# Posts

### September 22, 2014

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2:38 AM | Matching Three Forms of Linear Functions

My students have worked on slope-intercept form and standard form in Algebra. I want them to also learn point-slope form. I'm trying to avoid making that into a direct instruction lesson, and I am going to use these cards to help students make some observations about point-slope form. I'm planning to give pairs students this stack of cards and have them sort them into meaningful piles. I suspect they might start by sorting the graphs into one pile, the slope-intercept form […]

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This past week, I had the great pleasure of spending a few days thinking with some very smart people about issues in teacher education. They included Judith Warren Little, Magdalene Lampert, Elham Kazemi, Nicole Louie, Jessica Charles, Lynsey Gibbons, and Britnie Kane. We had a few other folks interested in teacher education drop in and […]

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One of the classic uses of Operations Research and, in particular of Linear Programming is to propose optimum alternatives for the logistics or transport of inputs and products from a group of suppliers to a group receivers or petitioners. When we consider that, in this process of transportation, intermediaries can participate, this is an extension […]

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1:56 AM | Origami Regular Octagon

We folded a square piece of paper as described in the Illustrative Mathematics task, Origami Regular Octagon. I didn’t want students to know ahead of time that they were creating an octagon, so I changed the wording a bit. We folded (and refolded … luckily, there was not a 1-1 correspondence between paper squares and […]

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1:27 AM | The beginning of autumn

is at 10:29 PM EDT, tomorrow (September 22) night, in the eastern United States.What's that mean?For many, time to finally feel OK about wearing sweaters.Time to pick apples.Time to clean chimneys for the winter ahead.Time for walks in the woods to watch the leaves and their colors.Time for pumpkins.Time for reflection on the year thus far.Time for an assessment of where one's been this year and what is left to do.Time for a deep breath and the realization that the sun will be overhead for less […]

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12:52 AM | Biking toward perseverance

Three weeks a year we go on Encounter Week. Most adventures are multi-age (grades 7-12) and range from backpacking to Acadia National Park to knitting. Students immerse themselves in something out in the world for a week. Most options include overnights and all students and faculty participate.Last week, for the fourth year in a row, I led the ninth grade bike trip. Fifteen ninth graders (the whole grade), an eleventh grade student leader and three faculty members biked […]

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primepatterns:
The animation below shows the first 120 rings of Ulam’s spiral with L varying between 1 and 100:
Below is the corresponding plot of the modified Mertens function, M’(r), for r = 1 to 120:
In mathematical notation, M’ is as follows:
where Rl is the lowest number in the ring with ring index, r, and Rh is the highest number in that ring and μ(k) is the Möbius function.
Below is the corresponding plot of our second modified Mertens function, M”(r), for r =
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12:38 AM | Planck: It’s Just Dust

The Planck paper with results on dust in the BICEP2 patch of sky is now out, see here. I’m sure experts will weigh in soon and I’ll link to such discussions, but my non-expert take is that Planck is saying … Continue reading →

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12:37 AM | #MTBoSChallenge Week 6 Summary

Week 6 Summary ... Grading ... it's going to get the best of me ... 3 reasons ... We have a new grade book that crashes almost every time I start to enter grades.We decided to give a non-calculator and calculator version of every test to prepare students for future big tests. That means I have 160 x 2 tests for each unit! The first unit was particularly picky to grade - domain, range, transformations, problem solving. And no, we don't do multiple choice
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12:11 AM | ¿Y si nuestro planeta no fuera bipolar?

Olvidé dejaros el enlace a mi entrada, me lié con las programaciones didácticas y olvidé anunciarlo. Mea culpa!.
http://masscience.com/y-si-nuestro-planeta-no-fuera-bipolar/
Espero que os guste
Un abrazo

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This year, I'm teaching Algebra 1 and Algebra 2 for the third time and Trigonometry for the first time. Every year, my school offers a different advanced math elective above Algebra 2. We've cycled through college algebra and statistics. They were both just okay. But, this year, I am LOVING trig. I think there are several reasons for this. First, it's my first year to do interactive notebooks with my advanced math class. I guess for my first two years of […]

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12:10 AM | Subtraction Strategies

Great ideas for teaching subtraction strategies in 2nd and 3rd grade. The actual structure is good for all grades. Notice how she frames the problems on the board, this is a great way to jumpstart mathematical conversations about strategies. videos Happy Mathing, Dr. Nicki

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12:09 AM | When does fall really start?

This year the autumnal equinox – which marks the point when the sun crosses the celestial equator – falls on September 22 in the United States (10:29 PM Eastern time, and earlier for the other time zones.) People seem to refer to this as the “first day of fall”. But this is the astronomical definition. […]

### September 21, 2014

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11:26 PM | Local Linearity

I haven't posted at all since school began over a month ago. It frustrates me that the periods I do some really great work in the classroom (or at least, I think so) are also typically the periods I have zero free time and hence the best blog posts potentially go unwritten.Le sigh.Well, regardless, here's something we did in calc a couple weeks ago...A big idea I want kids to come out of calc with is that if we zoom in on a differentiable function long enough then the function, no matter […]

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11:24 PM | Is Mathematics Limited?

