## Course Overview

## FIRST SEMESTER
Unit 1: Transformations, Congruence, & SimilarityThis unit will have students explore and describe the effects of translations, rotations, reflections and dilations of two-dimensional figures using coordinates. Students will understand congruence or similarity of two-dimensional figures if the second can be obtained from the first by a sequence of geometric transformations. Using informal arguments about side and/or angle relationships, students will show that two triangles are congruent or similar. Students’ work with congruence and similarity will allow them to make connections among proportional relationships, lines and linear equations in the upcoming units. Unit 2: ExponentsThis unit will begin with familiar number sense topics to help students transition into the Grade 8 content. Turning decimal expansions into fractions and deepening understanding of the meaning of decimal expansions to set a firm foundation for understanding irrational numbers. Students will learn that the square roots of perfect squares are rational numbers, and that the square roots of non-perfect squares, such as √2 or √7, are examples of irrational numbers. Students will understand the value of square roots and cube roots and use this understanding to solve equations involving perfect squares and cubes. Further work with exponents, including scientific notation, naturally flow from the understanding of squares and cubes. Through the course of this study, students build on their knowledge of solving equations to realize that there may be a single solution, infinite solutions, or no solutions. Generalizations of form for each situation are arrived at by noticing patterns in successive simplification of equations. The focus should be on the reasoning behind a solution or solution method as well as the actual procedure for solving. Unit 3: Geometric Applications of Exponents This unit will have students apply their prior knowledge of triangles to the specific qualities of right triangles and find the missing side lengths of right triangles in various real-world 2-D and 3-D situations. They will also apply the concepts of squares and square roots. In grade 7, students begin to reason about relationships among two-dimensional figures using scale and informal geometric constructions, and gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. Through application in real-world contexts, students solve real-world and mathematical problems involving area, surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. Students also learn the volume formulas for cylinders, cones and spheres. They then apply these formulas to not only find the volume of objects, but also missing dimensions such as the radius or height. Unit 4A: InferencesThis unit will have students build upon their understanding of statistics by examining how selected data can be used to draw conclusions, make predictions, and compare populations. |
## SECOND SEMESTER
Unit 4B: ProbabilityThis unit will have students develop a general understanding of the likelihood of events occurring by realizing that probabilities fall between 0 and 1. They gather data from simulations to estimate theoretical probability using the experimental probability. Students will make predictions about the relative frequency of an event by using simulations to collect, record, organize and analyze data. They will develop probability models to be used to find the probability of simple and compound events. Students will determine from each sample space the probability or fraction of each possible outcome.Unit 5: Functions This unit will have students understand that functions describe relationships and will be able to compare and construct a function. The equation y= mx + b will be interpreted as a straight line, where m and b are constants. Students will establish a routine of exploring functional relationships algebraically, graphically, and numerically in tables and verbal descriptions.Unit 6: Linear Functions This unit will have students understand that the equation y = mx + b will be interpreted as a straight line, where m and b are constants. Students will establish a routine of exploring functional relationships algebraically, graphically, and numerically in tables and verbal descriptions. When using functions to model a linear relationship between quantities, students learn to determine the rate of change of the function which is the slope of a graph. Unit 7: Linear Models and TablesThis unit will have students understand that functions describe relationships and will be able to compare and construct a function. They will learn to recognize linearity in a table when constant differences between input values produce constant differences between output values, and they can use the constant rate of change and initial value appropriately in a verbal description of a context. Students apply experience with coordinate planes and linear functions in the study of association between two variables related to a question of interest. They will analyze bivariate measurements on a scatterplot describing shape, center, and spread. The shape is a description of the cloud of points on a plane, the center is the line of best fit, and the spread is how far data points are from the line.Unit 8: Solving Systems of Linear EquationsThis unit will have students graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the x-value that will generate the given y-value for both equations. Students recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y-intercepts) have no solutions, and lines that are the same (same slope, same y-intercept) will have infinitely many solutions. |