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Fractions: Multiplying, Dividing, Simplifying

Grade Level Grades 3-8
Standards Alignment
Common Core State Standards
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Fractions, or parts of a whole, have often been difficult for students to understand. This is often the result of rhymes such as "Mine is not to reason why, just invert and multiply". But when we teach fractions this way, math become a set of mysterious rules and procedures that need to be memorized. But if we can show students why operations on fractions work the way they do, we take out the mystery of math. Then math begins to make sense.

CCSS: 4.NF.1; 4NF.2; 4.NF.3; 4.NF.4; 5.NF.1; 5.NF.2; 5.NF.3; 5.NF.4; 5.NF.6; 5.NF.7

Standards

Explain why a fraction ?/? is equivalent to a fraction (? × ?)/(? × ?) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Understand a fraction ?/? with ? > 1 as a sum of fractions 1/?.
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
Interpret a fraction as division of the numerator by the denominator (?/? = ? ÷ ?). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

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3.0
1 Review
Step by step visual directions
scappelli
July 30, 2013