In this topic, students explore sequences represented as lists of numbers, in tables of values, by equations, and as graphs on the coordinate plane. Students move from an intuitive understanding of patterns to a more formal approach of representing sequences as functions. In the final lesson of the topic, students are introduced to the modeling process. Defined in four steps—Notice and Wonder, Organize and Mathematize, Predict and Analyze, and Test and Interpret—the modeling process gives students a structure for approaching real-world mathematical problems.

In this topic, students focus on the patterns that are evident in certain data sets and use linear functions to model those patterns. Using the informal knowledge of lines of best fit that was built in previous grades, students advance their statistical methods to make predictions about real-world phenomena. They differentiate between correlation and causation, recognizing that a correlation between two quantities does not necessarily mean that there is also a causal relationship. At the end of this topic, students will synthesize what they have learned to decide whether a linear model is appropriate.

Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

Students will investigate patterns to make conjectures about geometric relationships and apply the definition of similarity, in terms of a dilation, to identify similar figures and their proportional sides and congruent corresponding angles.

Students will use proportional reasoning to develop formulas to determine the area of sectors of circles. Students will then solve problems involving the area of sectors of circles.

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties and relationships among the resulting segments.

The student will apply the formula for the area of regular polygons to solve problems.

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties of and relationships among the resulting angles.

Given a function in the form of a table, mapping diagram, and/or set of ordered pairs, the student will identify the domain and range using set notation, interval notation, or a verbal description as appropriate.

Given scatterplots that represent problem situations, the student will determine if the data has strong vs weak correlation as well as positive, negative, or no correlation.

Given verbal descriptions and tables that represent problem situations, the student will make predictions for real-world problems.

Given an experimental situation, the student will write linear functions that provide a reasonable fit to data to estimate the solutions and make predictions.

Given a situation that can be modeled by a quadratic function or the graph of a quadratic function, the student will determine the domain and range of the function.

Given a situation that can be modeled by a quadratic function or the graph of a quadratic function, the student will determine restrictions as necessary on the domain and range of the function.

Given verbal, graphical, or symbolic descriptions of the graph of y = ax^2 + c, the student will investigate, describe, and predict the effects on the graph when a is changed.

Given a quadratic equation, the student will use tiles to factor and solve the equation.

Given a quadratic equation, the student will solve the equation by factoring, completing the square, or by using the quadratic formula.

Given a quadratic equation, the student will make connections among the solutions (roots) of the quadratic equation, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.