Simplify Fractions Accurately Every Time!

#Mathematics

In my experiences teaching math to 4th, 5th, and 6th graders, few things in their math education pose greater stress or a lower level of self-confidence than simplifying fractions. Students tend to fall into one of three categories with this particular skill: 1) they have no idea what to do; 2) they can sometimes get lowest terms but it is stressful and their error rate is high; or 3) they can usually simplify a fraction accurately but they do not have a process that they feel confident works every time.

I had the great privilege of teaching every level of math learner imaginable; from those who speak very little English, to those who come to me fearing and hating math, to those who were born with mathematical gifts–and every type of learner in between.

4th, 5th and 6th grade are really “fraction-heavy” grade levels for math students. This is when they’re learning or perfecting all the prerequisite skills for fraction operations, learning to perform fraction operations, and learning how to convert between fractions, decimals, and percentages. Fractions, fractions, fractions!  Even the math teacher gets a bit burned out on the amount of time we have to spend on fractions. And don’t even get me started on standardized testing in which students must show mastery of fraction operations during these years. Is it any wonder all but the most gifted tend to strongly dislike their math education? They fear it. Math feels unnecessarily difficult and complicated to them. The first thing I taught kids when they got to my math classroom is “everyone can be successful in math”, because everyone truly can… I’m living proof.

I try to let easy things be easy and to think up ways to un-complicate things that look and feel complicated to kids (and to adults!). A frustrated child, a fearful child, an angry or crying child…is not a learning child. They need confidence so they can avoid these feelings and experiences. When we know we have a process for doing something that looks hard, and this process works every time, we have an easier time believing in ourselves. When we believe in ourselves we are not frustrated, not fearful, not angry, not crying. If I taught math to children but didn’t read their faces and body language and use what I saw to guide my instruction, I would be doing them a huge disservice. How they feel about it DOES matter. I’ve seen how students feel about fractions…

So I created a document that lays out the process I teach my 5th and 6th graders. I make them take the notes and use the process before I share it in Google Classroom, because writing it and being forced to refer back to it during practice is part of the process of truly knowing it. Eventually math notebooks are lost or trashed, and students move on to higher grade levels, so I do eventually give them access to this document. After a few summer breaks and some years go by, they can refresh their recollection and reaffirm their confidence in their ability to get lowest terms accurately and quickly with confidence that they got the right answer. Because they NEED confidence.

It is important to know that the more they use these steps carefully and in order, the less they’ll need to use them or to have a document for reference. Their mastery of these skills will deepen with practice and expand their understanding of the mathematical concepts. The behaviors will become automatic, and the memorized process will almost certainly deepen into conceptual mastery they can build upon as they grow in their math education. I posted it in Google Classroom for fifth and sixth grade math students. I wanted to put it out here for parents and for anyone else who needs it.

How to Get Lowest Terms Accurately and Quickly, or Prove You Already Have It

Know your prime numbers! Here is a link to chart that shows which numbers are prime. https://www.helpingwithmath.com/printables/tables_charts/4oa4-prime-numbers01.htm

Forgot how to factor? Watch this video: https://www.youtube.com/watch?v\

  1. Is the denominator prime? If yes, you have lowest terms. You cannot simplify this fraction any further. If no, go on to number 2.
  2. Is the numerator 1? If yes, you have lowest terms. If no, go on to number three.
  3. Is the numerator a factor of the denominator? If yes (meaning numerator divides evenly into denominator), divide denominator by numerator. Example: the fraction 5/25. The numerator is 5 which is a factor of the denominator. Divide both the numerator and the denominator by 5 and you have lowest terms (⅕) as proven by numbers 1 and 2 above. In this case the numerator is a prime number. This works even if the numerator is not prime. Take the example of the fraction 4/16. Four is not prime, but it is a factor of 16. Divide the numerator and the denominator by 4 and you get 1/4. You can prove this is lowest terms by refering to the rule in number two above; the numerator is now 1 so you have lowest terms-guaranteed.

If you’ve tried everything in 1 thru 3 above and don’t have lowest terms, start factoring. You will have to do this if the numerator is not Prime and you don’t know if it is a factor of the denominator.

Find the Greatest Common Factor (GCF) of both numerator and denominator. Divide numerator and denominator by that factor and you will have lowest terms. Use your rules of divisibility to speed up the process.

Keep in mind that knowing and using prime factorization makes finding lowest terms so much easier. Here is a great video on how to find all the prime factors of any number. https://www.youtube.com/watch?v=XGbOiYhHY2c&t=211s

Here are the rules of divisibility. Knowing these will help you a great deal throughout your entire math education.  

Use your tools! Be an efficient math student!

When teaching rules of divisibility I find that many students struggle with the rule for 7.  I teach them to lean on their math facts (do their 7’s in their head). The rule for 7 is confusing to students who already struggle with math so I don’t teach it, but I give it to them in the handout and instruct them to use it if they’re comfortable with it.

Happy mathing!

LW

This is a post I wrote a long time ago to help my own students. I wanted to move it out of my old defunct classroom blog and keep it out here for students and parents who are struggling with this aspect of math.

Sharing from “Life Lessons”

I did not write this! Full credit below.

This is such an important topic, and something I think absolutely everyone experiences but may not realize what’s being done.

Educate yourself on these tactics and make choices about if/how you respond. These are, perhaps, the single largest and most sinister tactics of media/social media in today’s world. The use of these tactics is changing our society in ways that are catastrophic to our societal structure. They are destroying the way we relate to each other as human beings. They are so sinister that we will have a world we can no longer recognize or fix before we ever know something terrible happened. This is being done to millions of people by a Constitutionally-protected free press and on every social media platform in existence.

Here is a link to the full post. It is worth the 5 minutes it might take you to read it. I hope you will. https://lifelessons.co/critical-thinking/kafkatrapping/

written by Michael Frank, a New Zealand blogger, and really intelligent writer.

7 linguistic tricks people use to deceive and manipulate you

Kafkatrap, kafkatrapping

In this article I’ll expose seven linguistic tricks people use to deceive you:

Let’s begin:

Kafka trap

The Kafka trap might also be called the SJW trap.

Author Eric Raymond coined the term Kafkatrapping in his 2010 article in which he presented a style of argument that is common today with SJW’s, but has it’s origins in The Trial a book written in 1915 by Franz Kafka.

In The Trial the protagonist is arrested and accused of serious crimes which are never specified. He receives no explanation or description of the charges, and his refusal to acknowledge that he must be guilty is what makes him guilty.  The only way to stop his abuse is to admit that he is guilty.

Keep reading here: https://lifelessons.co/critical-thinking/kafkatrapping/