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7-N-2-2

Page history last edited by Tashe Harris 6 years, 2 months ago

7.N.2.2 Illustrate multiplication and division of integers using a variety of representations

In a Nutshell

Integers introduce new rules for multiplication and division of numbers. Multiplying and dividing numbers with the same sign produces a positive solution. Multiplying and dividing numbers with different signs produces a negative solution. A variety of approaches such as colored counters, number lines, and tables allow application of multiplication and division of integers in real-world situations.

Student Actions	Teacher Actions
Develop accurate and appropriate fluency for multiplication and division of integers by applying the correct algorithm for that operation of signed numbers. Develop mathematical reasoning of multiplication of division of integers using a variety of models such as number lines and counters. Develop the ability to communicate mathematically the rules of signed numbers. Develop the ability make conjectures, model or generalize strategies and reasoning for solving multiplication and division problems with 3 or more signed numbers. Students will analyze and extend patterns to make sense of the problem.	Implement tasks that promote reasoning and problem solving of integers represented in a variety of ways such as using number lines, counters and patterns of positive and negative numbers. Use and connect a variety of mathematical representations of multiplication and division of integers to implicitly connect models to integer rules. Build procedural fluency from conceptual understanding of integers. Elicit and use evidence of student thinking of how integers can be used to represent real world situations.
Key Understandings	Misconceptions
Integers being multiplied or divided by an integer with the same sign will result in a positive solution. Integers being multiplied or divided by an integer with a different sign will result in a negative solution. When multiplying more than two integers, if the number of negative factors is even the product will be positive. When multiplying more than two integers, if the number of negative factors is odd the product will be negative.	Students may use the sign of the larger number for the product or quotient when multiplying or dividing integers with different signs. Students may use the sign of the number with the larger absolute value for the product or quotient when multiplying or dividing integers with different signs. Students may think the product or quotient will be negative when multiplying or dividing two negative numbers. Students may not understand absolute value is the distance from zero.