Review: Maths Resources

Last day of term today; a good time for a general review. Our schedule has not been working well for the last few weeks but I'm going to start with a review of the resources we are currently using ...

Maths

Josiah

Working through the Montessori Research and Development manuals. I modify the sequence a lot to suit Josiah: there's a lot of repetition that he would hate, and some concepts are only partially explained. Josiah gets annoyed when I present him with a maths rule without offering him a proof, or at least a good explanation of why it works. But I am not at all tempted to switch to a different maths curriculum: Montessori Research and Development's partial explanations of why things work are more than I've seen in any other maths curriculum or text book. I have been using the Internet successfully to fill the gaps in presentations.

We have just finished Elementary Maths Volume III, which concludes with calculating square roots. Not sure whether to go to Elementary Maths Volume IV next or finish Elementary Geometry Volume III, which we did some work from earlier this year but didn't complete (if I remember rightly). Might show Josiah the contents pages of each and let him choose.

Tessa

Tessa asked to be introduced to algebra, so that is what she has been working on for the last couple of months. We started with some activities invented by a Montessori teacher, which I read about on the Internet years ago and now can't find again. The activities use two identical, small trays with the "=" sign on a card in between them. For the first activity, on the right-hand tray there is a number of counters, and on the left-hand tray, an empty container representing "x" the unknown quantity, and a number of counters. The teacher explains that the two trays contain equal quantities and must remain equal. Therefore if we take away a number of counters from one tray, we must take away the same quantity from the other. This means that we can find out what quantity the empty container represents by taking away the counters from that tray and taking the same number of counters away from the other tray.

There are similar activities to demonstrate how to solve algebra problems with subtraction, negative numbers, multiplication and division. Tessa had fun with those and is now comfortable solving problems abstractly on paper.

Next I made up my own activity to demonstrate that the unknown quantities in algebraic equations can represent real things.

Since then, we have been working through the algebra chapters in Alpha Mathematics. This text book is aimed at kids two years older than Tessa, who have more familiarity with numbers and operations than Tess. But she is doing really well, working everything out.

We could continue, but it is probably a better idea to move to something different at the start of next term. I'd like to give Tessa a refresher course on the checkerboard. Then work through my "division by a two digit divisor" activities. That would take us to the end of the year.

Every week, I write up a sheet of maths practice problems for each child so that they get enough practice at new concepts to cement them in memory. I try to vary things to keep it fun and challenging.

Both kids have begun recording new maths concepts, with explanations, examples and notes on how to perform operations, in a notebook. The geometry notebooks the kids produced while working through Montessori Research and Development's Elementary Geometry Volume II were such lovely reference books that I thought it would be worth doing for maths too.

I'll post on other subjects over the next few days.