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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.
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.
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.
Interactive Math Glossary
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.
Determining Area: Regular Polygons and Circles
The student will apply the formula for the area of regular polygons to solve problems.
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.
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.
Solving Problems With Similar Figures
Given problem situations involving similar figures, the student will use ratios to solve the problems.
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.
Transformations of Exponential and Logarithmic Functions
Given an exponential or logarithmic function, the student will describe the effects of parameter changes.
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.
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.
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.
Determining the Perimeter of a Polygon (Series and Activity 1)
This activity provides an opportunity for students to investigate the perimeter of polygons.
Sunflower Biscuit Bones (PDF) | Martha Speaks
The PDF of the interactive, informational story "Sunflower Biscuit Bones" designed for in-classroom use.
Paint-a-long—Peg + Cat | PBS KIDS Lab
Use this game with children to combine shapes to draw Peg, Cat, and all their friends. Peg can help children every step of the way as they use their paintbrush and different colors to draw snazzy shapes or colorful characters.
6.08 Bonus Video: Law of Sines—The Ambiguous Case
The Law of Sines can be used to solve for sides and angles of oblique triangles. However, in some cases more than one triangle may satisfy the given conditions. We refer to this as an ambiguous case.
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.
Making and Verifying Conjectures about Three-Dimensional Figures
Students will explore volume conjectures and solve problems by applying the volume formulas to composite figures.