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Common Core: Math
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 The focus in Topic D is similarity within right triangles. Students examine how an altitude drawn from the vertex of a right triangle to the hypotenuse creates two similar subtriangles. Students...

 Student Outcomes Students understand that the altitude of a right triangle from the vertex of the right angle to the hypotenuse divides the triangle into two similar right triangles that are also...

 Student Outcomes Students multiply and divide expressions that contain radicals to simplify their answers. Students rationalize the denominator of a number expressed as a fraction.

 Student Outcomes Students use the distributive property to simplify expressions that contain radicals.

 Student Outcomes Students prove the Pythagorean Theorem using similarity. Students use similarity and the Pythagorean Theorem to find the unknown side lengths of a right triangle. Students are...

 Students link their understanding of similarity and relationships within similar right triangles formally to trigonometry. In addition to the terms sine, cosine, and tangent, students study the...

 In Lesson 26, students discover that the values of the and ratios in a right triangle depend solely on the measure of the acute angle by which the adjacent, opposite, and hypotenuse sides are...

 Student Outcomes Students understand that if α and β are the measurements of complementary angles, then sin α=cos β. Students solve triangle problems using special angles.

 Student Outcomes Students use graphing calculator to find the values of sin θ and cos θ for θ between 0 and 90. Students solve for missing sides of a right triangle given the length of one side and...

 Student Outcomes Students understand that the value of the tangent ratio of the angle of elevation or depression of a line is equal to the slope of the line. Students use the value of the tangent...

 Student Outcomes Students rewrite the Pythagorean Theorem in terms of sine and cosine ratios, and use it in this form to solve problems. Students write tangent as an identity in terms of sine and...

 Student Outcomes Students prove that the area of a triangle is onehalf times the product of two side lengths times the sine of the included angle and solve problems using this formula. Students find...

 Student Outcomes Students find missing side lengths of an acute triangle given one side length and the measures of two angles. Students find the missing side length of an acute triangle given two...

 Student Outcomes Students understand that the Law of Sines can be used to find missing side lengths in a triangle when you know the measures of the angles and one side length. Students understand...

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

 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 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...

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

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

 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...