## II.l Standards should result in all students being committed and equipped to be competent lifetime learners, well-prepared for further formal education and to pursue multiple careers.

Personal financial literacy, a strand embedded within the Revised (2012) Mathematics TEKS for kindergarten through grade 8, is included with a goal of preparing students to *manage one’s financial resources effectively for lifetime financial security*. High quality content related to these standards, which aim to secure our students’ financial future, is readily available to teachers as they work to design authentic learning experiences.

I have created a website which contains information related to the standards, resources for teaching and learning, information for parents, a connection to children’s literature, and specific content related to budgeting and paying for college. The website is linked below.

To access other high quality financial literacy content, browse the websites below. Each of these sites contain a wealth of resources for teaching and learning personal financial literacy.

Kayla Jarzombek, mathematics teacher at Coppell Middle School North shared a recent learning experience in her classroom via Twitter in which her students took a career quiz online:

Ms. Jarzombek’s students use their 1:1 devices to access and interact with authentic content related to personal financial literacy, including this career quiz!

To keep up with the latest in Ms. Jarzombek’s classroom, follow her on Twitter: @KJdoesmath.

]]>

Items: Length: Budget: Volume: (applies to all) Area: (applies only to fish)

Start: $50.00 Start: X,XXX Start: XXX

Fish A 4 in. – $X.XX – (4 in. x 230) – (4 in. x 30)

Fish B 8 in. – $X.XX – (8 in. x 230) – (8 in. x 30)

Misc. A 1/10 of volume -$X.XX – (2/10 x volume)

Misc. B 1/10 of volume -$X.XX

Money Left Over: $X.XX End V: XX End A: X

The “X’s” indicate whatever numbers you started with for V and A. Remember the 2/10 came from putting the 2 Misc. 1/10 items together, and this is just an example. Good luck!

]]>The tuning fork

Resonates

Tearing the fabric of space/ time

A continuum of

Matter

And

Energy souped up in

Nebulae of

Frustrations running down fault-lines

A seismic conundrum of vibrations

Shockwaves shifting tectonic plates on beds of

Chthonic magma.

Pi,

The tuning fork

Resonates

Tearing the fabric of space/ time

Uncreated matter trickling from

+-

Electricity unseen

Magnetic cohesion of bonds strengthened by

Pi,

The tuning fork

Resonates

Tearing the fabric of space/ time

Neither here nor there

In a fraction of air

Exists the heir

To undo

Creation

And it is known as

Pi,

The tuning fork

Resonates

Tearing the fabric of space/ time

Drumming on sesamoid bones

Pulsating jelly to

Eukaryotic

Cilia so sensitive to pick up

The flash

Of

The muzzle of a gun

Unburdening itself of

A lead bullet

Led into

An ever expanding universe

Where

Pi is,

The tuning fork

That

Resonates

Tearing the fabric of space/ time

Transcending

Ephemeral biochemistry

© Sena Frost 2k16

]]>The concept was first introduced in the philosophical literature by David Kellogg Lewis in his study *Convention* (1969). The sociologist Morris Friedell defined common knowledge in a 1969 paper.^{[2]} It was first given a mathematical formulation in a set-theoretical framework by Robert Aumann (1976). Computer scientists grew an interest in the subject ofepistemic logic in general – and of common knowledge in particular – starting in the 1980s.^{[1]} There are numerous puzzles based upon the concept which have been extensively investigated by mathematicians such as John Conway.^{[3]}

The philosopher Stephen Schiffer, in his book *Meaning*, independently developed a notion he called “mutual knowledge” which functions quite similarly to Lewis’s “common knowledge”.^{[4]}

You visit a remote desert island inhabited by one hundred very friendly dragons,

all of whom have green eyes. They haven’t seen a human for many centuries and

are very excited about your visit. They show you around their island and tell you

all about their dragon way of life (dragons can talk, of course).

