On solving percent problems.

 

What is percent?

 

Percent means for every hundred. since per means for every, and Cent means hundred, then we can think of percent as parts per hundred.

 

suppose you wanted to find 8 percent of 300.

 since there are 3 one hundred parts, we can draw three shapes representing hundreds each. like so.

 

                        

 here you can simply add 8+8 +8 or 24. so 8% of 300 is just 24. very straight forward. 

 Now suppose you wanted to calculate 15 percent of 400

 you simply need four bubbles like above, and repeat process with different numbers, such as

 

 

 since we have four hundred, we used four bubbles, as drawn above and count the 15's

like so.

15 + 15 + 15 +15 which give 60. 

so 60 is 15 percent of 400. 

Now suppose you needed to see what 7 percent of 250 was. your approach is no different, 

since there are two and one half hundreds, you need three bubbles to start with. 

 so we add 7 + 7 + half of 7 we get

7+7+3.5 which gives 17.5

we can also use a little algebra for this and use a proportion equation

like so.

 

solve for x first by cross multiplying and getting

7(250) = 100x.

and dividing on both sides by 100. (note, you can simply multiply on both sides by 250, but those new to algebra know how to cross multiply first).

getting the final result of 17.5 which is the desired result. 

 

you can find more example like this with worksheet at

 Teachers Pay teachers

 

 

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.

 

 

My Teachers pay Teachers Store.

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. 

 

 My TpT product list

 

PROBLEM OF THE DAY

This problem is a physics problem, for those in an algebra 2 or higher should be able to work this out, with some thought. A person needs to know how deep a well is, but has no way to measure it since its to dark. He drops a large pebble into the well, and hears the sound of the pebble hit the water 5 seconds later. How deep is the well? also, is it possible to determine the speed of the pebble right before it hit the water? Do your best, and please leave some comments.

PROBLEM OF THE DAY day two

Geometry is a very interesting in mathematics, however its a rather tricky subject as well.

Here is a typical geometry word problem that involves triangles.

The firs side of a triangle is two inches less than twice the second side. The third side is ten inches longer than the second side. If the perimeter is 12 feet, find the length of each side.
don't forget to comment if you do find the solution.
good luck.
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Solution

PROBLEM OF THE DAY

For today's problem my focus is algebra. Many of my students were having problems with, you guess it, word problem. Word problems are tricky, and it takes quite a bit of practice to get good at them.

Here is Today's problem, which I will solve and post the following day, followed by a new problem. Not all problems will be algebra, they could be geometry, calculus, physics and even chemistry.

1).. Two airplanes leave Los Angeles, at 10:00 am., one towards Europe at 600 miles per hour, and the other in a direction opposite to the first, at 150 miles per hour. When will they be 900 miles from each other? and how far have they each traveled?


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Solution to yesterday's problem..

this is quite simple if you know how to use the rtd equation.. namely, Distance = rate x time.

My thoughts on Quantum Mechanics

I am here to write about things that interest me, or others such as mechanical things, electronic things, and things that are hard to explain by ordinary observation. Of the many things that totally fascinate me is the thing called Quantum mechanics. For some times now, and after I graduated from college some time ago, it has left me with a feeling of, should I say, some what of a weird feeling that maybe I just din't get what the idea was about. I managed to understand enough to be able to solve most problems that I was responsible for, simple potential wells problems, harmonic oscillator was a bit more challenging, etc. But some years later, I wish to know more about how this stuff called quantum mechanics works, and why it works the way it does. Why was Einstein so against it, and what other explanations could there be for the way nature works. Maybe God does plays dice with the universe, I sure wish he had a place to find the cheat codes, ;)..