Project Info Re-Posted

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!

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.

Chapter 6 Review Answer Key

Click here: http://dl.dropbox.com/u/39411274/Review%20Answers%20Ch%206.pdf

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:

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

:)

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

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

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.

http://www.schooltube.com/video/5b3ebaca5377c2d10e59/Solving-Systems-of-Linear-Inequalities-by-Graphing

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.

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.

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.

:)

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 numbers 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.

5.6 p. 275 #7 Form

For the Confidence Intervals assignment you need to find an article online and answer two questions about it.

Complete the question by filling out this form:
https://docs.google.com/spreadsheet/viewform?hl=en_US&formkey=dDdkVkVvTXRCSlJfTnAzMDhUbGlhdUE6MQ#gid=0

This must be complete by Friday, December 2.

Thanks.

Project

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!

Statistical Analysis Exam

On Monday, November 21 there is an Open Book exam on sections 5.1-5.4.

The key concepts are:

• mean
• standard deviation
• frequency distribution tables
• histograms
• frequency polygons
• Normal distribution

Standard Deviation Calculator

Here are a couple of online tools to calculate standard deviation (among other things)!

http://www.numberempire.com/statisticscalculator.php   On this one, check off Mean and Standard Deviation

http://www.miniwebtool.com/standard-deviation-calculator/  Works like a charm!

Good luck with your assignment!

5.4 NORMAL DISTRBUTION CURVE

To day we did 5.4 the normal distribution we looked at 4 different kinds of histograms

The first one is called a single point histogram or NORMAL DISTRBUTION CURVE the pink one is skewed
The blue one is a bi- modal and the orange one is uniform
Than we did a thing that involved rolling a dice 50 times and recording the sum of the numbers
Than we combined the whole class’ results and made the histogram
It was like the purple one with the top ones being 7 and 8
Than we looked at this graph

And this gave the standard deviation purpose. Telling us a lot about one set of data
Next is joel

Standard Deviation

We started section 5.3 today. We got a hand out and did the following question together:

"The coach of a girls' basketball team keeps stats on all of the players. Near the end of one game, the score is tied and the starting point guard gets fouled out. He needs to make a substitution. There are five girls on the bench who can sub in for the point guard."
The stats for the players were stated next.

Then we were asked which player was most consistent. We found that Paige was most consistent because her percentages were all between 33-35. They were not scattered, therefore they were consistent.

After that it said that the coach found that Paige and Patrice's values were close in value. He compared them more closely using standard deviation (a measure of the dispersion or scatter of data values in relation to the mean.)

We followed these steps to calculate the standard deviation for Paige:
-Determine the mean of Paige's shooting percentage.
(add all of Paige's percentages then divide by the amount of percentages there is. In this case there is ten.) We found that Paige's mean was 33.9.

-Calculate the deviation of each field goal percentage.
(Take one percentage and subtract it from the mean. Continue doing this with all the percentages.)
EX. 34-33.9=.1

-Calculate the squares of the deviations.
EX. The square root of .1 is .01. (Square root all deviations.)

-Fill in the values into the chart on the second page of the handout.

-Determine the standard deviation by:
-determining the mean of the squares of deviations.
(add all the squares of deviations and divide by 10)
Our answer was .69

-determining the square root of the mean from the step above^:
The square root of .69 is .8307.

Then we did the steps above for Patrice.
Next, we were asked who was more consistent between the two players. Our answer was Paige because .8307 is a smaller standard deviation than 1.4976(Patrice's standard deviation) and a smaller number means that here is more consistency.

We then calculated the mean and standard deviation using a graphing calculator. To do this, you must follow these steps:
-Stat
-Edit
-Enter the numbers
-Stat
-Calc
-1-var stats
-Enter.
(I probably forgot a step.)

We didn't finish the whole sheet but we will be finishing the rest in class tomorrow.
Next up is Colby.

5.1 Exploring Data

On Friday we started a new unit called Statistical Reasoning. This is about collecting data from a set of numbers or statistics. We learned new terms like: outliers, range, mean, median, and mode and how to draw a line plot. Alex did a pretty good job of summarizing those in the last post which makes it unnecessary for me.

Today we were supposed to hand in our diagnostic tests which the majority of people didn't do, so remember to hand those in asap. We then worked on a sheet given to us on section 5.1 Exploring Data, and we had to find the mean, median, mode and range for the life of a car battery. We discussed the results and found that based on our data neither brand x nor brand y were a better choice, but it depended on whether or not the consumer was willing to take a risk on purchasing a battery that could either last longer or shorter than the average time. We learned one new term which was dispersion.
Dispersion is a measure that varies by the spread among the data in a set; dispersion has a value of zero if all the data in a set is identical, and it increases in value as the data becomes more spread out.
After that we were assigned Pg. 212 #2 and 3.
The next person to write the blog will be Brydon. :)

Chapter 5: Statistical Reasoning

On Friday we began our next chapter: Statistical Reasoning. This chapter is to help us understand and apply standard deviations, confidence intervals, confidence levels, margin of error, z-scores, and more.

