The trouble with triples

what in the world is a triple? We can conj our up some kind of meaning by looking at the word Triplet. first it has the tri part of it, it implies there could be something to do with three's. for example, my wife had triplets the last time we wanted a child. No not really, we didn't have triplets, but you knew it had to do with three of something. you could be trilingual, meaning that you could speak three languages, or triangles, meaning that there are three angles in some figure, or should we say polynomial? 

But the triples I wan to talk about are Pythagorean triples what the heck is a Pythagorean triple? sounds like something out of Babylonian periods. 

actually, a triple refers three numbers that when you square them it represents a right triangle, for example

 

As you can see, the numbers 3,4,5 make a right triangle. when you square the first two, namely 3 and 4, see above, you get five squared. this makes a perfect right triangle. say you take another triple, such as 5,12,13 does that give us a triple?

lets see.As you can see here, it also does.

You can find an infinite number of triples that make a right triangle, not to mention scaled up triples. say you take ( 3,4,5) and double each number.  they then become 

(6, 8, 10) because 36 + 64 gives you the third number of 100. and it too is a triple. check for yourself and have some fun finding more triples. which leads to the Pythagorean theorem we all love.

 

This implies that the edge of each square gives the area of each box, when added together give the area of the larger box. That to me is the coolest thing ever. 

so, the next time you hear about a triple, you'll be thinking of Pythagoras as much as me.

 

 

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Mathematics

    For many teachers having to come up with what to teach is a daily chore that we all have to get used to. Some of us like spending countless hours creating meticulous lesson plans to make sure that our kids understand what it is they have to learn. Aside from the effort of creating these lessons, we must have prepared lesson plans because administrators expect to see written out plans for each and every day. After a while, we get to a point where we've accumulated enough material that we can plan entire weeks if not months of what we should be teaching. I got to a point that I could walk in my room, look at my lesson book and knew exactly what I would be teaching that day. 

    However, for those new teachers, its not so simple. many still do not know how to write a proper plan for a day, let alone a week. This is one of those things that education courses do not do a very job teaching future teachers. 

    thank goodness for TpT. teachers pay teachers. that is a website that one can find lessons just about anything, because they are written by teachers to sell to other teachers. Suppose you are a substitute teachers, and have no idea what to teach, you could go to this site and look for something that the regular teachers had been working on, for example how to factor a quadratic equation, or solve a linear equation, you do a search under those tittles and immediately you'll get hundreds of already written out assignments for those type of problems. Many are even free. Sellers on this site are obligated to start with a least one free lesson, and this goes up to at least 5% of the number of lessons they have for sale. that means those must be offered for free. Its good for customers and sellers because this improves relationships with the sellers and the customers as well. It also has a rating system to communicate to seller how the customer found the material.

   When I first started teaching, back almost 30 years ago, they did not have this type of help. Things were much more difficult back then, The type writer was the main source of technology. However, administrators were so demanding as they are now. Most are trying to justify their high salaries by making the teachers work harder so they can look good. All I can say is, I am grateful for this type of resources available for new teachers. 

 

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