Student Actions

Teacher Actions

• Develop the ability to communicate mathematically by explaining the relationship between various remaindersand 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 which includes the use of mathematical language and terms.

• Implement tasks that promote reasoning and problem-solving through 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 a 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 in which 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. 

  Knowledge Connections

Prior Knowledge

Leads to 

• Use strategies and algorithms based on knowledge of place value, equality, and properties of operations to divide a 3-digit dividend by a 1-digit dividend by a 1-digit whole number divisor, with and without remainders. (4.N.2.5) 

• Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships. (6.N.4.2)

• Multiply and divide fractions and decimals using efficient and generalizable procedures. (6.N.4.3)

• Use mathematical modeling to solve and interpret problems including money, measurement, geometry, and data requiring arithmetic with decimals, fractions, and mixed numbers. (6.N.4.4)

The Oklahoma State Department of Education is releasing sample assessment items to illustrate how state assessments might be designed to measure specific learning standards/objectives. These examples are intended to provide teachers and students with a clearer understanding of how the state assesses Oklahoma's academic standards and their objectives. It is important to note that these sample items are not intended to be used for diagnostic or predictive purposes. Ways to incorporate the items.

• 5.N.2.3 Cluster Remainder