The Magic to Divisibility

The Magic to Divisibility 

      It is still the fourth week of elementary math where we are working with divisibility. I have a few secrets that I would like to share with you that has helped me out and has made math a lot easier and faster. The secret is...how to test numbers to see if they are divisible. 

    We all know that if a number is divisible by 2, the number ends in a even number or if the number is divisible by 5 it ends in a 5 or a 0 but what about 3,4,7 and 8? I will tell you! 

    When we are trying to find if a number is divisible by 3 all we have to do is add the digits in the number and divide by 3. 

           Example: 528    

First, add all the digits: 5 + 2 + 8= 15 

Next, divide 15 by 3= 15/3 = 5 

Then we know 528 is divisible by 3! 

Is the same number is divisible by 4? To find out if it is divisible by four all we have to do is look at the last 2 digits of the number. 

Example: 528

First, we look at the last two digits= 28 

Next, divide 28 by 4= 28/4= 7

Then we know 528 is divisible by 4! 

When trying to find if a number is divisible by 7, it is a little more tricky. We have to first divide the number into sections of 3. We then take the even portions and add them together, then the odd portions and add them together and then subtract the two. Once we have subtracted then we take the number and divide by 7. Don't worry I will show you an example! 

Example: 41002536960

Wow!! That's a huge number!! 

First, separate the number into groups of 3. 41002536960

Next, take the even portions; 536 + 41= 577 

Then the odd portions; 960 + 002= 962

Now subtract the two answers= 962-577 =385 

Finally, take 385/7 = 55 

Yes! We know it is divisible by 7!! You can actually do the same exact steps to find out if it is divisible by 11 and 13. Just change the step where you divide by 7 and change it to 13 or 11. 

Finally, we look at if a number is divisible by 8. This is very easy as well, all we do is look at the last 3 numbers of a given number. 

Example: 5,224

First, find the last three digits in the number

Next, divide that number by 8

224/8 = 28 

So we know that 5,224 is divisible by 8. 

These are some great technique to use with large numbers to see if it is divisible by a particular number.  Hope you enjoyed these new techniques and can apply the magic to your own numbers! 

Working through the Steps 

        We are in our fourth week of learning elementary math at Central Lakes College. This week we are learning all about divisibility of numbers. A secret I would like to share with you when trying to find the divisibility of numbers is a great technique called the Factor Tree. 

        The factor tree is a diagram used to break down a number by dividing it by its factors until all the numbers left are prime (a number that is only divisible by one and itself). For myself, I am a visual learner, so looking at this diagram and working through the steps has really helped me. With any given number, I start with the first "branch" or factor being divisible by 2. I then work my way down from their until I can not divide the numbers any longer. Here is a great example so you can see the diagram for yourself. Once you have examined the Factor Tree, cover up the answers and try it for yourself! 

Setting ourselves up for Success 

In order to compete successfully within our own economic system and internationally we have to set ourselves up for success, especially with mathematics. We need to start by believing everybody can be an excellent mathematician when given the right tools! The tools that we need in order to become successful in the United States are changes to the common core along with a fewer set of standards. The common core needs to be "fewer, higher, deeper”. This means we need to teach the common core with a smaller number of standards with focus on understanding and application. (Common Core Facts) Each state will be composed of different standards, but the number of standards needs to be less.This will give the teachers more time to teach and the students more time for understanding and exploration. With fewer standards our curriculum then needs to be more demanding with higher expectations as well. 

In order to be successful internationally we need to be using the same assessments that the rest of the world are using to excel in math. This type of assessment is called PISA, it is the worlds metric for evaluating learning outcomes at school. (cnn.com) This type of assessment helps set meaningful targets in terms of measurable goals achieved by the worlds educational leaders. We also need to start introducing and teaching material at an earlier age. In middle school the students should be learning algebra and geometry, today in the U.S., we are still learning arithmetic at the elementary age level. 

Today we rank 36th out of 65 countries in mathematics, I believe If we apply all of these different tools we can become one of the top five high performing countries in mathematics. 

http://www.npr.org/blogs/ed/2014/05/27/307755798/the-common-core-faq

http://edition.cnn.com/2013/12/03/opinion/education-rankings-commentary-schleicher/