Piecewise Functions <b>Scaffolding</b> Up the Wahzoo

Out of habit (aka. a compulsive need to organize my work), my lessons are always digitized and numbered sequentially/labeled with keywords, collected into chapter folders and further grouped by classes. At the end of every school year, I zip up the entire folder tree and archive it in multiple places, labeled by year. At the beginning of the school year, I download all of the past archives onto each computer I might be lesson-planning on (one at school and one at home), so that when I need to look up an old lesson, it'd be in front of me in a matter of minutes, complete with handouts and relevant quizzes and tests.

So, anyway, the other day I started to teach my Precalc kiddies the basics of piecewise functions. After the first 1.5 lessons or so (in which I had introduced the mandatory Christmas bonus breakdown in El Salvador and had asked the kids to graph the bonus and to graph a simple progressive tax system*, and also had gone over the basics of evaluating a piecewise function), I thought of digging through my old stuff to pull up some scaffolding material for writing piecewise function equations.

I pulled some of my favorite scaffolding things together into one packet this year. Here it is (I threw a couple of word problems in there for fun, since this packet I intend on grading as a project):








I am posting it because maybe you'd find it helpful to see how I break down piecewise equations into, well, pieces! (If your kids don't need these skills broken down quite so much, you might want to check out Sam Shah's collection of piecewise worksheets, which is a little more comprehensive in the skills they need. Again, I make no claims that my worksheets are comprehensive! They just step in and break it down a little more, like the problems in the textbook don't do...)

*Speaking of which, funny thing about tax systems: I randomly wondered the other day whether there are any countries in the world that actually implement a flat tax. Found this article that talks about how Estonia and two of its neighbors implement the flat tax system, and some of its less-apparent benefits and drawbacks. (For example, did you know that when neighboring countries all implement flat tax systems, it becomes a negative competition sort of thing, where each country may keep lowering their taxes, in hopes of staying competitive?) I shared some of the interesting tidbits with my kiddies, and even they thought it was fun!

And, coincidentally, El Salvador's own tax brackets are exceedingly simple. I am going to give it to the kids sometime next week, as additional practice for making graphs and writing equations.

View the original article here

Synergy Aluminium Scaffolding Tower

Scaffolding: Parts And Functions

Looking at repairing your house or having extensions done to it? If it has to be done from the outside, there is going to be a few weeks when the beauty of your house will be affected. This is because of scaffoldings.

What are scaffoldings? Scaffoldings are temporary frames erected outside the house which is under repair or construction. This frame is usually made of metal pipes or tubes and in some places it is still made of bamboo sticks. The purpose of a working scaffold is to provide a safe place of work with safe access suitable for the work being done, for instance, if the work has to be done at a great height or higher floor, which is not accessible from the ground.

The basic materials used for erecting a scaffold are tubes, couplers and boards. The tubes are either steel or aluminium and are either galvanized or black. They come in various lengths but are of a standard diameter. The boards provide a working surface for users of the scaffold. It is on these boards that the workers stand or sit while working. The boards are made of seasoned wood and are made according to specific thickness. Their ends are protected by metal plates called hoop irons or nail plates. Couplers are the fittings which hold the tubes together firmly. The most common are called scaffold couplers, there are three basic types: right-angle couplers, putlog couplers and swivel couplers. To join tubes end-to-end joint pins (also called spigots) or sleeve couplers are used, or both together. Only right angle couplers and swivel couplers can be used to fix tube in a ‘load bearing connection’. Single couplers are not load bearing couplers and have no design capacity. Apart from these three basic materials there is a need for ladders, ropes, anchor ties, sheeting etc.

Since scaffolding need to be very strong and stable, a good foundation is important. The scaffolding should be able to carry the load as well as spread it evenly. The working platform also needs to be strong and stable so as to carry the load.

Once a proper scaffolding has been erected, half the job is done as it will make working, repairing or constructing much easier.

View the original article here

Synergy Aluminium Scaffolding Tower

Scaffolding: Parts And Functions

Looking at repairing your house or having extensions done to it? If it has to be done from the outside, there is going to be a few weeks when the beauty of your house will be affected. This is because of scaffoldings.

What are scaffoldings? Scaffoldings are temporary frames erected outside the house which is under repair or construction. This frame is usually made of metal pipes or tubes and in some places it is still made of bamboo sticks. The purpose of a working scaffold is to provide a safe place of work with safe access suitable for the work being done, for instance, if the work has to be done at a great height or higher floor, which is not accessible from the ground.

The basic materials used for erecting a scaffold are tubes, couplers and boards. The tubes are either steel or aluminium and are either galvanized or black. They come in various lengths but are of a standard diameter. The boards provide a working surface for users of the scaffold. It is on these boards that the workers stand or sit while working. The boards are made of seasoned wood and are made according to specific thickness. Their ends are protected by metal plates called hoop irons or nail plates. Couplers are the fittings which hold the tubes together firmly. The most common are called scaffold couplers, there are three basic types: right-angle couplers, putlog couplers and swivel couplers. To join tubes end-to-end joint pins (also called spigots) or sleeve couplers are used, or both together. Only right angle couplers and swivel couplers can be used to fix tube in a ‘load bearing connection’. Single couplers are not load bearing couplers and have no design capacity. Apart from these three basic materials there is a need for ladders, ropes, anchor ties, sheeting etc.

Since scaffolding need to be very strong and stable, a good foundation is important. The scaffolding should be able to carry the load as well as spread it evenly. The working platform also needs to be strong and stable so as to carry the load.

Once a proper scaffolding has been erected, half the job is done as it will make working, repairing or constructing much easier.

View the original article here

Synergy Aluminium Scaffolding Tower