I learned how to write programs in BASIC on one of the very first time-share networks, 45 years ago. Keep in mind: I’m no Luddite! I realized early on that in math, science, and art, computers would be very, very useful. (Not all – I got officially reprimanded for telling my department chair that ‘Renaissance Math’ was either a ‘pile of crap’ or a ‘pile of shit’ to my then-department head, in the hearing of one of the APs, on a teacher-only day. Also when I was required to use them in my own classes, over a decade ago, I and most of my colleagues found them a waste of time. God, what a waste of time – from personal experience attempting to be a volunteer community math tutor at such a school, and also from my experience as a paid or volunteer tutor in helping many many students who have had to use such programs as homework. It would be a lot better use of computers than forcing kids to painfully walk through (and cheat, and goof off a lot) when an entire class is forced to use one of those very expensive but basically worthless highly-centralized, district-purchased computer-managed-instruction apps. * assuming that the teacher are still allowed to initiate and carry out interesting projects for their students to use, and aren’t forced to follow a scripted curriculum. Placing one mirror at a slight angle causes the reflections to curve. When two mirrors are parallel to each other, the number of reflections is infinite. I am reproducing a couple of the images and text that Angel Gilding provides on their website(which they set up to sell silvering kits (about which I’ve posted before, and which I am going to attempt using pretty soon, on a large astronomical mirror I’ve been polishing for quite some time)). (You can find many easy directions online for doing just that some kits are a lot more optically perfect than others, but I don’t think I’ve even seen a kaleidoscope that had its mirrors set at any angle other than 60 degrees!) Students could also end up making their own kaleidoscopes – either with little bits of colored plastic at the end or else with some sort of a wide-angle lens. This could be done with actual mirrors and a protractor, or with geometry software like Geometer’s Sketchpad or Desmos. We’re here to help.Here is some information that teachers at quite a few different levels could use* for a really interesting geometry lesson involving reflections involving two or more mirrors, placed at various angles!Ĭertain specific angles have very special effects, including 90, 72, 60, 45 degrees … But WHY? If you are struggling financially, please do contact your local credit union. Amend as you see fit, but it could be a good place to get started. It also has projected and actual costs, as well as savings and loans. It contains sections for most of your incomings and outgoings, from household rent to entertainment, food and pets. To help, we’ve created a monthly budget planner for you to download and populate. To get started, have a look at our blog on how to manage a reduced household budget. Mapping out a household budget can seem daunting. Even for those not affected finanicially by COVID-19, many are aware of the importance of being prepared, of having a stronger grip on the household budget. For many families, they have to examine and manage finances in new ways, to comb through outgoings in finer detail. Our household items, bills, food – our daily dreams and indulgences rounded up, confined into neat lines, reduced to a number on a page. Meticulous planning is admirable but to many of us it may seem odd overseeing life’s expenses the same way we would a business budget. Their holiday to the south of Spain mapped into orderly categories like itinerary and accommodation, logistics. You know the perfect ones - the people who manage their life via excel.
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