Mathematical Reasoning Day 3: Multiplication and Division with Rational Numbers

Overview

The use of Multiple Groups Problems in Day 2 will help teachers understand ways to introduce ideas related to multiplication and measurement division involving fractions. Day 3 will build on this knowledge to help teachers understand how to sequence instruction of fraction multiplication and division of fractions using both number types and models. This approach emphasizes the development of fractions as operators.

• Will learn how to use the number line to help students understand this problem as  and furthermore understand the operator interpretation when they divide the 12 by four and multiply this result by three. This moves student thinking of multiplication from an iterating process to more of a partioning and iterating process. The use of models and the operator interpretation helps students make sense of situations involving the multiplcation of two fractions. Teachers will be able to help their students develop reasoning that justifies the algorithm for multiplying two fractions.
  
• Will learn to use problems involving measurement division to provide instruction related to division of fractions and the development of the common denominator algorithm. The measurement interpretation will be emphaiszed in the models as they make sense of division and the algorithm.

Standards Specifically Addressed

Minnesota Academic Standards:

Grade 6 - Multiply and divide decimals, fractions and mixed numbers; solve real-world and mathematical problems using arithmetic with positive rational numbers.
Grsade 7 - Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.

NCTM Process Standards:

• Problem Solving
• Connections
• Reasoning and Proof