Is Mathematics Limited? Pure Mathematicians like to think that mathematics is some form of abstract truth, something that's a property of the universe independent of us. But Mathematics is a product of the human mind and as such is limited, probably in ways we can't even conceive. But wait, mathematics is unbelievably successful in physics, and physics describes the universe, so mathematics must be much bigger than us. Right? Wrong. Mathematics is our invention. Sure, it's incredibly helpful to […]

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11:00 PM | On This Day in Math - September 22

Nothing is too wonderful to be true if it be consistent with the laws of nature.~Michael Faraday in his Laboratory NotebookThe 265th day of the year; 265 is !6 (sub-factorial 6), the number of ways that six ordered objects can be mis-ordered so that each is in the wrong spot. See Subfactorial The term "subfactorial "was introduced by Whitworth (1867 or 1878; Cajori 1993, p. 77). Euler (1809) calculated the first ten terms. For example, the only derangements of {1,2,3} are {2,3,1} and {3,1,2}, […]

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10:44 PM | Full text

One of the benefits of the pressure for open access from funding bodies and governments is that academic publishers have opened their archives, and full text is typically available for papers from five years after publication. This is particularly valuable … Continue reading →

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10:38 PM | Il più grande robot del mondo

Oltre ai problemi di pubblicazione, la gestazione del post è stata sicuramente la più complessa di tutta la serie dedicata ad "Astro Boy". Il post che segue ha subito almeno un paio di riscritture a partire da un testo di base iniziale, che vi posso assicurare alla fine è risultato completamente stravolto. La versione alla fine pubblicata non mi ha comunque soddisfatto appieno, ma se avessi continuato a limare, probabilmente non avrebbe visto mai la luce e non avevo altre appendici da
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10:14 PM | new kids on the block

This summer, for the first time, I took three Dauphine undergraduate students into research projects thinking they had had enough R training (with me!) and several stats classes to undertake such projects. In all cases, the concept was pre-defined and “all they had to do” was running a massive flow of simulations in R (or […]

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For Teachers/Parents/StudentsSubscribe now to start immediately receiving CCSS/SAT/ACT Twitter Challenge Problems with DETAILED Solutions, Extensions, Strategies and Common Core Implementation Ideas!Subscribe in Sidebar to the right...Half Price Until 9-30-14!After 9-30-14, price will be $39.99Subscription covers 2014-15 School Year through Summer 2015Your subscription will also include --Download of MathNotation's Challenge Math Workbook --Additional Summer 2015 ProblemsWhen payment is
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9:23 PM | Number Talk – Phone Battery

Had a fascinating experience with a number talk last week. Question was: After 3 hours, your phone battery is at 93%. How long do you expect it will last before it dies? I was fascinated and concerned by the students answers: A small but significant number of students used estimation or proportional reasoning strategies to […]

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9:17 PM | Exponential Models – Updated

I posted last week with my model for Arawaks on Hispaniola — using exponential decay to model native populations after Columbus arrived and link to some US History content. I sat down with our US History teacher and put together two more graphs with different data sets — we now have Arawaks on Hispaniola (1491 […]

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9:16 PM | I Will Derive

A fun song about derivation to solve displacement, velocity and acceleration problems.

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9:04 PM | The Mean, Median and Mode Toads

A short story to help students remember what is meant by mean, median and mode.

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8:06 PM | Curious Corridors of Numbers

Each row begins with the number 1 at the left. Skip counting by 2, 3, 4, 5, and so on gives the rest of each row. The diagram can be continued as far as desired. Adding the numbers in each L-shaped region forms a well known mathematical sequence; what pattern shows up? Another mathematical pattern is formed by [...]

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Video is now available of David Gross’s colloquium this past week at NYU, which had the title Quantum Field Theory: Past, Present and Future. It’s quite interesting to compare his current point of view to that of ten years ago. … Continue reading →

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7:35 PM | Feedback Roundup, Vol I

Effective feedback continues to be a preoccupation of this blog. Here are some posts from other teachers who are thinking hard about feedback and related issues.Do you just sit down with a stack of papers and a red pen and let loose? Mary Dooms suggests that a certain amount of planning needs to precede the actual writing of feedback. She recommends looking through the entire class set of work before committing pen to paper. (link)John Burk gave a student some detailed written feedback, and on
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7:17 PM | Wissenschaftsausgaben und Selbstmordrate

Es liegt in der Natur einer Messung, dass sie nicht beliebig genau sein kann. Und selbst bei einer genauen Messung wird man Schwankungen des Meßwertes feststellen und häufig lassen sich solche Schwankungen sogar statistisch beschreiben. Als etwa 2002 der große Wissenschaftsskandal in der Festkörperphysik aufflog, da war man unter anderem deswegen stutzig geworden, weil die…

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A little over a year ago, I teased Grey Matters readers with a mystery skill. First, they had to learn to easily multiply by 63, then learn how to easily multiply by 72. The skill itself was revealed to be how to roughly convert any whole number of years into seconds!
In this post, you'll learn a similar skill: how to convert weeks into minutes instantly!
Back in the days before computers and