Decimal-Crazed Lunatics

I’ve always like fractions. No surprise there.

Math with Bad Drawings

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How to Edit Your Math Pessimism

Channeling Dr. Jo Boaler: the learning is in the struggle; mistakes are the best thing you can make!

Math with Bad Drawings

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Back in the Box

We’ve been out since the 17th of December, having left Literal Equations in a hasty pile by the door, somewhat obscured by a blur of ugly Christmas sweaters, Mid-Quarter Comments, administering the baseline evaluation for the Eighth Graders, Khan-in-the-Octagon, and my own Final Exam in Reva Kasman’s wonderful MSM717 “History of Mathematics”.  MSM701, “Patterns, Relations and Algebra” starts January 19th, with Dr. Kasman!

So now it’s the Saturday before we return. I have done nothing to plan for my classes on Monday. No lessons, no quizzes, no activities, only feeding my own curiosity about the connection between Perfect Numbers and Mersenne Primes, starting to work through Euler’s “Elements of Algebra”, and binge-watching “The Walking Dead” on AMC. Plus Christmas, New Year’s, and a few tutoring sessions. I’m supposed to relax on break, no matter how hard it is.

I have started as I always start, with a calendar. (My calendar of choice is the Moleskine Weekly Notebook, 5.5X8.5).  We have 13 days until the Second Quarter ends on January 22nd; then we have 13 days until February Break. 26 days. We are going to finish Chapter 2 and have a 2-day Chapter Test. So I think that we’re going to skip rate and unit conversions in favor of Proportions, Similar Figures, Percents and Percent Change. This is essentially two units exploring theory and practice.

I’m going to spend a few hours this afternoon with Grant Wiggins’ and Jay McTighe’s “The Understanding by Design Guide to Advanced Concepts in Creating and Reviewing Units“, Module O.  Keeping in mind that I have to give two tests between now and the end of the quarter, and each will absorb one full class period. I want to use Khan Academy; I may even give an overnight assignment in Khan.  I also want to use Formative, maybe as a prep period prior to the test. Most importantly, I need to define proficiency in each of these.

Magic Squares

The Lo Shu

 

 

 

How can a square be magic?  Its symmetry has an aesthetic appeal, and the shape is useful for everything from sock drawers to houses to game boards.  But when you create a square table with equal rows and columns of carefully chosen numbers, that square takes on unusual properties that for some hold sacred meaning, for others a research tool in Number Theory, and for others a pleasant diversion on a rainy afternoon.  A Magic Square is an array of cells in three rows and three columns, each containing a non-negative integer, such that the sum of each column, each row, and both of the main diagonals is the same; the magic constant or the magic number.^1,2 The number of rows or columns is called the order, or N, and since the numbers are a sequence from 1 to , we can write a formula to calculate the magic constant as: or more simply: ³ The square remains magic under each of eight transformations: rotations through multiple degrees of 90⁰, including zero, and the complementary mirror images.

Magic Squares

 

 

 

 

Pascal’s Triangle and the Binomial Coefficient

Really enjoying this playlist on the Binomial Coefficient. These are not in order; part of the fun for me is moving back and forth between them. Many thanks to Richard Rusczyk of Art of Problem Solving for providing such a clear and fun path into understanding the relationship between the Binomial Coefficient and Pascal’s Triangle. It’s in the struggle that we learn.

Maths Project #1

Maths Project #1

This is the first maths project. The objective is to create a situation where students can explore rates, proportions, variability, how values depend on other values that change over time, and anything else I might not have thought of. There are no rules other than that you must try to explore every possible relationship using mathematics. Make assumptions if you don’t have specific information.

Project #1
Two cars, one bicycle, one road. Two cars traveling in opposite directions on a two-lane road, one bicycle traveling in the same direction as one of the cars. Why do all the objects seem to pass the same point at the same time?

Things to think about:
At Time t, how far apart are the cars?
how fast are they traveling?
how far is the bicycle from each car?
has fast is the bicycle traveling?
do we assume that all objects have a constant speed?
what is the relative speed of the objects?
what happens when we vary the distance between the objects?
what happens when we vary the distance between the objects?

youcubed.org at Stanford University

Thanks to Dr. Jo Boaler, Professor of Mathematics Education, Stanford University

did he say “maths”, or is that a typo?

Status Update from a Frustrated Mathematician

stuck on a problem

Math with Bad Drawings

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Fearing the Unknown

“we have nothing to fear, but fear itself…” apologies to Mr. Churchill. I try my very best to make failure survivable in my classroom. It’s OK to fail. It’s OK to be wrong. It’s not OK to not try.

Math with Bad Drawings

Or, How to Avoid Thinking in Math Class, Part 5
(See Also Parts 1, 2, 3, and 4)

Sometimes I fantasize about making scarecrows of myself.

They’d wear jackets, ties, and expressions of thoughtful patience. I’d scatter them around my classroom—maybe even one every desk (if scarecrow manufacturers happen to give bulk discounts). And they’d work wonders for my students, because a lot of the time, the students don’t actually need me.

They just think they do.

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“But when will I ever need to use this, Mr. B?”

“The New York Times Doesn’t Know Any Math Teachers”

this is why I follow Dan Meyer.  I would pose this to my students as: “can you help the innumerate New York Times?”

The Art of Cell Structure and Function

6th Grade Project work at  MCCPS Exhibition #1 2014-2015.  This installation was informed by our visit to the Calder Exhibit at the Peabody Essex Museum and consists of abstract images of cell organelles. The writing below each image describes the structure of the organelle and how its function contributes to the cellular system.  Visitors to Exhibition remarked on the kinetic nature of the installation and its accessibility to them as viewers.  They were also impressed by the integration of Art and Science and the students’ discussions of how artists use Science to understand, interpret and create their art. The hanging rectangular prisms are recycled pizza boxes from a recent School Pizza Lunch.