![]() Unit 4, Functions, introduces students to the concept of a function, which relates inputs and outputs. Students also make informal arguments, which prepares them for more formal proofs in high school geometry. Studying similarity, students observe how ratios between similar triangles stay the same, which sets them up for understanding slope in Unit 5. They experiment with, manipulate, and verify hypotheses around how shapes move under different transformations. In Unit 3, Transformations and Angle Relationships, students formalize their understanding of congruence and similarity as defined by specific movements of figures in the coordinate plane. Including this unit at this point in the year allows time for spiraling and incorporating these skills into future units. Students solved equations in sixth and seventh grades, and in eighth grade, students become more efficient and more strategic in how they approach and solve equations in one variable. In Unit 2, Solving One-Variable Equations, students continue to hone their skill of solving equations. They reach back to skills learned in sixth grade to simplify complex exponential expressions and to represent and operate with very large and very small numbers. In Unit 1, Exponents and Scientific Notation, students start off the year with a study of patterns and structure, using this structure to formalize properties of exponents. Lastly, students study figures, lines, and angles in two-dimensional and three-dimensional space, investigating how these figures move and how they are measured. Functions emerges as a new domain of study, laying a foundation for more in-depth study of functions in high school. They learn that linear equations can be a useful representation to model bivariate data and to make predictions. Students extend their understanding of proportional relationships to include all linear equations, and they consider what a “solution” looks like when it applies to a single linear equation as well as a system of linear equations. ![]() In eighth grade, students make several advances in their algebraic reasoning, particularly as it relates to linear equations.
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