15. Understand the relationships between two rational numbers (C)
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Lesson objective: Understand that relationships between two rational numbers result in three possibilities for a and b: a < b, a > b, or a = b.
Students bring prior knowledge of integer relationships and opposite numbers from 6.NS.C.5 and 6.NS.C.6.A. This prior knowledge is extended to include all rational numbers as students use number lines to determine either the equality or type of inequality of two rational numbers. A conceptual challenge students may encounter is knowing which inequality symbol to use to describe the relationship as well as understanding how to compare the absolute value to actual value of rational numbers (i.e. 9____ 8).
The concept is developed through work with a number line, which shows students a visual model of the value of rational numbers that relate together.
This work helps students deepen their understanding of equivalence. Using the equal sign and symbols of inequality to symbolize equivalent and nonequivalent values allows students to be flexible with different forms of numbers and to represent relationships among quantities, which are both crucial aspects of algebraic thinking.
Students engage in Mathematical Practice 4 (model with mathematics) as they use number lines and symbols of inequality to understand, explain, and justify relationships between rational numbers.
Key vocabulary:
 equivalence
 greater than
 inequality
 integer
 less than
 rational