Understanding Fractions
Understand fractions as quantities, not symbols — pizza slices, chocolate bars and number lines first, then the notation that shorthand them. The right entry point for grades 2-4.
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Fractions
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Fractions are the moment in the K-8 curriculum where a lot of confident learners suddenly say “I’m not good at math anymore.” It almost never has anything to do with the learner — fractions get taught as new symbols and new rules without first being grounded in the part-of-a-whole picture they’re abstracting from. Show the picture first and the rules look like the obvious shorthand they are.
These lessons cover the fractions topics in the order an elementary curriculum touches them. We start with understanding fractions (a fraction is a thing, not a process — three-quarters of a pizza is a definite quantity you can hold). We move into comparing fractions (with like denominators, then like numerators, then unlike both — the three cases that cover every textbook problem). We cover equivalent fractions and the rule for finding them. We treat fractions equivalent to whole numbers as their own lesson because that’s the bridge between fractions and the integers students already know. And we cover ordering fractions as a multi-fraction extension of comparison.
Every lesson uses visual models — pizza slices, chocolate bars, number lines — before any symbolic manipulation, and works through every example in full so the why of each step is on the page.
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FractionsCompare fractions
A very important skill in math is comparing fractions, because this skill helps you to understand how much of something there is and how to apply that…
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FractionsComparing Fractions with Like Denominators
Compare fractions with the same denominator using clear visual models — when bottom numbers match, the bigger numerator is greater. Worked examples for grades 3-4.
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FractionsComparing Fractions with Like Numerators
Fractures are compared differently when they share the same numerator versus when they share a common denominator. The common denominator becomes the basis…
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FractionsEquivalent Fractions
Equivalent fractions encompass different types of fractions that represent equal values, or portions, as a whole. Although they have different forms, both…
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FractionsFractions Equivalent to Whole Numbers
Any fraction with a whole number as its numerator represents a whole number quantity, as there is no remainder left in addition to this fraction’s decimal.…
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FractionsOrder fractions
To order fractions: we start by determining which fraction is smaller and which is larger. We follow this process to determine the sequence we want.
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FractionsFractions
Fractions are numbers that represent parts of a whole. They help us describe situations where something is divided into equal pieces. Fractions are…
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