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Common Core: Math
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 Student Outcomes Students use the inscribed angle theorem to prove other theorems in its family (different angle and arc configurations and an arc intercepted by an angle at least one of whose rays...

 Student Outcomes Students use tangent segments and radii of circles to conjecture and prove geometric statements, especially those that rely on the congruency of tangent segments to a circle from a...

 Student Outcomes Students discover that a line is tangent to a circle at a given point if it is perpendicular to the radius drawn to that point. Students construct tangents to a circle through a...

 In Topic C, students explore geometric relations in diagrams of two secant lines, or a secant and tangent line (possibly even two tangent lines), meeting a point inside or outside of a circle. They...

 Student Outcomes Students apply their understanding of arc length and area of sectors to solve problems of unknown area and length.

 Student Outcomes When students are provided with the angle measure of the arc and the length of the radius of the circle, they understand how to determine the length of an arc and the area of a...

 Student Outcomes Congruent chords have congruent arcs, and the converse is true. Arcs between parallel chords are congruent.

 Student Outcomes Define the angle measure of arcs, and understand that arcs of equal angle measure are similar. Restate and understand the inscribed angle theorem in terms of arcs: The measure of an...

 Topic B defines the measure of an arc and establishes results relating chord lengths and the measures of the arcs they subtend. Students build on their knowledge of circles from Module 2 and prove...

 Student Outcomes Use the inscribed angle theorem to find the measures of unknown angles. Prove relationships between inscribed angles and central angles.

 Student Outcomes Prove the inscribed angle theorem: The measure of a central angle is twice the measure of any inscribed angle that intercepts the same arc as the central angle. Recognize and use...

 Student Outcomes Explore the relationship between inscribed angles and central angles and their intercepted arcs.

 Student Outcomes Inscribe a rectangle in a circle. Understand the symmetries of inscribed rectangles across a diameter.

 Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle.

 Student Outcomes Using observations from a pushing puzzle, explore the converse of Thales' theorem: If triangle ABC is a right triangle, then A, B, and C are three distinct points on a circle with...

 Topic A leads students first to Thales' theorem (an angle drawn from a diameter of a circle to a point on the circle is sure to be a right angle), then to possible converses of Thales' theorem, and...

 This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle. New tools are introduced...

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 Student Outcomes Visualize crosssections of threedimensional objects. Have an understanding of how a 3D printer works and its relation to Cavalieri’s principle.

 Student Outcomes Students give an informal argument using Cavalieri’s principle for the volume formula of a sphere and use thevolume formula to derive a formula for the surface area of a sphere.

 Student Outcomes Students use Cavalieri’s principle and the cone cross section theorem to show that a general pyramid or cone has volume 1/3Bh where B is the area of the base and h is the height by...

 Student Outcomes Students understand the principle of parallel slices in the plane, and understand Cavalieri’s principle as ageneralization of the principle of parallel slices. Students use Cavalieri...

 Student Outcomes Students understand that given similar solids A and B so that the ratio of their lengths is a:b, then the ratio of their volumes is a3:b3. Students understand that if a solid with...

 Student Outcomes Students understand the precise language that describes the properties of volume. Students understand that the volume of any right cylinder is given by the formula area of base×...