### What To Expect This Year

Transformations and Congruence - Students will learn about different types of transformations (reflections, rotations, translations). They will use transparent paper to explore the connection between each transformation. Students will also learn what makes two figures congruent. This exploration will lead students to study new angle relationships (vertical, alternate interior, alternate exterior) within parallel lines when they are intersected by another line.

Dilations, Similarity, and Introducing Slope - Students will learn how to dilate (shrink or enlarge) a figure. This concept connects with the previous unit as dilations, and the 7th grade concept of scale factor, are added to sequence of transformations. This unit also helps students differentiate between when two figures are similar or congruent.  Thinking about similarity in movement students are introduced to constant change, or slope, of a line.

Linear Relationships - Students review proportional relationships from 7th grade. Then students are introduced to linear relationships. Students will understand that linear relationships have an initial value (y intercept) and a constant change (slope) effecting inputs. Students will learn to analyze graphs, tables, and equations for linear properties. Students will also be able to differentiate between proportional and linear.

Linear Equations and Systems - Students have solved two step equations in 7th grade. Most 8th grade two step equations include the distributive property or combining like terms before solving for the missing variable. They will build on 7th grade knowledge by solving for when two equations are set equal to each other. Systems of equations are created when we ask ourselves the question "When are these lines intersecting?" or "When do these two equations use the same input and get the same output?"

Functions and Volume - Students how to tell if a table, graph, or equation is a function or not. A function is when one unique input creates one output. Input referring to x and output referring to y. Students will be explained this with the analogy of a vending machine. Students will also look at graphs and determine a story that could explain the graph they see. Students will also investigate the formulas for volume of a cylinder, cone and sphere.

Associations in Data -  Students will learn how to analyze scatter plots. They will learn the difference between positive and negative correlation, whether a plot looks linear or non linear, or whether a plot has a cluster or outlier. Students will learn how to judge lines of best fit that are superimposed on the graphs.  Students will also work through percent questions based on frequency table.

Exponents and Scientific Notation - Students will learn all operations (addition, subtraction, multiply, division) necessary to simplify exponents with numerical bases. They will also learn the rules of writing a number in scientific notation.

Pythagorean Theorem and Irrational Numbers - Students will prove the Pythagorean Theorem through investigation. After acquiring the theorem students will show mastery by using the theorem to answer real world questions. Students will then work to understand the difference between the two number groups: rational and irrational. Irrational numbers require approximation skills using division and knowledge of perfect square roots. Students must show the ability to approximate these complex numbers.

Course 1

Module A - Equations and Introduction to Functions: This module is broken down into three outcomes. Outcome 1 is all about creating, solving, and justifying solutions to linear equations and inequalities. Outcome 2 is about applying the concept of a function. Outcome 3 is about identifying key terms of a function. Students will also learn many strategies of solving for information when given a graph, table or equation of a linear function.

Module B - Linear Functions: This module contains two outcomes. Outcome 1 is about creating and analyzing linear functions. Outcome 2 is about solving and creating linear inequalities.

Module C - Statistics: This module is separated into two outcomes. Outcome 1 is about comparing two sets of data by using graphs and summary statistics (mean, median, standard deviation, etc.). After students become familiar with different statistics graphs, they work to match linear models to each situation in Outcome 2.

Module D- Exponential Functions: This module has three outcomes. Outcome 1 has students rewriting expressions using exponents. Outcome 2 introduces students to the exponential function. Outcome 3 has students solving exponential equations and inequalities.

Module E - Sequences: This module has students build functions to model arithmetic and geometric sequences.

Module F - Geometry: Within two outcomes students learn to use coordinates to solve geometric problems involving line segments. Students will become familiar with the distance formula and the Pythagorean theorem. In the second outcome students work to understand the relationship between the slope of parallel lines or perpendicular lines.

Module G - Quadratics: In outcome 1, students learn to build and interpret quadratic models. After they learn key features, they work on analyzing quadratics functions. Once they understand the function itself, they work to solve for the roots of the function.

Module H- Systems of Linear Functions: In the first outcome students create and solve linear systems of equations when given context. After working on creating systems and understanding of the relationship between the functions, students are taught to solve linear systems and systems of inequalities.