They seem to be quite normal, as far as dragons go, but then you find out

something rather odd. They have a rule on the island which states that if a dragon

ever finds out that he/she has green eyes, then at precisely midnight on the day of

this discovery, he/she must relinquish all dragon powers and transform into a longtailed

sparrow. However, there are no mirrors on the island, and they never talk

about eye color, so the dragons have been living in blissful ignorance throughout

the ages.

Upon your departure, all the dragons get together to see you off, and in a tearful

farewell you thank them for being such hospitable dragons. Then you decide to tell

them something that they all already know (for each can see the colors of the eyes of

the other dragons). You tell them all that at least one of them has green eyes. Then

you leave, not thinking of the consequences (if any). Assuming that the dragons are

(of course) infallibly logical, what happens?

If something interesting does happen, what exactly is the new information that

you gave the dragons?

Mixing natural items with manmade materials is common practice in the Honeysuckle Vine room. Such a textured, elaborate conglomerate of natural and manmade items. All week I noticed arrays such as this one, each with its own story, combining science, mathematics, literacy, conversation, individual work/play and collaborative work/play.

]]>*Approaching Infinity* by Michael Huemer

“Infinity” is a concept that, if you’re not careful, can really bite you in the ass. In his latest book, *Approaching Infinity*, the philosopher Michael Huemer attempts to sharpen our idea of infinity to address two areas of concern.

One is the nature of infinite regresses. A famous one is the Regress of Causes, where one event needs to be caused by another event, but that event needs to be caused, etc all the way down the line. Thomists’ attempt to to address this regress is to stipulate an uncaused “unmoved mover” that starts the whole process going. Note that this was a regress that people thought they needed to solve; Huemer calls it thus a “viscous regress”. Other regresses are classified as “benign” though, like starting from the postulate that some proposition P is true. Then it’s true that P is true. It’s also true that it is true that P is true. And so on. Nobody really complains about that regress.

The other area is a number of famous “paradoxes of the infinite”. Examples include Zeno’s paradox, Thomson’s lamp, Galileo’s paradox, and Hilbert’s hotel (there are 17 paradoxes discussed in all). In each case, there’s a paradox that occurs when we assume an infinity is involved. Take Galileo’s paradox (please!): which are great in extent, the natural numbers (1, 2, 3, 4, 5, …) or the perfect squares (1, 4, 9, 16, 25, …)? At first it seems like there should be more natural numbers, since for any finite list of numbers from 1 to n there will be both perfect square and non-squares like 7 or 18. But you can map every natural number to a square (just square the number!) so (1 ↔ 1), (2 ↔ 4), (3 ↔ 9), (4 ↔ 16), and so on. Since every spot on that ladder is filled, it looks as though there are just as many perfect squares as natural numbers. A paradox!

Huemer goes over two classical accounts of the infinite, that of Aristotle and that of Georg Cantor, and finds both wanting in various ways. There are multiple chapters of the philosophy of numbers, sets, and geometrical points that I think fairly present the views of the usual Cantorian orthodoxy before poking holes in them. Even if you ultimately disagree with Huemer’s account, I think it’s a very readable and enjoyable introduction to issues in the philosophy of mathematics.

We then come to Huemer’s own account: *extrinsic* infinities are allowable or at least possible, whereas *intrinsic* infinities are not. An extrinsic property is one that changes when you change the “size” of the object in question. So things like size itself, volume, mass, energy content, etc. If you double the size of a block of wood, you double its mass. An intrinsic quantity is one that is comparably scale-invariant; things like temperature, speed, color, etc. If you imagine one cup of boiling water and then bring another cup of boiling water together with it, the temperature of the water does not change.

With this theory of the infinite in hand, Huemer is able to (mostly) resolve the 17 paradoxes and give an account of viscous and benign regresses. For the case of the Regress of Causes, and infinitude of causes going back in time is an extrinsic one, and so in principle non-problematic. The Thomist proposal of an “unmoved mover” who is infinitely powerful fails on this account, though, since such an entity would involve infinite intrinsic magnitudes.

