Mathematical Reasoning Day 2: Reasoning with Rational Numbers using the Quotient Interpretation

Overview

Teachers will also learn how to use Multiple Groups Problems to help students understand key ideas involving fractions. Students solve these problems using strategies that include direct modeling, repeated addition, grouping and combining, and multiplicative. They will learn how to write and pose Multiple Groups problems, assess student strategies, and then based on this knowledge plan for further instruction. Teachers will learn how to help their students develop more sophistication in their problem solving strategies and help them move from additive reasoning to reasoning that is considered more multiplicative. Teachers will learn how these problems can be used to help students use relational thinking to highlight algebraic ideas related to fractions.

•  Will learn how to use equal sharing problems to assess student understanding of rational numbers and learn how to sequence examples to help them make sense of this difficult interpretation.
• Will learn how to use Multiple Groups Problems to help students understand key ideas involving fractions. These problems can be solved using strategies that include direct modeling, repeated addition, grouping and combining, and multiplicative. Teachers will learn how to write and pose Multiple Groups Problems, assess student strategies and use this knowledge to plan for further instruction.
• Will learn how to help students develop more sophistication in their problem solving strategies and help them move from additive to more multiplicative reasoning.
• Will learn how these problems can be used to help students use relationsional thinking to highlight algebraic ideas related to fractions.

Standards Specifically Addressed

Minnesota Academic Standards:
Grade 3 - Understand meanings and uses of fractions in real-world and mathematical situations.
Grade 4 - Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent quantities.
Grade 5 - Read, write, represent and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-world and mathematical situations.
Grade 5 - Add and subtract fractions, mixed numbers and decimals to solve real-world and mathematical problems.
Grade 6 - Read, write, represent and compare positive rational numbers expressed as fractions, decimals, percents and ratios; write positive integers as products of factors; use these representations in real-world and mathematical situations.

NCTM Process Standards:

• Problem Solving
• Reasoning and Proof
• Representation
• Communication