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3.23 MB | 22 pages of student work pages
This is a 22-page exploration of the inverse relationship between multiplication and division as it relates to both multiplication and division with fractions (it’s impossible to discuss division of fractions without also discussing multiplication).
Beginning with unit fractions to clarify the concepts, students see the connection between division by a whole number and multiplication by a fraction, and make sense out of the “Invert the divisor and multiply” procedure. They also see how they have already been employing the procedure when multiplying whole numbers by fractions.
They also correlate verbal expressions of division with the mathematical notation:
For instance, the expression "4 divided by one-third" is asking, “How many thirds fit into 4?” This relationship is easily illustrated with Fraction Towers, but examples of how to model division equations with paper folding are also provided in the notes. Students gain familiarity with the terms Invert, inverse, and reciprocal by writing “inverse” and “reciprocal” expressions and numbers.
Students practice dividing whole numbers by proper fractions, fractions by whole numbers, and fractions by fractions, including problems in which the quotient is a mixed number.
Six pages of word problems are included which can be used to introduce different sections of these pages. There are word problems requiring division of whole numbers with fractional divisors, fractions with whole number divisors, and fractions with fractional divisors, with quotients both more and less than one.
Common Core Standards:
6.NS.1: “Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions...”
5.NF.7: “Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions...”
5.NF.7.a. “Interpret division of unit fraction by a non-zero whole number, and compute such quotients...”
5.NF.7.b. “Interpret division of a whole number by a unit fraction, and compute such quotients...”
5.NF.7.c. “Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions...”
Subject: Math, Fractions, Word Problems
Level: Grades 5 – 6
Length/Duration: 22 pages of student work, 3-5 days