the SmartBoard ahead of time. Email my mrbanow at gmail.com account. If you have any materials that are not digital, please bring them the day of your presentation and hand them in to me.
If you have questions now or over the break, email me and I will get back to you fairly quickly.
Good luck and have some fun! I hope your topic interests you!
Saturday 31 December 2011
Friday 16 December 2011
Next Stages in the Project: Data and Controversy
In chapter 5, we studied measures of central tendency and Normal Distributions. Depending on your topic, this may relate to your project. If you have done a survey or have collected data (even from online), then you will want to consider how to analyze your data:
- will you discuss mean, median, or mode?
- is your data Normally distributed?
- do you know that sample size and margin of error/confidence level for the data you found online?
- see pages 284-286 for more suggestions
Now that you have completed some research, you will want to scrutinize your data for any controversial issues.
- have you found two sources that provide contradictory information or data?
- does the contradictory data represent different viewpoints? (eg. is the data being provided by a group that would want a certain outcome?)
- see pages 352-353 for more ideas
Everyone needs to follow this link and complete the short survey regarding your controversial issue(s).
CLICK HERE ----> Complete this once you have done a significant amount of research
If applicable, discuss the controversial data in your presentation.
Wednesday 14 December 2011
6.6 Optimazation Problems: Linear Programming
On Tuesday we started 6.6 Linear Programming. Linear Programming is a mathematical technique used to determine which solutions in the feasible region result in the optimal solutions of the objective function.
To solve this, first you find the linear inequalities and put them on a graph. After that you fine the maximum and minimum values of the objective function. You can do this by using a vertex/value chart. Then using the information from this chart make a statement showing your results.
We were given five steps in using Linear Programming to solve an optimization problem which includes the information we have learnt in 6.4 , 6.5, and 6.6.
The steps are as followed:
The steps are as followed:
1. Define: - Variable
- Domain/Range
- Inequalities (Constraints)
- Objective Function
2. Graph
3. Evaluate the objective function at the vertices's
4. Analyse and Interpret - choose desired solution
5. Verify
After we went through EX.1 on the handout Mr.Banow gave us. Question found below in picture.
For practise we got assigned Page 341-345 # 1,2,4,6,11,13
:)
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6.4 and 6. 5 Optimization Problems
:)
In 6.3, we learned that what kind of numbers were dealing with contribute to our answer. This still applies to 6.4.
In 6.4, we learned about optimization problems. In an optimization problem, it asks you for the maximum and minimum possible solution.
Optimization problem
a problem where a quantity must be maximized or minimized following a set of guidlines or conditions.
Constraint
A limiting condition of the optimization problem being modelled, represented by a linear inequality.
Objective function
in an optimization problem, the equation that represents the relationship between the two variables in the system of linear inequalities and the quantity to be optimized.
Feasible region
The solution for a system of linear inequalities that is modelling an optimization problem.
The area in yellow represents the feasible region.
When graphins linear inequalities we must remember which part of the inequality goes on certain areas of the graph.
We then went over the last page of our 6.4 booklet.
We found out that you can tell you're dealing with an optimization problem if you have to find the minimum or maximum.
We found that the constraints are the linear inequalities in the problem.
We did practice on pages 330-331 # 2,3,5,6.
In 6.5 we looked at the race car and suv problem again.
We realised that the maximum and minimum was on the vertices of the feasible region, but we had to find out which two vertices.
The objective function to optiimize was: C = 8r + 12s
C = cost
r = race cars
s = suvs
We found that (60, 40) was the maximum.
C = 12(60) + 8(40)
C= $1040
We found that (30, 40) was the minimum.
C = 12(30) + 8(40)
C = $680
But does the minimum cost satisfy all the constraints?
Constraints:
r<40 (less than or equal to)
s<60 (less than or equal to)
s+r>70 (greater than or equal to)
YES IT SATISFIES ALL CONSTRAINTS!