If you’re interested in understanding infinite quantities which if you’ve done any work in the STEM fields you’ll have come across, I wholeheartedly recommend *Approaching Infinity*.

Chemistry interrupted their Hearts…

Physically apart,

TanviPatil

]]>TED-Ed presented a riddle last week based on a classic probability problem. However in the riddle there is a small and seemingly insignificant detail that changes the calculation. In this video I present the pertinent details of the frog riddle, explain its connection to the boy or girl paradox, and then do a detailed calculation of what I believe is the correct probability.

TED-ED frog riddle: https://www.youtube.com/watch?v=cpwSG…

Blog post (another calculation if the probability a male frog croaks is p): https://wp.me/p6aMk-4wD

Ron Niles made a video that shows the probability visually and explains an interpretation of a male frog croaking with probability p:https://www.youtube.com/watch?v=K53P5…

Matt Parker shows off his Magic Square party trick (unlike magicians, mathematicians often reveal their secrets).

By: Numberphile.

Ted Shearer’s **Quincy** for the 1st of March, 1977, rerun the 25th of April, is not actually a “mathematics is useless in the real world” comic strip. It’s more about the uselessness of any school stuff in the face of problems like the neighborhood bully. Arithmetic just fits on the blackboard efficiently. There’s some sadness in the setting. There’s also some lovely artwork, though, and it’s worth noticing it. The lines are nice and expressive, and the greyscale wash well-placed. It’s good to look at.

**dro-mo** for the 26th I admit I’m not sure what exactly is going on. I suppose it’s a contest to describe the most interesting geometric shape. I believe the fourth panel is meant to be a representation of the tesseract, the four-dimensional analog of the cube. This causes me to realize I don’t remember any illustrations of a five-dimensional hypercube. Wikipedia has a couple, but they’re a bit disappointing. They look like the four-dimensional cube with some more lines. Maybe it has some more flattering angles somewhere.

Bill Amend’s **FoxTrot** for the 26th (a rerun from the 3rd of May, 2005) poses a legitimate geometry problem. Amend likes to do this. It was one of the things that first attracted me to the comic strip, actually, that his mathematics or physics or computer science jokes were correct. “Determine the sum of the interior angles for an N-sided polygon” makes sense. The commenters at Gocomics.com are quick to say what the sum is. If there are N sides, the interior angles sum up to (N – 2) times 180 degrees. I believe the commenters misread the question. “Determine”, to me, implies explaining *why* the sum is given by that formula. *That’s* a more interesting question and I think still reasonable for a freshman in high school. I would do it by way of triangles.

David L Hoyt and Jeff Knurek’s **Jumble** for the 27th of April gives us another arithmetic puzzle. As often happens, you can solve the surprise-answer by looking hard at the cartoon and picking up the clues from there. And it gives us an anthropomorphic-numerals gag for this collection.

Bill Holbrook’s **On The Fastrack** for the 28th of April has the misanthropic Fi explain some of the glories of numbers. As she says, they can be reliable, consistent partners. If you have learned something about ‘6’, then it not only is true, it *must* be true, at least if we are using ‘6’ to mean the same thing. This is the sort of thing that transcends ordinary knowledge and that’s so wonderful about mathematics.

Fi describes ‘x’ and ‘y’ as “shifty little goobers”, which is a bit unfair. ‘x’ and ‘y’ are names we give to numbers when we don’t yet know what values they have, or when we don’t care what they have. We’ve settled on those names mostly in imitation of Réné Descartes. Trying to do without names is a mess. You *can* do it, but it’s rather like novels in which none of the characters has a name. The most skilled writers can carry that off. The rest of us make a horrid mess. So we give placeholder names. Before ‘x’ and ‘y’ mathematicians would use names like ‘the thing’ (well, ‘re’) or ‘the heap’. Anything that the quantity we talk about might measure. It’s done better that way.