We looked at page 207 and discussed on how statistics help monitor the polar bear population, and how it can determine whether the population is stabilizing or taking a decline. We figured that by using inductive reasoning, one could predict the future outcome of the population.


Math.

Next, we looked at page 208 and 209 to apply our potentially new-found knowledge of mean, median, and mode values. The definitions for these terms are as follows:

Mean: A measure of central tendency determined by dividing the sum of all the values in a data set by the number of values in the set.

Median: A measure of central tendency represented by the middle value of an ordered data set.

Mode: A measure of central tendency represented by the value that occurs most often in a data set.

An example in which we can apply these terms is:

Let's say that this represents the size in cm of the diameter of school spheres. The mean is 47.857 cm (add the numbers up, 335, and divide by the amount of numbers, 7). The median is 50 cm (the middle column holds the 50 cm), and the mode is 20 (the only number repeated twice).

We also went over questions A-E on page 209. From doing so we learned about ranges (the difference between the maximum and the minimum value), outliers (a value in a data set that is very different from the others), utilized our knowledge about central tendencies to determine values for the 3 companies' salaries on page 208, and learned about line plots.

At the end of class, we were given our marks for our Oblique Triangle Trigonometry test, and were assigned the Chapter 5 diagnostic test, which was expected to be done by Monday.

The next person to make a blog will be Nina.

How to Rewrite Your Sine and Cosine Laws Exam

Many of you struggled with this exam.  I know that most of you can calculate sides and angles using Sine and Cosine Laws.  That is part of our goal for this unit, but we also need to be able to:

• understand and apply the Ambiguous Case
• solve written problems involving oblique triangles

I encourage you to attempt to improve your mark on this outcome.  To do this, you must:

• talk to Mr. Banow about coming in at a lunch hour to practice
• hand in all assignments from Chapters 3 and 4
• complete p. 200 #3, 5, 6, 7, 8 and p. 195 # 11 (I used to have 8 on this list - skip it) - You need to show all diagrams and calculations.  You may work on this during the lunch hour you come to work
• schedule a second lunch hour to write the exam

Good luck!

4.4 Solving Problems Using Obtuse Triangles

Today we continued using Sine and Cosine laws. We also solved problems that can be modelled by one or more obtuse triangles.
        Example. a surveyor in a helicopter wants to know the width of Garibaldi Lake. He starts 1610m above the forest and observes the angles of depression to both ends measuring 45 degrees and 82 degrees.

He the figured out the angles in the triangle to be 45 degrees 37 degrees and 98 degrees then used the right triangle it made with the trees and found the far distance to the lake and it was 2237.9m
using sine law he found the lake to be 1384m in width.

Summary of the Process for Solving Triangles

We were assigned pg. 193-197

The Solving Triangles Assignment is due Thursday Nov.3 Remember not to do # 4,8

Next to go is Alexander ! :)

November 1st

Yesterday in class we went over the ambiguious case and did an assignment to help us practice. This assignemnt was on pg. 183 #, 1,2,4,5,6,10,12.

If you need help or would like to review the ambiguious case, please look at Allysa's previous post or talk to Mr.Banow.

Next is tanner

Carrying Out Your Research Link

https://docs.google.com/spreadsheet/viewform?formkey=dDI0dWRUR1QwSGFUdlZVNFRYTDlnMXc6MQ

4.3 The Ambiguous Case of the Sine Law

On Friday, we started 4.3 and learnt Ambiguous cases. Ambiguous means unclear, unknown. An ambiguous case is a situation where two triangles can be drawn given the available information; the ambiguous case can occur when the given measurements are the lengths of two sides and the measure of an angle that is not contained by the two sides. (A.S.S. to remember).

We learnt that after you calculate 'h' using SOH CAH TOA you can determine how many triangles you can make. If 'h' is longer than the given side (5.5) you can only form 1 triangle. If 'h' is shorter than the length you calculated (3.5) you cannot form any triangles, and if the length of 'h' is in between what you calculated (3.5) and the given side (5.5) you can make 2 triangles.

