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45-45-90 Triangles

To learn the pattern of the side lengths of a 45-45-90 triangle, students complete a gallery walk, a card sort activity starting with using the Pythagorean theorem, and activity to locate if there is an error in a presented problem and if so to identify what the error is.

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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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Creating Nets for Three-Dimensional Figures

Given nets for three-dimensional figures, the student will apply the formulas for the total and lateral surface area of three-dimensional figures to solve problems using appropriate units of measure.

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Drawing Conclusions about Three-Dimensional Figures from Nets

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.

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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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Solving Problems With Similar Figures

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

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Introduction to Logical Reasoning

This activity provides the opportunity to explore the validity of the converse, inverse, and contrapositive of statements. It also assists in recognizing the connections between biconditional statements and true conditional statements with a true converse.

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Introduction to Probability

This activity provides the opportunity to explore the difference between finding the probability of independent events and dependent events. It also addresses how to use a tree diagram when calculating conditional probabilities.

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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.

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Coordinate Geometry: Slope

Given coordinate points, the student will use slope formulas to solve problems.

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Describing and Drawing Cross Sections

Given a verbal and/or pictorial description of the intersection of a plane with various three-dimensional geometric figures, the student will describe and/or draw the intersection.

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Determining Area: Composite Figures

Given information about composite fiugres, the student will determine the area of composite 2-dimensional figures comprised of a combination of triangles and parallelograms using appropriate units of measure.