How Can You Tell?

How can you just tell if a number goes into another number evenly with out dividing? With these simple rules.


Divisibility by two: If the last digit, is even, the original number is divisible by two.


This number works: 2012 (two is even), this number does not work: 2011 (one is odd)


Divisibility by three: If the sum of the digits is divisible by 3, then the original number is divisible by 3.


This number works: 2136 (2+1+3+6=12, 3 goes into 12 evenly) This number does not: 2137 (2+1+3+7=13, 3 does not go into 13 evenly)


Divisibility by four: if the last two digits form a number that is divisible by four, then the original number is divisible by four.


This number works: 2136 (4 goes into 36 with no remainder) This number does not: 2134 (4 does not go into 34 evenly)


Divisibility by five: If the last digit is either 0 or 5, then the original number is divisible by 5.


This number works: 2155, This number does not: 2151


Divisibility by six: if the number is divisible by 2 AND 3, then it is divisible by 6.


This number works: 2136 (follows rules of divisibility by 2 AND 3) This number does not: 3242


Divisibility by seven: don't, just get out the calculator or a pencil and paper.


Divisibility by eight: If the last three digits form a number that is divisible by eight, then the original number is divisible by eight.


This number works: 133,760 (8 goes evenly into 760) This number does not: 133,766


Divisibility by nine: If the sum of the digits is divisible by 9, then the original number is divisible by 9. 


This number works: 3,465 (3+4+6+5=18, 9 goes evenly into 18) This number does not: 3,565


Divisibility by ten: If the last digit is 0, then the original number is divisible by ten.


This number works: 5730 This number does not: 2343


Divisibility by twelve: If the number is divisible by 3 AND 4, then it is divisible by 12. 


This number works: 24 (both 3 and 4 go into 24 evenly) This number does not: 30 (even though it is divisible by 3 it is not divisible by 4, therefore it is not divisible by 12)


Those are the basics of division, you'll never need a calculator again! :)

& You Thought You Knew How To Add & Subtract..

Kids these days aren't being taught the same way as you and i were taught.  I was taught start with the numbers on the right when you add, carry the first digit if there was one, leave the other number below, and add the next column so on and so forth. 
  10
+11
  21


Now, kids are learning more efficient ways of adding. It might mix kids up to add right to left and read left to right, and the reason for doing it that way, simply "because".


A way to teach kids to add is to start at the left, and work right. like this
                         3000
                   +   4999
                        7000
                          900
                            90
                               9
                        7999
So basically i started in the thousands place and did 3000+4000. Then wrote the answer in the first line. Then did the same thing with the hundreds, tens and ones. It makes more sense in kids minds to add left to right, and they can see why 3000+4999=7999. 

Scary Technology Realization

Ever since the early 1900's there has been a spike in the invention and discoveration of new technology.  A lot of this has been great and improved the quality of life.  After the invention of cars and the research of newer better technology we have the cars of today, that will only keep getting better until eventually they will probable be able to drive themselves with no human input.  The internet was invented in the 1990's but no one really used it, except if you were wealthy or a researcher. Now, most people carry the internet with them in their pockets all the time, cell phones.  People socialize not in person but on facebook or twitter. Based on this technology in education time line, kids will be using technology in the class room, at home, all of the time. Technology will be embedded into people, there wouldn't be a way you could tell your students to turn off their cell phones, because it's a part of them.
http://www.educationfutures.com/resources/timeline/
This is a link that talks about a possible pathway of the future in technology and education. What will the main, the standard or the bottom-line of what is acceptable for technology.  Many of things that are used today will be obsolete, such and the newest computer software and smart-phone cell phones.
Many new advances are coming our way in the near future. We have to be prepared to accept some of the technology and learn about it, and how to use it. Some of this technology will be great for classroom interaction, and some of it will be very detrimental and eliminate jobs.  If we don't keep up, it will run us over and the "smart" people such as teachers that don't, will become janitors and lunch ladies.
Let's keep up and make our world a better place for everyone.

Multiplication

There is not just one way to multiply.  The traditional way is to line up the one's, ten's and so on, then multiply up and across from the bottom right number then the same thing for the bottom left number and add the answer. Like shown below:

 12

x 2

 24

Other ways are lattice and the partial methods.

Lattice method uses a box.

This example is multiplying 134x39 and the answer is across the bottom, 5226.

The Partial method multiplies the bottom number by the top numbers but using its place value. As shown below: 

Whatever way you choose to multiply is fairly simple, with some practice.

Egyptian Numbers

I've been learning about different numbering systems from around the world and ancient times.  It's very interesting to see different ways and techniques used to count.  Some systems have a numbering system where it matters the order the symbols or numbers are placed.

For example the Egyptian numbering system uses a series of lines for numbers 1 through 9 and then symbols for 10 on, as shown in the picture. In the Egyptian numbering system, the order does not matter in which the symbols are entered. So, i could write line, astonished man or astonished man, line and it would mean the same thing, 1,000,001. Learning about different numbering systems was very intriguing.