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11 OnTRACK Grade 8 Math: Proportionality

Students learn to to use proportional relationships to describe dilation; explain proportional and non-proportional relationships involving slope; and use proportional and non-proportional relationships to develop foundational concepts of functions.

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Transformations of Absolute Value Functions

Given an absolute value function, the student will analyze the effect on the graph when f(x) is replaced by af(x), f(bx), f(x – c), and f(x) + d for specific positive and negative real values.

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Using Logical Reasoning to Prove Conjectures about Circles

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

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Generalizing Geometric Properties of Ratios in Similar Figures

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.

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Determining Area: Sectors of Circles

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.

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Making Conjectures About Circles and Segments

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.

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Determining Area: Regular Polygons and Circles

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

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Making Conjectures About Circles and Angles

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.

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Domain and Range: Numerical Representations

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.

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Solving Problems With Similar Figures

Given problem situations involving similar figures, the student will use ratios to solve the problems.

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Transformations of Square Root and Rational Functions

Given a square root function or a rational function, the student will determine the effect on the graph when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values.

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Transformations of Exponential and Logarithmic Functions

Given an exponential or logarithmic function, the student will describe the effects of parameter changes.

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Solving Square Root Equations Using Tables and Graphs

Given a square root equation, the student will solve the equation using tables or graphs - connecting the two methods of solution.

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Functions and their Inverses

Given a functional relationship in a variety of representations (table, graph, mapping diagram, equation, or verbal form), the student will determine the inverse of the function.

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Rational Functions: Predicting the Effects of Parameter Changes

Given parameter changes for rational functions, students will be able to predict the resulting changes on important attributes of the function, including domain and range and asymptotic behavior.

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Applying Pythagorean Triples to Solve Problems

Given verbal and pictorial representations of problem situations, the student will apply patterns from right triangles whose sides are Pythagorean Triples to solve the problems.

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Introduction to Coordinate Geometry

The students will use multiple representations of undefined terms on a coordinate plane to solve problems.

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Coordinate Geometry: Parallel and Perpendicular Lines

Given characteristics of two lines, such as slopes and equations, the student will determine whether the lines are parallel, perpendicular, or neither.

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Coordinate Geometry: Special Segments

The student will derive and use the slope and midpoint formulas to verify geometric relationship that include parallelism and perpendicularity of lines. Then, the student will determine an equation of a line parallel or perpendicular to a given line.

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Coordinate Geometry: Length and Distance

Given coordinates of points, the student will use the distance formula to solve problems involving length and distance.