December 29, 2006
His story is spellbinding. There's a really important message for you in the last two minutes ... but you won't really understand it unless you watch the whole thing.
Click on the picture. (18 min. 48 sec.)
December 28, 2006
Rather than simply receiving financial support, winners of the TED Prize are granted something extraordinary: something which children dream about, but which adults assume is merely the stuff of fairy-tales.
They are granted three WISHES to change the world.
They may wish for anything. And TED will seek to make their wishes come true.
Bono won the TED prize in 2005.
Rock star and activist Bono accepts the 2005 TEDPrize with a riveting talk about our moral obligation (and economic incentive) to help lift Africa out of poverty. He unveils his TEDPrize wishes by challenging the TED community to help build a social movement of more than one million American activists for Africa; to tell people one billion times about the ONE campaign; and to connect every hospital, health clinic, and school in one African country, Ethiopia, to the Internet.
Click on the picture. (28 min. 37 sec.)
For more: Read the update on Bono's wishes.
December 27, 2006
Click on the picture. (3 min. 40 sec.)
December 26, 2006
The pictures are just stunning.
Click on the picture. (18 min. 42 sec.)
December 25, 2006
Watch how he displays and talks about statistics. He'll make you laugh and he'll make you think.
December 22, 2006
Thanks to everyone who helped put this together. I found this to be a great experience for me as a teacher I hope it was also valuable to you as a student.
Anyway, here it is, version 1.0 fresh out of beta. ;-)
Flickr Assignment Rubric
It is paramount that the picture be in tune with the purpose of the assignment. It should show, first of all, the student's understanding of how the photo is related to mathematics. The hot spots are important too, because that's essentially your way of teaching other people. Creativity is a factor, because keeping one's interest in the photo contributes to the learning process. Finally, the picture quality should be kept in mind too. If we can't see the picture, it's going to be hard achieving all the other requirements.
The picture must be tagged properly with the course tag and assignment tag. If tags are misspelled or no tags are present the photo cannot be graded and will receive a grade of ZERO. Not tagging your photo properly and accurately is analogous to not handing in your work or not putting your name on it.
| Classification ||Mathematical Content (50%)||Hot Spots (35%)||Photograph (15%)|
| Level 4 ||Packed with mathematical concepts/facts. (Minimum 7 concepts/facts.)||All hot spots accessible; i.e. "smaller" hot spots are "on top" of larger ones, they do not obscure each other. All hot spots are actually labels and relate to parts of the photo (not on blank space with filled in notes). One or more hot spots include a link to a relevant supporting resource on the internet. Minimum 7 hot spots.||In focus or appropriately focused for effect. The subject of the picture occurs "naturally," it is not a contrived shot. Really makes the viewer "see" math in a place they hadn't realized it existed. (Example: trigonometry)|
| Level 3 ||Significant number of concepts/facts included. (Minimum 5 concepts/facts.)||All hot spots accessible. Most hot spots are actually labels and relate to parts of the photo. Not more than one hot spot on blank space. One or more hot spots may include a link to a relevant supporting resource on the internet. Minimum 5 hot spots.||In focus or appropriately focused for effect. The subject of the photo has been "set up" or contrived yet still illustrates math found in "the real world." (Example: derivative)|
| Level 2 ||Some effort to include content evident. (Minimum 3 concepts/facts.)||Most hot spots accessible. Most hot spots are actually labels and relate to parts of the photo. More than one hot spot is on "blank" space. May or may not include links to relevant supporting resource on the internet. Minimum 3 hot spots.||In focus or appropriately focused for effect. Although it is a "real world" picture, objects have been used to "draw" the math. An obviously contrived shot. (Example: trigonometry)|
| Level 1 ||Very scarce content related to assignment.||Less than three hot spots are visible or have information related to the theme of the assignment.||It is evident that little effort went into finding and shooting a picture that reflects the theme of the assignment.|
| Level 0 ||Content unrelated to theme of assignment.||No hot spots or mostly unrelated to the theme of the assignment.||Out of focus and/or otherwise difficult to look at.|
Creativity (up to 5% bonus)
The maximum possible mark for this assignment is 105%. You can earn up to 5% bonus marks for being creative in the way you approach this assignment. This is not a rigidly defined category and is open to interpretation. You can earn this bonus if your work can be described in one or more of these ways:
- unique and creative way of looking at the world, not something you'd usually think of;
- original and expressive;
- fresh and unusual;
- a truly original approach.
