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Common Core: ELA
Common Core: Math
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 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...

 Overview The New York State grade 10 curriculum modules offer a variety of rich texts that engage students in analysis of literary and journalistic nonfiction as well as poetry, drama, and fiction....

 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×...

 Student Outcomes Students understand the definition of a general pyramid and cone and that their cross sections are similar tothe base. Students show that if two cones have the same base area and the...

 Student Outcomes Students understand the definitions of a general prism and a cylinder and the distinction between a crosssection and a slice.

 Students study the basic properties of twodimensional and threedimensional space, noting how ideas shift between the dimensions. They learn that general cylinders are the parent category for...

 Student Outcomes Students describe properties of points, lines, and planes in threedimensional space.

 Student Outcomes Students use inscribed and circumscribed polygons for a circle (or disk) of radius r and circumference C to showthat the area of a circle is 1/2Cr or as it is usually written, πr2.

 Student Outcomes Students understand that a similarity transformation with scale factor r multiplies the area of a planar region bya factor of r2. Students understand that if a planar region is...

 Student Outcomes Students understand properties of area: 1.Students understand that the area of a set in the plane is a number greater than or equal to zero thatmeasures the size of the set and not...

 Student Outcomes Students review the area formula for rectangles with rational side lengths and prove the area formula for anarbitrary rectangle. Students use a square grid to estimate the area of a...

 Students begin their work with 3dimensions by first developing a stronger sense of area in two dimensions. They find approximated areas of curved figures by “squeezing” them between inscribed and...

 Student Outcomes Students develop an understanding of how to determine a missing angle in a right triangle diagram and applythis to real world situations.