Everyday situations involve the use of real numbers. Mathematical proficiency with real numbers is dependent upon studentsâ ability to recognize relationships among properties and operations of the various number systems. This unit provides opportunities to build upon what students have learned previously, to recognize connections between various number systems, and to apply this knowledge to new situations. The concepts learned in this unit are applied throughout the year and prepare students to explore increasingly complex problems.
Mathematical properties introduced in previous courses are used to simplify and speed mental computation. Multiple strategies for applying the associative, commutative, and distributive properties to numeric and algebraic expressions are explored and compared. Students also use their understanding of these properties to investigate characteristics of a group. Group properties are revisited and applied to other operational systems in Unit 6.
In previous courses, students solve authentic problems with whole numbers and progress to problems with rational numbers, (e.g., decimals, fractions, and integers). In this unit, students extend their knowledge to applications of irrational and real numbers. As new number systems are explored, students compare and make connections to the properties of, operations with, and relationships among familiar number systems.
Prior to this course, studentsâ knowledge of exponents and proportionality has been limited to solving problems with rational numbers. This unit broadens studentsâ understanding of the relationships between roots and powers. Rules of exponents and powers of ten are further developed and applied to solve problems. Students understanding of proportional reasoning is extended and applied to authentic problems, including rate of change, discount, commission, sales tax, and interest.
A thorough study and understanding of the number relationships, properties, and operations in this unit prepares students to explore and analyze a wide variety of authentic problems.
Instructional flow (PDF)
Unit 2 Standards for Investigations into Mathematics (IM)(PDF)
Explanation of what your child should understand by the end of each unit (enduring understandings), how he/she will get to that understanding (essential questions), and how he/she will be evaluated (indicators).
Content map for IM Unit 2 (PDF)
Associative, Commutative and Distributive Properties
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