Understanding Fractions
Lessons in this chapter
About Understanding Fractions
Understanding Fractions takes the number-line idea from 3rd grade and makes it procedural: kids now generate equivalents rather than just recognize them.
Represent Fractions Greater Than 1 is a genuine conceptual step. Seven quarters is more than one whole, which contradicts the way fractions were introduced as parts of a single thing, and the number line is what rescues it: seven quarters simply sits past 1.
Generate Equivalent Fractions turns recognition into a method. Multiplying or dividing the numerator and denominator by the same number gives a different-looking fraction of the same size, and that method is what makes comparing and adding possible.
Compare and Order Fractions then applies it. Two fractions with different denominators cannot be compared until they are rewritten with a common one, which is where the least common multiple from the previous chapter does its work. For a child who skipped that, this is where it shows.
Represent Fractions Greater Than 1, Generate Equivalent Fractions and Compare and Order Fractions each open as a worksheet inside the page, so the fractions for fourth graders here get worked rather than read. The equivalent fraction worksheet is marked question by question as you go. All three lessons are free to try, with no login needed for your first 3.
Frequently asked questions
Represent Fractions Greater Than 1 is the conceptual step, since seven quarters is more than one whole and the number line is what rescues it. Generate Equivalent Fractions then turns recognition into a method, and Compare and Order Fractions applies it, because two fractions with different denominators cannot be compared until they are rewritten with a common one. The chapter sits in the Common Core domain Number and Operations with Fractions (4.NF).
One where the numerator is larger than the denominator, like seven quarters. It is more than one whole, and it sits past 1 on the number line.
Multiply or divide the numerator and denominator by the same number. Two thirds becomes four sixths by doubling both, and it is the same amount.
Rewrite them with a common denominator first, usually the least common multiple of the two, then compare the numerators.
Because fractions were introduced as parts of one whole, so more than a whole seems contradictory. The number line resolves it: the fraction just sits past 1.
Directly. The least common multiple gives the common denominator for comparing, and the greatest common factor simplifies the result.