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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.

Given multiple representations of linear functions, the student will develop the concept of slope as a rate of change.

Given problems that include data, the student will generate different representations, such as a table, graph, equation, or verbal description.

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 pictorial or tabular representation of a pattern and the value of several of their terms, the student will write a formula for the nth term of a sequences.

Given problem situations that include pictorial representations of irrational numbers, the student will find the approximate value of the irrational numbers.

Given problem situations, the student will express numbers in scientific notation.

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

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

Given a net for a three-dimensional figure, the student will make conjectures and draw conclusions about the three-dimensional figure formed by the given net.

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.