December 21, 2006
December 20, 2006
December 19, 2006
- FLICKR.com RUBRIC: Reminder to students that this is for your benefit. Putting in your voice nto this document will affect how your flickr assignments are graded. This document should be about how you want your assignments to be marked, and how the assignments should be done. Get crackin'!
- NEXT FLICKR ASSIGNMENT: The next flickr assignment will be to take a picture of TRIGONOMETRY. Be unique and creative and find a photo no one else will have. This won't be due until the first tuesday after winter break. We'll be given a great amont of time for this assignment, but don't procrastinate!
Today, we added in some more notes into our math dictionary:
Here are a few examples of some arguments:
Example 1 and 2 both are true and valid statements. The reason being the premises of each example makes sense with what the conclusion says. The conclusion makes sense of what has been stated and flows naturally. This is called a sound argument.
SOUND ARGUMENT: an argument that is both valid and true.
AN EXAMPLE OF A FALSE ARGUMENT:
"All men are mortal.
Mr. K is a man
... Mr. K wears glasses."
That was a false statement because, even if the three statements alone are true, together as an argument, it's not. The conclusion doesn't flow naturally with the premises, and it doesn't make sense.
We also discussed different TYPES OF REASONING that we go over in this unit of Logic:
Induction: When we observe several particular examples that identify a pattern and conjecture that it must always be that case.
QUESTION: Will the sun rise tomorrow?
ANSWER: It has every day before, so it will rise again tomorrow.
*That's the answer because through all the years we've been living, a reoccurring pattern of the sunrise has always taken place.
NOTE: To view more examples of inductive reasoning, look over all the investigations we worked on in our circle geometry unit!
Deduction: When we argue from basic, unarguable truths, to a valid conclusion.
An example of deductive reasoning is the process of proving THALES' THEOREM.
In logic, we also look at relationships between different sets, and compare them in Venn Diagrams.
In the following images, we see how sets are made, and how we can compare two different sets using a venn diagram.
TOMORROW'S THE DAY! CIRCLE GEOMETRY UNIT TEST
I HOPE YOU GUYS ENJOYED MY SCRIBE..
blogger was being a pain in the behind and erased my
first draft and I had to start all over again!
BUT, I DID IT AGAIN. YET ANOTHER SCRIBE POST BY ME!
TOMORROW'S SCRIBE WILL BE ...
(just cuz he told me to pick him!)
Have you added any really good links to our del.icio.us box lately? ;-)
- Proof of Congruence (5 questions - refresh the page for more quizzes)
- More Congruence (5 questions - refresh the page for more quizzes)
- Circles (5 questions - refresh the page for more quizzes)
- Arcs &Angles (5 questions - refresh the page for more quizzes)
- Arcs & Chords (5 questions - refresh the page for more quizzes)
- Inscribed Angles (5 questions - refresh the page for more quizzes)
- Tangents (5 questions - refresh the page for more quizzes)
- Polygons (5 questions - refresh the page for more quizzes)
Whew! More quizzes than you can shake a stick at! ;-)
December 18, 2006
Mr.K asked us if the sun is going to rise tomorrow and if i'm not mistaken almost everyone thinks that the sun is going to rise tomorrow based on the fact that the sun has been setting and rising every single day of our lives so far. That brings us to inductive reasoning and deductive reasoning
Inductive reasoning is when you come up with a hypothesis based on examples or observations to make a general rule more specific.
Deductive reasoning is when you use fundamental trues to create a rule. An example of deductive reasoning is Thales' theorem.
Something like this would be inductive:
Draw the next two.
With the next two it would look like this:
Something like this would be deductive:
Draw the next figures.
There really is no right answer for this question, you can look for a pattern but you must explain 3 things: the square, the curve, and the dot.
Here is a true or false questions:
1. The square of a number is larger than the number.
- this is false because the square of 1 is not larger than 1 (12 = 1)
A sentence like "This sentence is false." is what we call a paradox. It is true and false because it refers to two things at the same time and it is a self-reference.
valid means it flows natuarally from the premisis.
invalid means it does not flow naturally from the premisis.
All men are mortal
Mr.K is a man
Mr.K is mortal
^^ This is what we call a sound argument because it is both true and valid
A few examples of unsound arguments are:
All men are squibbles
Squibbles are pink
All men are pink
^^ This is unsound because it is valid but it is false.
All men are mortal
Mr.K is a man
Mr.K wears glasses
^^ This is unsound because it is all true but it is also invalid
All men are green
Mr.K is a man
Mr.K is green
^^ Something like this is also unsound because it is valid but most of it is false
SO THAT IS WHAT WE DID TODAY. HOMEWORK IS EXERCISE 45
CONSUMER MATH - WAGES ASSIGNMENT **due on friday
NEXT SCRIBE IS LAURESSA
December 17, 2006
I'm happy that I reviewed before the pre-tests and quizzes because that's where it came in place, piece by piece I began to understand what was going on and why different angles are the same or two times larger. This happened on Thursday I believe. It was like someone had replaced a light bulb to the lighthouse in my head. However, I wasn't prepared enough. So, my options are study harder or study harder (haha).
The up side is, I understand the theorems and I look for different triangles and angles. The down-side is, sometimes I doubt myself and have second thoughts about some things, which makes me to change my answers (which were right in the beginning). But, most of the things, I understand. Well, I hope that everyone does well and studies hard. See you all tomorrow fellow class mates!
This semester is almost over too. (tear*)
The circle geometry unit was a lot of fun. I really liked this unit, mostly because it involves looking at a real image and trying to figure out measures. I like how everything all connects, when you find one part you can also find another. The trouble I have is remembering the theorems. I'll just have to look over my math dictionary more. That's all for now, good luck!!
December 16, 2006
The usual human brain can only remember at max 7 items, according to Mr. K. In remembering a phone number, we chunk the 7 digits into 2 groups so its easier to remember. Just like remembering a phone number, we chunk all the theorems into 4 categories.
next scribe is crysta! go crysta! i'm sure you'll find some new innovative way for learning just like what u did with that bubbleshare thingy! =)
December 15, 2006
THe test is postponed FOR MONDay.
December 14, 2006
WELL GOOD LUCK AND GOOD NIGHT :)
11 days until christmas!
Determine the measure of ےECB, ےBDC, ےBAD, and ےDBE, where E is the centre of the circle.
So first of all we always start with a table that has STATEMENT on one side and REASON on the other.
It's obvious at this point that BE and CE are radii, therefor triangle BCE is an isosceles triangle. This also means that ےEBC and ے BCE are the same.
We now know the exact amount of ےBCD and according to cyclic quadrilateral theorem ے BCD's and ےBAD's sum should equal 180°. So in order to find ےBAD, we subtract 30° and 40° from 180° and come up with 110°. Therefore ےBAD is 110°.
Another thing we looked at were the two triangles that are subtended by the same arc; triangle BCE and triangle BCD. Since all of us know of the central inscribed angle theorem ( AKA the star trek theorem ) we can easily point out that ےBDC is half the amount of ےBEC. As a result ےBDC = 100°/2 which equals 50°.
