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Algebra: you use the letter ‘x’ more than you ever have done in your whole life!

I started my first algebra unit with Year 7 on Monday.  It’s the essentials of algebraic manipulation: adding, subtracting, multiplying and dividing terms, including those with indices, as well as expanding and factorising single brackets, all pretty standard beginnings in algebra.  In the past I think my first lesson on algebra would consist of a brief introduction then some simple collecting like terms.  From what I’ve seen, that’s generally what comes up first in most schemes of work.  This time, though, I’ve tried to be more deliberate and more pedantic over the details.  Really, really pedantic, because it’s insecurity with the small details that causes so many mistakes for the rest of our students’ experience.  I’m starting out by assuming they have done no algebra.  Many of them have done a little but I’m not prepared to risk that all their different primary experiences were the same, or solid.  (This is a not a criticism of primary teachers, more that I want to take sole responsibility for something so important). Continue reading “Algebra: you use the letter ‘x’ more than you ever have done in your whole life!”

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Adventures in Mastery 3: Prognostic Practice

When rewriting our scheme of work for years 7 to 11 I was conscious that there were some perennial problems I wanted to try and solve.  One such problem was that of algebraic misconceptions that arise year-in, year-out.  I decided that I would try to address these with what I can best describe as prognostic practice, which is practice that directly prepares the students for the algebraic work earlier on in the year.  Here are some of the problems, and the associated practice we will do: Continue reading “Adventures in Mastery 3: Prognostic Practice”

Flight and Fight

Back in 2010 I, and 12 million other people, became slightly addicted to a little game called Angry Birds.  I stopped playing after a couple of months, like I always do with these things, not sure what happened to it then, probably petered out like so many other overnight success stories.

The premise of the game was to get your little birds to destroy some nasty green piggies who were stealing your eggs by launching them from a slingshot at the pigs’ defences.  I can see why those birds were angry, I would be if I were repeatedly being launched, projectile-style, at towers of wood and ice and stone.  That’s gotta hurt.

The programmers use some fairly simple mathematics to get those birds to move in a realistic way.  You intuitively expect the birds to move through the air in the way they do because all objects move like that, unless some force causes them to change their path.  Picture it now – imagine throwing a tennis ball, what shape does the path of the ball take? What about a diver jumping off a diving board, or a bullet flying through the air, or water spouts from a fountain? Continue reading “Flight and Fight”

Maclaurin & Taylor Series (Desmos)

Nothing original, but this model demonstrates how increasing the number of terms in a Taylor or Maclaurin series improves the approximation.  You can hide/reveal the graph of appropriate series and change the value of the pivot in the Taylor series.

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