]]>Thought begets Mathematics.

Mathematics begets Physics.

Physics begets Chemistry.

Chemistry begets Biology.

Biology begets Thought.

__Calculation Task__

Find the product by suitable rearrangement:

(a) 4 × 166 × 25 (b) 8 × 291 × 125

(c) 625 × 279 × 16 (d) 285 × 5 × 60

[Time: 10 minutes MI: Logical RBT: Analysis]

]]>

Dear Learners,

Complete Exercise 2.5 in NB 2)

**Note: There will be an internal assessment of maths on Monday (2/05/16)**

Be neat in your work.

Draw lines after every sum.

Do your calculations in rough column.

]]>Namely from our friend, the set theory, point of view set A = {0} is not empty, there *is *something, namely number zero. If one would say, that 0 is nothing, in set A weren’t anything. In our case there clearly now is something, element 0.

Somehow philosophically 0 isn’t in same extent ”nothing”, that it would lead from view of set theory as the only element in the set to same state as the empty set ({} or ∅), that is so empty, that there simply is nothing; the empty set is more ”nothing” than 0. As a number, zero is considered as neutral element in *some* cases. But it obviously is more… What?

As to empty set, more philosophical question is, does the empty set contain itself – and is it then empty.

Emptyness and nothingness have their differences.

Let us imagine an empty room where there is four walls and a roof. Emptyness gives there space. And also this emptyness, space, has many meanings; if the room has only little space you would probably feel quite uncomfortable there.

In music the fact the there isn’t a note is known as pause. In this case emptyness in the notes gives rhythm to the music, without this non-existence of a note (nothingness from point view of sound?) we would’n have music as we know it.

In speech silence, a pause, can give one some kind of power to the speech itself.

Emptyness and nothingness really are powerful from their beings!

I consider ”nothing” as something that doesn’t exist. Still it does.

]]>On wednesday you all will have a internal assessment (subjective) of maths based on unit 1 (Real number) .Prepare well and come.Wishing you all the best for test.

With regards,

Asha Joshi

]]>** Direction** : Matt Brown .

** Plot** : S.Ramanajun was an ill educated maths whiz . He was a pious Brahmin and the man who knew infinity is about his journey from Madras to Cambridge and the challenges he faces there .

** My view** : The man who knew infinity is based on the book by the same name .

It starts in Madras and slowly moves to England.

Ramanujan played by Dev Patel is devoid of emotions , he looks blank throughout the movie . With all due respect to S.Ramanujan , the work he did in mathematics , especially without a formal education , is definitely a great feat by itself . But the movie failed to capture the essence of it . The movie’s fails to generate a feeling of inspiration .Jeremy Irons as Hardy takes time to realise the brilliance of his student and thus is late to rise to the occasion.The emotional rapport between the two could have been explored better .The movie has a serious tone through out and the 109 minutes I sat through felt like a torture I inflicted on myself . I would recommend watching ‘The Man Who Knew Infinity ‘ only if you have the patience to .

** Quotes that caught me** :

It was faster in my head .

I was told you love numbers more than people .

Great knowledge comes from humblest of origins .

A little humility will go a long way.

I am what you call atheist .

We could compare him with Newton.

You theorem is wrong.

** Remometer** : 1.5 /5

Remometer Legends :

1 : I ran out of the theater.

1.5 : I stopped myself from running out .

2 : I will never watch this again.

2.5 : average . Can skip watching on big screen.

3 : One time watch on the big screen.

3.5 : Fan girl. Will definitely watch again , that too on big screen.

4 : Overwhelmed. Can’t stop thinking of it . Deeply moved .

*Image courtesy: imdb.com*

In this Problem of the Week video, Chloe explains how to perform a u-substitution to simplify the integrand in a given integral. For the full problem and solution transcript, visit our blog: http://bit.ly/1qCMmEk

By: Worldwide Center of Mathematics.

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