We only have one angle left! Angle DBE! So if we look closely at triangle BCD you'll realize that we only have one angle left to find, ےDBE. We also know that every the angles of a triangle sum up to be 180° and by subtracting every angle that we have we'll be able to come up with the value of ےDBE! :D
Which in this case in 20°! =)
Once you've found your information and proofs, your table (including "Statement" and "reason") should look something like this:
In the diagram below, R, S, T, U are points on the circle with RS = RU = UT and SU = ST. Find the measure of ےUST.
e) none of these
The first thing you should always do is mark down what is given to you. Have a wishful thinking colour, a colour used for given facts and a colour used for things you have proven! ( it comes in handy :D )
I'll use purple as the facts that are given, blue for what we're looking for and orange for the facts i prove. =)
There's no particular order to do this in, but what i looked at first was the isosceles triangles. We can easily point out that ےRSU and ےRUS are the same and ےSUT = ےSTU.
Now if we look at RS, RU and UT they are all the same length. Which means that the angles subtended by this chord length will all be the same. SOOO.. ےRST = ےRUT = ےUST.
In order to find the exact degree that angle is we make three equations. (this is like going back to substitution in linear equations). Here are the three equations (let ےSRT = w):
1. w + z = 180
2. 3y + z = 180 --> z = 180 - 3y
3. w + 2y = 180 --> w = 180 - 2y
If we substitude 2 and 3 into 1, we can find out what Y is, which is ےUST.
180 - 2y + 180 - 3y = 180
180 + 180 - 180 = 2y + 3y
180 = 5y
36 = y
And there you have it!
c) 36° is the correct answer. =)
That's all for tonight! Sorry for the late entry, i had to go and watch my brother's christmas concert! haha. =) Well, no homework tonight, just study! Test tomorrow. Good luck guys!
HAPPY HOLIDAYS! =]
And the next scribe will bee..... -Zeph! Enjoy. =)
I think everyone will do very good on this test...and some excellent(its not u Lauressa..jk)
goodluck on the test everyone! ;D
Oh well, nothing to worry about. I honestly think that this unit, for me, was easier to understand than the ones we've had in the past. There's just something about circles, triangles and geometry that make them easy to learn. There were times when I hated this unit because of all the PROVING we needed to do. But I guess, the more proving we did in class, the easier it seemed, and my hatred lessened. Today we had the pretest in class, and I don't think I did my best. Although, I did put in my first effort, and got about 70% of the questions right! "Sweeeeeet!" Anyway, good luck to everyone on the test tomorrow!
December 13, 2006
So yes, its me EEDCE.
(1) In the diagram below, AB and CB are tangents to a circle with radius 10. If angle AB find x, the shortest distance from B to the circle.
h = 10/cos50
h = 15.557units
x = h - 10
x = 15.557 - 10
x = 5.557 units
(2) Given: Circle with centre C
- Angle 1 = Angle 2
Angle 1 = Angle B given
BC ~= CD ~= AC radii
Triangle ABC is isoscles from above
Triangle ACD is isoscles from above
Therefore, AB cannot be congruent to CD.
8. Complete the proof:
Diagram clarification: E, D, C are collinear
Given: EA is tangent to the circle at A
AD // BC given
EA is tangent at A given
Angle 8 = Angle 7 Tangent-Chord Theorem
Angle 7 = Angle 5 Alternate Angles
Angle 6 = Angle 8 - Angle 9 Tangent-Chord Theorem
Angle 1 = Angle 2 Triangle ABC ~ Triangle AEC
Okay. thats it folks.
homework is to finish the rest of this pre-test if not yet done so.
SANDY will take it away tomorrow.
Today, for all you naughty kids that skipped (haha jk), we worked on five different circle problems that Mr. K had put up for the class to do. They were:
1) A chord that is 10cm long is 12 cm from the centre of a circle. Find the radius.
2) Line AB and line CD are two parallel chords in a circle. Line AB is 10cm and Line CD is 14 cm. Find the radius if the chords are 3cm apart.
