An Introduction to Fractions
Lessons in this chapter
About An Introduction to Fractions
An Introduction to Fractions is where fractions become numbers. Until now they described parts of shapes; here they get a place on the number line.
Understand Unit Fractions starts with one part out of several, which is the building block. Once a child sees a third as one of three equal parts, two thirds is two of those, and the whole notation follows from one idea.
Understand the Fractions of Whole and Find the Fraction of a Collection keep both pictures going, part of one thing and part of a group, since kids who only see one struggle with the other.
Plot Fractions on Number Line is the lesson that changes what a fraction is. Putting three quarters between 0 and 1 says it is a number with a size and a position, not just a description of a cut-up shape, and that is what makes fraction arithmetic possible later.
Compare Fractions and Recognize Equivalent Fractions Visually close the chapter. The hard idea is that a bigger denominator means smaller pieces, so a fifth is less than a third, which is the opposite of what whole-number experience suggests.
Understand Unit Fractions, Plot Fractions on Number Line and Compare Fractions each open as a worksheet in the page, scored as your child answers. The number line lesson is the one worth slowing down on, because comparing fractions gets much easier once a fraction has a position rather than a picture. Six lessons, all free.
Frequently asked questions
Unit fractions first, then fractions of a whole, then plotting fractions on a number line, finding a fraction of a collection, comparing fractions, and recognizing equivalent fractions visually. Generating equivalent fractions waits until 4th grade. It sits in Number and Operations: Fractions (3.NF), the domain that opens at this grade.
A fraction with 1 on top, like one third or one fifth: a single part out of however many equal parts the whole is split into. Every other fraction is built from it.
Because it makes a fraction a number with a position and a size, rather than a description of a shape. That shift is what lets kids add, compare and order fractions later.
Because splitting something into five parts gives smaller pieces than splitting it into three. A bigger denominator means more, smaller pieces, which is the reverse of whole-number intuition.
Different fractions naming the same amount, like one half and two quarters. 3rd grade recognizes them visually; generating them comes in 4th grade.
A fraction of a group of objects rather than of a single shape. A third of twelve counters is four.