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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.

Kid2Kid videos on determining the meaning of slope and intercepts in English and Spanish

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.

Given verbal and symbolic descriptions of problems involving exponents, the student will simplify the expressions using the laws of exponents.

Given problem situations involving exponents, the student will use the laws of exponents to solve the problems.

Given verbal descriptions of situations involving systems of linear equations the student will analyze the situations and formulate systems of equations in two unknowns to solve problems.

Given a quadratic equation, the student will use graphical methods to solve the equation.

Given algebraic, tabular, and graphical representations of linear functions, the student will determine the intercepts of the function and interpret the meaning of intercepts within the context of the situation.

Given verbal, symbolic, numerical, or graphical representations of problem situations, the student will interpret and predict the effects of changing the y-intercept in the context of the situations.

The student will represent linear inequalities using equations, tables, and graphs. The student will solve linear inequalities using graphs or properties of equality, and determine whether or not a given point is a solution to a linear inequality.