3. a) O is the centre of each circle. Find the measures of the indicated angles. Justify your answer.
-Line AC is tangent at B
- Angle 1 is congruent to angle 2
Prove: Line BD // Line FC
So yeah that's what happened in class. Homework was posted up on the blog by our very own math teacher, Mr. K. And I choose........................................................................................SANDY cheeks to be our scribe for tomorrow's class.
December 12, 2006
Remember, as I said in class, if you start working on one of these questions and get the horrible feeling in the pit of your stomach ... STOP. Go on to the next problem and try it out. If that happens with all 8 problems take a break and come back to them later ... lather. Rinse. Repeat. ;-)
We'll go over all the questions in class tomorrow.
December 11, 2006
December 10, 2006
Did you know I can see your classroom from two windows?!
My first window is your blog. I am excited by what I see and hear! I never cease to be amazed by the quality and sophistication of your scribes; you constantly achieve new heights in illustrating and annotating your scribes. More than that I am so impressed when you celebrate each others’ learning, when you are creative, and when you critically reflect upon your learning in your BOBs.
Did you know Mr. K’s blog is my second window? I admire and respect what I see and hear here too! Did you know that Mr. K celebrates your learning on his blog? that he reflects upon what best helped you to learn and why? that he unselfishly shares all he knows with those who read his blog? that he learns from the conversations on his blog? that he writes with passion and is creative? and that he commits many random acts of kindness by honoring other teachers’ accomplishments in his posts? Did you know all he expects of you, he shares those same expectations for himself?
Did you know that because of all that and more, Mr. K.’s blog has been nominated for “Best Teacher Blog 2006” on the Edublog Awards website?
I just happen to think that no one deserves this honor more than Mr. K.
What about you?
December 06, 2006
We did investigation 8 today. Here were the instructions.
(a) Construct a chord AB in the circle.
(b) Construct a tangent, RS, to the Circle at A. The tangent should not be perpendicular to AB.
(c) Measure the angle of RAB.
You can plot down the points anywhere you'd like. Just be sure that your chord and the tangent line aren't perpendicular. I measured angle RAB and ended up with 35° with mine.
(d) Construct a point, C, on the circle, on the opposite side of chord AB from angle RAB.
Some of us where have a few problems plotting down C. We did plot C opposite of the chord AB, but had it plotted down inside the circle. The question asks to plot it on the circle, meaning on the circumference. What we did was plot it down in the circle which was different from what was being asked. So, just look out for those small things and read the question carefully.
(e) Construct and measure inscribed angle ABC. What do you notice?
From looking at the slide below, you will notice that angle ACB is the same as RAB.
(f) Measure angle SAB.
As you can see, angle SAB measures 145°.
(g) Construct a point, D, on the circle, on the opposite side of the chord AB from angle SAB.
(h) Construct and measure inscribed angle ADB. What do you notice?
Angle SAB and ADB are the same.
Here is sort of a final drawing on all the angles that were measured.
THIS HERE IS CALLED THE TANGENT-CHORD THEOREM.
(i) Can you articulate a general rule for what you have found? Your sentence should begin:
"If an angle is formed between a tangent line and a chord, then...."
The rule here is simply that "If an angle is formed between a tangent line and a chord, then the inscribed angle subtended by the opposite side of the chord is congruent."
IF AN ANGLE IS FORMED BETWEEN A TANGENT LINE AND A CHORD, THEN THE INSCRIBED ANGLE IS SUBTENDED BY THE OPPOSITE SIDE OF THE CHORD IS CONGRUENT.
The HOMEWORK for tonight is to Re-do the questions we had trouble with in EX. 33. And also EX. 34.
REMINDER: There will be a quiz maybe tomorrow, or the next day after.
I chose the next scribe to be Natnael.
December 04, 2006
After that he showed us some examples of the 40s student's trigonometry pictures, so have a better clue of what to do with our quadratic function pictures. Make sure it has a lot of details a quadratic function should have.