We then did practice questions on pages 334-335 #1-3
here is a math video to brighten your day! lolol
http://www.youtube.com/watch?v=cgEuUzHYvOY">
Next will be Aaron :D
Friday 9 December 2011
Extra Assistance for Graphing Linear Inequalities
Graphing an Inequality Video
Writing an Inequality for a Given Graph Video
Solving a System of Linear Inequalities Video - note: @ 3:50 he accidentally says 6/4 equals 6. The b-values and y-intercept should be 3/2 or 1.5, not 6. Also, in this video he has three inequalities. For 6.2 and 6.3 we only had two in a question.
Online Quiz - Choose Check Answer to verify if you have done it correctly
Writing an Inequality for a Given Graph Video
Solving a System of Linear Inequalities Video - note: @ 3:50 he accidentally says 6/4 equals 6. The b-values and y-intercept should be 3/2 or 1.5, not 6. Also, in this video he has three inequalities. For 6.2 and 6.3 we only had two in a question.
Online Quiz - Choose Check Answer to verify if you have done it correctly
Wednesday 7 December 2011
6.3 Graphing to Solve Systems of Linear Inequalities
Today, we started off the class by reviewing some examples from the 6.2 unit, Exploring Graphs of Systems of Linear Inequalities. A quick summary of that that is, a set of two or more linear inequalities that are graphed on the same coordinate plane; the intersection of their solution regions represent the solution set for the system.
Next, we moved on the 6.3 Graphing to Solving Systems of Linear Inequalities. Systems of inequalities are similar to systems of equations. A solution is still an ordered pair that is true in both statements. The video below shows Graphing and Solving Systems of Linear Inequalities, therefore I'm not putting pictures up because that seems to explain everything I need to say.
Mr. Banow assigned Practice pp. 317-319. It wasn't due, we just heard about it briefly at the end of class.
The next person to go is whoever has not gone their second time.
Monday 5 December 2011
6.0 Systems of Linear Inequations
Today in class we looked at graphing inequalities. An inequality says that two values are not equal.
We also did a work sheet about Amir buying nuts and raisins with $200, no more. We worked out the inequality of 25x+8y=200 to a y=mx+b formation so that we could graph it. (the picture is just an example) 
The line that was created was to be dashed to signify that we can only use information under the line, or Amir would be going over budget. We than did a test point to make sure all the information was correct. To do a test point, choose two points, under or over the line and substitute them for x and y and figure out the equation. The results should come out correct if the line is right.
The line that was created was to be dashed to signify that we can only use information under the line, or Amir would be going over budget. We than did a test point to make sure all the information was correct. To do a test point, choose two points, under or over the line and substitute them for x and y and figure out the equation. The results should come out correct if the line is right.
ex.Inequality: x-3y>6
graphing formula: Y=1/3x-2
Test Point: (below) (2,2): 2-3(-2)>6 =8>6 <-yes, this is correct, 8 is greater than 6.
We than did three more examples of graphing inequalities before we were assigned the pages 303-305 #1-3,4,6,a,c,e,7,10
This lovely post was done by Amy,
I don't know who else has to go so Mr banow can choose.
:)
Saturday 3 December 2011
Review of Terms and Connections
On Friday we reviewed what we need to know in order to start chapter 6 on Monday. We went over terms and definitions of words which was a helpful hand for people who completely forgot what any of those terms meant.We briefly went over the real numbers classification system, which looks like the rings of a tree. It has natural numbers in the centre, whole numbers around that, integers around that, real numbers on the outside, then rational and irrational number
s in the very outside. We also reviewed applying number concepts, number classifications, working with linear equations ans linear inequalities, rearranging equations, rearranging inequalities, verifying solutions to equations, solving systems of linear equalities on a Cartesian coordinate plane. The Cartesian plane's quadrants go counter-clockwise with the 1st quadrant in the upper right hand corner.
s in the very outside. We also reviewed applying number concepts, number classifications, working with linear equations ans linear inequalities, rearranging equations, rearranging inequalities, verifying solutions to equations, solving systems of linear equalities on a Cartesian coordinate plane. The Cartesian plane's quadrants go counter-clockwise with the 1st quadrant in the upper right hand corner.
This was a good review for the upcoming chapter 6, so hopefully everyone got a good weekend because today is crack down time!
Next up: Whoever Mr. Banow picks from that list of names that I completely forgot who's on! Yaaay.
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