To start solving an ambiguous case you have to:

1. Calculate the minimum length to make 1 triangle.

2. Compare minimum length to given length

This will show you the amount of triangles you will be able to make. Once you have completed this and two triangles can be made, you have to cr

eate two cases to show the two possibilities of what the triangle could look like using sine or cosine law, which we learnt in previous units.

The next person will be Brydon! :)

4.1 exploring the primary trigonometric ratios of obtuse angles

we did a chart and
sinx=sin(180-x)
cosx=cos(180-x)
tanx=tan(180-x)

There are relationships between the value of a primary trigonometri ratio for an acute angle and the value of the same primary trigonometric ratio for the supplement of the acute angle.

We used sin and cosine laws to determine the sine lengths and angle measures in acute oblique triangles.

the next person to write the blog is the person with the smallest hands

Bonus Problem!

The interior angles in a triangle are 120 degrees, 40 degrees, and 20 degrees.  The longest side of the triangle is 8 cm longer than the shortest side.  Determine the perimeter of the triangle to the nearest cm.

Complete and submit this problem before Wednesday, Nov. 2 to receive credit for it.  There is no penalty for not doing it, but if you will receive marks for getting it correct.

Project Link

Here is the link to the project form to fill out on Wednesday, October 26.

https://docs.google.com/spreadsheet/viewform?hl=en_US&formkey=dGg5QTE3d3A4OHpmMFFHLTVnTFNsZ0E6MQ#gid=0

Oblique Triangle Trigonometry

Today we started unit four. In this unit we will be learning the following:
-How to use sine law to determine side lengths and angle measures in obtuse triangles.
-How to use the cosine law to determine side lengths and angle measures in obtuse triangles.
-Solving problems that can be modelled using obtuse triangles.

In class we worked on a problem together. The problem is as follows:

On a dogleg hole, golfers have a choice between playing it safe and making the green in two shots or taking a chance and trying for the green in one shot. Jay can hit a ball between 170 and 190 yards from the tree with a 3-iron. Is it possible for Jay to make it to the green at this hole in one shot with a 3-iron? Explain.
This is the diagram we drew:

We figured out what side “a” was by using cosine law.
a(squared)= 51(squared) + 160(squared) - 2(51)(160) cos110
a=184 yrds.

Therefore, yes he could make it to the green in one shot.

After that, we filled in the chart on page 162 and compared our answers with a partner.
Next is Allysa! (:
By Kelsey.

Solving Problems Using Acute Triangles

Today we used the cosine law hte sine law and the primary trigonometric ratios to figure out the side lengths angle angle measures of acute triangles. we did an example in class where manuel wanted to see how high the worlds tallest free-standing totum pole was. Manuel walked out how far the shadow was 42m and then saw the angle of elevation of the sun was 40 degrees. Manuel realized there was a 5 degree slope to the ground. he found the angle at the base of the totum pole was 85 degrees and that the other angle to the ground was 45 degrees he then found the third angle to be 50 degrees using sine law he found the height to be 38.768m tall










next will be Allysa

By: Brydon

Today in class we continued learning about the sin law. Also we learnt about cos sin law. We looked over the books examples on pg. 132,133 and examined the formula for cos sin law.

next is: who ever hasn't done one yet

Proving and Applying the Sine Law

Today we learned about the sin law, which can be used to determine unknown side lengths or angle measure in acute angles. To use the sin law you need to know either two side lengths and a angle opposite to a known side, or two angles or any side. If you know the measure of two angles in a triangle, you can determine the third angle because all triangles have to add up to 180. We used the formulas shown below to find all unknown angles and side length.

We we went through the examples on pages 118-123 to get more of a clearifiactaion as to how to use the formulas.

We finished class off with an assignment on page 125.

Next will be Tanner! :)

Chapter 3

today we needed a calculator.

at the beginning of class we looked at a picture of an acute triangle over an area of land. as a class we determined that someone such as a geographer or pilot would need to know the exact distances of this triangle between cities.

as a class we also decided that a triangle must be a right triangle to directly use triganometry ratios.

we then did the lacrosse problem on page 114.

We found that you must add a line segment to use trig ratios. We split the 6 ft line in half and joined it with the vertex across from it. We now formed two 90 degree angles. We then used sine to find the length of the unknown side. We continued by using trig and found that the goal was 5.43 feet. ... We were wrong. The answer is still unknown.

We then did our chapter 3 diagnostic test.

Next will be the girl who sits beside me.
:)

2.4 angle properties in polygons

key idea....