*Reminder it should be uploaded on flickr by Thursday.
We went over some question in our exercise #32 which were # 10, 12, 13
#10 was a question that didn't really fit in with any unit we did so far but it was a fun question to solve.
#12 this question we had to find the ticket price that will yield maximum profit.
This is a good review for our Analytic Geometry unit.
revenue = (# ticket) (cost/ticket)
let x = 1 discount of $3.00
R (x) = (1000 + 100x) (60 - 3x)
roots @ x= -10 x= 20
We ended up with the price $45 per ticket.
A) y= x and y = -1/2x+2
After going over some homework we started on our Investigation #7
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"If two tangents are drawn from a common point, exterior to a circle, then...the tangent lines are the same measure"
"If a radius intersects a tangent line, then...the angle is 90 degrees"
After all of that the next step is to go back and construct a new point S exterior to the circle and repeat steps b, c and d for point S.
Today's homework is exercise #33
Make sure to attempt every question. The ones you are really stuck on should be looked at in class.
And most of you may notice that the scribe list is now on our fourth cycle!! that's a lot of scribing!. I just wanted to say I'm really proud of every one's work. Look how far we came with our scribing, we're using a lot more tools to make our post explained to the best of our abilities.
Okay enough of that...the next scribe for Wednesday (Tuesday afternoon NO SCHOOL!) is... MERIAN!
December 01, 2006
To start off today's class we all congratulated Crysta on her Fantastic! scribe post. Once again, great job Crysta! Mr. K was also trying to explain to us the meaning of how much one million (1000000) really is. If we broke it down to how long it would take to reach one million by receiving one penny each second. When we finished calculated it, it took 11.5 hours. Then we decided to calculate how long it would take to reach a billion (1000000000). We all found out that it would take 32 years to reach that. We also realized that we haven't even lived for a billion seconds yet AND one billion penny's will fit into 5 school buses. Quite interesting, don't you think? If you're wondering how Mr. K knew all this, he went to this website
Anyway, once we got back onto to track we discussed questions that we had trouble with from last nights homework and we did Investigation 5.
(a) Choose 6 different points on the circumference of the circle. Do not space them out evenly. Label these points A, B, C, D, E and F.
So this part is pretty straight forward. We start with a blank circle and add 6 points anywhere on the circumference.
(b) Construct angles ACB, ADB and AEB.
For this part of the investigation, we're pretty much making chords, but these are to make angles.
(c) Measure the angles formed at C, D and E.
So here we take the angles and measure them. It's best to write them down that way we can keep track of them. instead of just adding it to the picture.
When I completed this step in class, i got this:
ACB = 13°
ADB = 13°
AEB = 13°
Notice a pattern?
(d) Construct angles EAF, EBF and ECF.
Here, we will repeat what we did for (b).
(e) Measure the angles formed at A, B and C.
Here we'll do the same as (c).
EAF = 60°
(f) What do you notive about all these angles? Can you articulate a general rule for what you have found? Your sentence should begin:
"If two (or more) inscribed angles are subtended by the same arc, then..."
Have you seen the pattern to these? Well, If you have you've noticed that all the angles come out to equal the same. To complete the sentence can be said in different ways.
i) ... they have the same measure.
ii) ... are congruent
iii) or in your own words!
So there you have it! investigation 5! I don't know if it's just me but these things are super fun to do. haha. (:
Anyway. Homework for the weekend is:
1. Attempt to complete Investigation 6. (but if you get frustrated with it, then leave it be)
2. Exercise 31.
3. Project (due monday)
4. Picture of a parabola put onto Flickr. (due thursday)
REMEMBER TO DO YOUR HOMEWORK, GUYS. =)
As for the next scribe.. i think** the only person left is MELISSA! .. haha. if i'm wrong, correct me, otherwise, Have a great weekend!