5-N-1-3

Page history last edited by Christine Koerner 6 years, 2 months ago

5.N.1.3 Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal and consider the context in which a problem is situated to select and interpret the most useful form of the quotient for the solution.

In a Nutshell

Students will understand the equivalent relationship between remainders, fractions, mixed numbers, and decimals. They must know the best form to represent their remainders, depending on the real-world problem, and be able to justify why they used that form to represent their remaining part.

Student Actions	Teacher Actions
Develop the Ability to Communicate Mathematically by explaining the relationship between various quotients and their representations, leading them to discover the most efficient way to display solutions for a given situation. Develop a Productive Mathematical Disposition by determining that in certain situations a particular representation of the remainder needs to be used. Ex. Using decimal remainders for money and metric units, using fractional remainders with cooking and customary units. Develop Mathematical Reasoning by making generalizations to see if an answer makes sense within the context of a situation and justify your reasoning.	Establish mathematics goals to focus learning on the interpretation of the remainder and provide contexts that require a variety of representations of remainders. Implement tasks that promote reasoning and problem solving through having a variety of real world situations. Pose purposeful questions that have the students thinking about what the problem is asking and what the remainder means for the given context. Elicit and use evidence of student thinking by having them express what the remainder means, why they chose the format they used, and how they got their answer.
Key Understandings	Misconceptions
Understand and interpret the quotient. Write the quotient with a remainder as a whole number, a fraction, or decimal. Find equivalent numbers by adding a decimal and 0’s if needed after the whole number to complete the division problem. Select the most appropriate remainder for a given situation. Understand that there are certain contexts that you can not have a remainder. Understand that interpreting remainder includes how much is left over and how much you need to make another whole	Apply a procedure that results in remainders that are expressed as “R#” or “remainder #” for all situations, even those for which such a result does not make sense. Think that decimal quotients can also have remainders.