• you can prove properties of angles in polgons using other angle properties that have already been proved

need to know

• the sum of the measures of the interior angles of a convex polygon with N sides can be expressed as 180 degrees(n-2)


• the measure of each interior angle of a regular polygon is 180 (n-2)

_____

n

• the sum of the measures of the exterior angles of any convex polygon is 360 degrees

ex: if a polygon has 15 sides what is the sum of the interior angles

answer: 15-2=13

13x180=2340

2340/15=156

answer is 156

next is sarah donald!!!

this is finally my post :)

Angle Properties in Polygons

we learned how to find the sum of interior angles using (s-2)180. This only works with convex polygons not concave, to be convex no angles can be bigger than 180

We also learned about the sum of exterior angles, as shown in the diagram below

w=180-A

x=180-b

y=180-c

z=180-d

s=w+x+y+Z = (180-a)+(18o-b)+(180-c)+(18o-d)= 720-a-b-c-d

720 -1(a+b+C+D)

720-360= 360

this is how we found out the exterior angle sum for this 4 sided figure.

next is stelzer
Drawing and painting online tool

Math 20 Foundations Exam

This week will be a busy week in Math Foundations 20.

On Wednesday, Oct. 5 we will write a Practice Exam for Chapter 2.

On Thursday we will be in the Writing Lab. We will work on our Logo Design Assignment (Chapter Task 2) and also select a topic for our Course Project. The Logo Design task is due on Tuesday after the long weekend, October 11.

On Friday, October 7 we will be writing the Chapter 2 Exam.

Have a great week. If you need any extra help, come and see me!

Long-Awaited Thursday Post (Now With More Friday!)

On Thursday, the class didn't do much. We took sheets of paper and drew straight lines from two of the vertices to a point on the opposite side of the paper, then cut them out, creating two right triangles and one acute triangle (Oooh facinating). We noticed that when we put the two right angled triangles on the bigger accute triangle, they matched up the same. Using our knowledge of supplementary and alternate angles, we were able to figure that the sum of the interior angles of any triangle equals 180 degrees (Wow what magic!)
On Friday we talked about non-adjacent interior angles (Sounds fun)! Non- adjacent Interior Angles are two angles of a triangle that do not have the same vertex as an exterior angle. In the picture, angle X and angle Y are non-adjacent interior angles to angle Z! We discovered that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non- adjacent interior angles (which is pretty cool because it shows the neat relations between the sides of a triangle!). We had an assignment to do and it was page 90, #1-3, 5, 6, 8, 9, and 12! Big assignment, but I'm sure we all got it done, RIIIIIGHT??

Next up is Colby!!

Mid-Chapter Review

We started the class off by reviewing a few questions from our previous assignment. We also reviewed that proofs need to be based on facts. For example if two parallel lines are cut by a transversal, and we need to prove that angle  d is 73°, we would say that angle c is 107° because it is the corresponding angle to the one labeled 107°. Next we would say that since angle d is supplementary to c, and c is 107° therefore angle d is 73° because supplementary angles must add up to 180°.

  We then got into groups where each group was assigned a question from the mid-chapter review from pg. 84. We were to answer the question we were given, and then show and explain our work on the overhead projector. Since it was a half day and we did not have time for anything else, we dispersed joyfully when the lunch bell rang. A diagram has been provided to accurately represent the level of joy.
The next to post in the blog will be Tanner.

Angles Formed by Parallel Lines

We started off class by looking over our Chapter 2 diagnostic work sheet and correcting a classmates to show Mr.Banow our knowledge in this unit so far.

Converse is a statement that is formed by switching the premise and the conclusion of another statement.

Next we worked on page 72 which is reviewing parallel lines and transversals.

We reviewed what Alternate Interior and Exterior angles were.

Alternate interior angles are two non-adjacent interior angles on opposite sides of a transversal. Which is angles 3,6 and 4,5.

Alternate exterior angles are two exterior angles formed between two lines and a transversal, on opposite sides of the transversal. Which is angles 1,8 and 2,7.

We also reviewed what Supplementary and Complementary angles were. Two angles are Supplementary angles if they add up to 180 degrees. These two angles (140 degrees and 40 degrees) are Supplementary Angles, because they add up to 180 degrees. These two angles (40 degrees and 50 degrees) are Complementary Angles, because they add up to 90 degrees.

The next person to blog will be, AARON. :)

OH YAH, and don't forget to bring a compass, protractor and ruler ASAP.

