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!”
The human adult spine has 33 vertebrae, the bones that support the rest of the body. The lumbar vertebrae, in the lower back, bear the weight of the upper body and are very flexible. If you have lower back problems, it’s often your lumbar vertebrae that are struggling under the weight they have to bear.
Multiplication is a lumbar vertebra in the spinal column of mathematics. Multiplication supports the weight of, amongst other things: Continue reading “Please, no more rubbish about times tables!”
I taught my year 7 class today and had the most wonderful time. I really love my year 7s, they’re so enthusiastic. So far this year we’ve done place value, rounding, four operations (with natural numbers and decimals), powers, roots and primes, negative numbers, order of operations, fractions (including four operations) and are early into our unit on percentages. Today it was common FDP conversions (quarters, eighths, fifths, thirds, ninths, etc).
We looked at 1/3 and 2/3, which led us to the fact that 0.999999….. = 3/3, which is, of course, 1. I love teaching this fact, I tell them I’m about to blow their minds, and when I show them the initial reaction is always something like, “but it can’t be 1, it’s less than 1″. Continue reading “Adventures in Mastery 5: Making Connections”
In my maths department we are starting on a journey of building a new curriculum based on the principles of mastery. To find out what mastery is, read Mark McCourt. Implementing something different comes with all sorts of challenges but, if it’s a good thing to do, it brings benefits too. One of the benefits I am finding this year is the liberation from the compulsion to produce a three- (or four- or five-) part lesson with objectives and mini-plenaries and some kind of forced activity to (falsely) demonstrate the “progress” my students have made over the course of an hour. By having a curriculum with clear aims and (hopefully) coherent thinking underpinning every aspect I feel more confident to teach the way I feel will be most effective rather than making my lessons a conflation of lots of “best practice” techniques in order to satisfy a checklist. Continue reading “Adventures in Mastery 4: Lesson Sequences”