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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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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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Converting Between Measurement Systems

Given a real-world situation with measurements in either metric/SI or customary units, the student will solve a problem requiring them to convert from one system to the other.

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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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Finding the Probabilities of Dependent and Independent Events

Given problem situations, the student will find the probability of the dependent and independent events.

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Recognizing Misuses of Graphical or Numerical Information

Given a problem situation, the student will analyze data presented in graphical or tabular form by evaluating the predictions and conclusions based on the information given.

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Evaluating Methods of Sampling from a Set of Data

Given a problem situation, the student will evaluate a method of sampling to determine the validity of an inference made from the set of data.

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Approximating the Value of Irrational Numbers

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

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Expressing Numbers in Scientific Notation

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

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Comparing and Ordering Rational Numbers

Given a problem situation, the student will compare and order integers, percents, positive and negative fractions and decimals with or without a calculator.

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Determining if a Relationship is a Functional Relationship

The student is expected to gather and record data & use data sets to determine functional relationships between quantities.

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Graphing Dilations, Reflections, and Translations

Given a coordinate plane, the student will graph dilations, reflections, and translations, and use those graphs to solve problems.

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Graphing and Applying Coordinate Dilations

Given a coordinate plane or coordinate representations of a dilation, the student will graph dilations and use those graphs to solve problems.

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Developing the Concept of Slope

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