Exploring Parallel Lines

In our last class we started chapter 2. We learned about identifying relationships among the measures of angles formed by intersecting line. We learned about transversall lines which is a line that intersects two or more other lines at distinct points. We learned about exterior angles which is the angle that is formed by a side of a polygon and the extension of an adjacent side.  We learned about interior angles which are any angles formed by a transversal and two parallel lines that lie inside the parallel lines. We learned about corresponding angles which is one interior angle and one exterior angle that are a non-adjacent and on the same side of the transveral. Converse is a statement that is formed by switching the premise and the conclusion of another statement. A key summary to follow is when a transversal intersects a pair of parallel lines, the corresponding angles that are formed by each parallel line and the transversal are equal. things you need to know is when a transversal intersects a pair of non-parallel lines, the corresponding angles are not equal. There are also other relationships among the measure of the eight angles formed when a transversal intersects two parallel lines. To do all of this you will need some materials such as a dynamic gemoetric software or a ruler and protractor.

Our class did a hand out assignment on this and then we went over all the answers as a class and i believe it went very well because our class is very smart.

Next will be michelle :)

properties of angles and triangles. :)

yesterday (thursday) mr banow was not present. therefore we had Mrs. Smith as a sub.
we worked on a sheet to test our knowledge about triangles and angles and then worked on a dog activity on page 68. Most groups failed at the objective of making a dog using polygons.
this is all.
peeace.
next is............. cody. :)

Analyzing Puzzles and Games

On Friday, in class we discussed more about analyzing puzzles and games in section 1.7. the goal of this section was to determine, explain, and verify a reasoning strategy to solve a puzzle or to win a game. We looked at example one which was on using reasoning to determine possible winning plays in a game of darts. example two was on using deductive and inductive reasoning to determine a winning strategy while playing the toothpick game. We discussed Alice's solution into winning the game every time. Alice discovered in order to win she must leave Nadine 3, 6, 9, 15, or 18 toothpicks. This strategy will work and Alice will win every time and long as she goes first.
In summary: Both inductive and deductive reasoning can be useful for determining a strategy to solve a puzzle or win a game. Inductive reasoning is useful when analyzing games and puzzles that require recognizing patterns or creating a particular order. Deductive reasoning is useful when analyzing games and puzzles that require inquiry and discovery to complete.

we ended class with an assignment on page 55. #5,6,7,9,11

Next post will be from Amy! yay!

1.6 Recap & 1.7: Analyzing Puzzles and Games

A synopsis of the day:

We were given ample time to thoroughly complete and review our previous assignment. This section helped improve our ability to decide whether to use inductive, deductive, or both types of reasoning on certain problems.

An example of one of the problems in our assignment is as follows:

Use inductive reasoning to determine the number of diagonals that can be drawn in a decagon.

Since we are limited to inductive reasoning, we must first illustrate a specific polygon and then form a pattern, of which can be applicable for a plausible conjecture.

Just look at that craftsmanship.

We can determine that a pentagon will have 5 diagonals. If we looked at a picture of a hexagon, we would see that it will have 9 diagonals; a heptagon, 14. We notice that as the number of sides increase, we increase the addend by an increment of 1 each time. If we follow that pattern, then our conjecture would have to be that a decagon will have 35 diagonals.

After reviewing the assignment, we proceeded to briefly start section 1.7. This section shows that finding a strategy to solve a puzzle or win a game can be achieved via both inductive and deductive reasoning.

We then investigated the math by trying to solve a leapfrog problem. The lowest amount of moves needed to solve the game with 3 pieces on each side was 15; with 2 pieces 8; and with 5 pieces 24.

That was the conclusion of our lesson. Our assignment for Friday is pg. 55 (5, 6, 7, 9, 11).

The next person writing the blog shall be Taryn.

Reasoning To Solve Problems

Summary:
To improve problem solving it would help to understand inductive and deductive reasoning. Deductive reasoning is based on facts that lead to a logical explanation, where as inductive reasoning is based on simple patterns to try and solve the problem.

Example of a deductive problem:
Mammals have hair. Dogs are mammals. So therefore, dogs have hair.

Conclusion:
Based on the statement, the answer is deductive because it demonstrates proof in the original statement.
Mammals have hair. (Which is all mammals, not just dogs)
Dogs are mammals. (Mammals have hair)
So we can come to the conclusion that, yes, all dogs have hair because there are mammals. There is proof stated, so the answer cannot be inductive, the statement is deductive.

- Next is Alex :)

SEPT 13

proof that is not valid

summary:
a single error in reasoningwill break down the logical argument of a deductive proof. this will result in an invalid conclusion, of a conclusion that is not supported buy the proof.
trying to divide by 0 will always cause a proof to be wrong, leading to an conclusion that is also wrong. also try avoid circular reasoning. when you write a proof try to keep is that it don't take a rocket scientist to make sense of it.

an example of to days work:
identify the error: all squares have 4 right angels. Quadrilateral PQRS has 4 right angels. therefore, PQRS is a square.

answer: not true quadrilateral PQRS could be a rectangle

Next is Joel

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