Fractions
With Base Ten Blocks.

Just saving my work so it doesn't get lost. If you found your way here check back in a week or two...there will be pics and vids and links and stuff meantime click that other page that says FRACTIONS which is not much better but soon this page will replace that one...

Using base ten blocks to teach fractions makes life easier for everybody. The fact that fractions are so misunderstood has become a joke. What you will find on this page besides the basics and links to videos and blog posts are some of the reasons WHY so many fail at not only understanding fractions but why so many teachers fail to teach them well.

I have found that next to long division, fractions are one of the most reviled topics in mathematics until we get to algebra.  I myself went to summer school because of fractions but after just one day with a good teacher I understood basic operations with fraction and I distinctly remember telling my mother I had it wired and didn't really need to go back but I wanted to because of all the other cool stuff that was going on there...she tested me and I got every question right. What was made clear is that the rules didn't change when we got to fractions...once a few misconceptions were cleared up the rest was easy. I never really did learn WHY you invert and multiply until I met Jerry Mortensen...and even then he didn't explain it to me he made me explain it to myself.

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray.https://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html

"One of Ma's four questions was to divide 1 3/4 by 1/2 and to make up a story for this problem. Only 9 of the 23 American teachers gave the correct answer in an appropriate form (3 3/4 or 7/2 or 3.5). Several gave incomplete answers like 14/4 or 28/8, whereas six gave no answer. All 72 Chinese teachers gave the correct answer in an appropriate form. Many of the American teachers who answered correctly were merely recalling a procedure (invert the denominator and multiply) that they could not explain. The Chinese teachers not only knew how to divide fractions; most of them could also suggest alternate methods that would have enabled them to connect division of fractions to a student's prior knowledge, or to alert a good student to approaches that might be simpler under some circumstances."

https://www.americanscientist.org/bookshelf/pub/chinese-wisdom

https://crewtonramoneshouseofmath.blogspot.com/search/label/fractions

https://crewtonramoneshouseofmath.blogspot.com/search/label/Fractions%20Tile

https://crewtonramoneshouseofmath.blogspot.com/search/label/Fractions%20Problem%20Solving

Kirk's fraction PDF

Fraction - a rational number of the form a/b where a is called the numerator and b is called the denominator. WOW! I'm having a heck of a time getting this page built, go to my blog and search "fractions" meantime...this page isn't going to look anything like this when I'm done...this week jan 15 2011 this page will transform...hmmm never transformed...lol now it's Dec 2011..this is now top of the list... I have made quite a few blog posts on the topic. (More than 30.) So for now there will be a lot of links to my blog as I build this page out. Go to my blog find the search box and type "fractions"... You can start with very young students because fractions are math and math is just counting. Keep in mind the five basic concepts, and start simply...even with older students. Lets say you run into a student who lacks multiplication skills and fractions skills. Teach both at the same time using this method. You can start the journey here: https://crewtonramoneshouseofmath.blogspot.com/2010/12/fractions-intro.html Soon there will be lots of pictures vids and all the things you find elsewhere here at the house of math. https://crewtonramoneshouseofmath.blogspot.com/2011/01/equivalent-fractions-with-wee-ones.html This vid needs re-doing I don't know what my processor was doing but you can hear it working overtime and it messed up the audio and video although I kind of like the video effect... Go here for a simple fraction worksheet.
Math Terms/Definitions: Fractions
These all need drawings/pictures or examples or video. Cancellation - simplifying the multiplication of fractions, the process of abridging operations in division by rejecting equal factors. If a numerator is equal to or a multiple of a denominator one of the numbers may be divided into the other. If the numerator and the denominator have the same number, these two numbers cancel out. If, after these, the numerator is larger than the denominator, there is a remainder when they are divided. Complex Fraction - a fraction whose numerator, or denominator, or both, are fractional. Denominator - the number below the fraction bar that indicates how many parts into which the whole is divided. Farey Sequence - the sequence obtained by arranging in numerical order all the proper fractions having denominators not greater than a given integer. Fractional Numbers - express parts of a number. Fractional Parts - portions of an object or quantity which has been divided into smaller pieces. Improper Fraction - a simple fraction whose value is equal to or greater than one, the numerator is greater than the denominator. Least Common Denominator - the smallest number that can be used as the common denominator for a group of fractions. Lowest Common Denominator - the smallest number that is exactly divisible by each denominator of a set of fractions. Lowest Terms - a fraction in which the numerator and denominator have no common factor. Numerator - the number above the fraction bar that indicates the number of parts of the whole that are in a rational number, the number in the top half of the fraction. Proper Fraction - a simple fraction whose value is less than one, the numerator is smaller than the denominator. Ratio - a rational number of the form a/b where a is called the numerator and b is called the denominator, a comparison of numbers, the quotient or result of one quantity divided by another (fraction). Rational Number - a number that can be written as a fraction with integers as the numerator and denominator. Rationalize the Denominator - a process that gets rid of the radical in the denominator. Simple Fraction - one which has a single integral numerator and denominator. Solidus - the slanted line in a fraction such as a/b dividing the numerator from the denominator. Unit Fraction - a fraction whose numerator is 1. Vinculum - the horizontal bar in a fraction separating the numerator from the denominator. Playing with improper fractions: