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Common Core: Standard
Common Core: ELA
Common Core: Math
165 Results
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- In this topic, students first distinguish between discrete and continuous random variables and then focus on probability distributions for discrete random variables. In the early lessons of this...
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- In this topic, students extend their understanding of probability, building on work from Grade 11. The multiplication rule for independent events introduced in Grade 11 is generalized to a rule that...
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- Student Outcomes Students apply the law of sines or the law of cosines to determine missing measurements in real-world situations that can be modeled using non-right triangles, including situations...
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- Student Outcomes Students prove the law of cosines and use it to solve problems.
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- Student Outcomes Students prove the law of sines and use it to solve problems.
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- Student Outcomes Students prove the formula Area = 1/2 bc sin(A) for a triangle. They reason geometrically and numerically to find the areas of various triangles.
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- Students derive sophisticated applications of the trigonometric functions in Topic B including: the area formula for a general triangle, the law of sines, the law of cosines, and Heron’s formula. ...
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- Student Outcomes Students construct a tangent line from a point outside a given circle to the circle.
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- Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is...
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- Student Outcomes Students will be able to give an informal argument using Cavalieri’s principle for the formula for the volume of a sphere and other solid figures.
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- Student Outcomes Students learn to graph equations of the form x2/a2 - y2/b2 =1 . Students derive the equations of hyperbolas given the foci, using the fact that the difference of distances from the...
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- Student Outcomes Students derive the equations of ellipses given the foci, using the fact that the sum of distances from the foci is constant.
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- Student Outcomes Students convert between the real and complex forms of equations for ellipses. Students write equations of ellipses and represent them graphically.
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- Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...
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- Student Outcomes Students determine the area of a cyclic quadrilateral as a function of its side lengths and the acute angle formed by its diagonals. Students prove Ptolemy’s theorem, which states...
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- Student Outcomes Students show that a quadrilateral is cyclic if and only if its opposite angles are supplementary. Students derive and apply the area of cyclic quadrilateral ABCD as 1/2 AB·CD·sin(w...
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- The module concludes with Topic E focusing on the properties of quadrilaterals inscribed in circles and establishing Ptolemy's theorem. This result codifies the Pythagorean theorem, curious facts...
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- Student Outcomes Given a circle, students find the equations of two lines tangent to the circle with specified slopes. Given a circle and a point outside the circle, students find the equation of the...
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- Student Outcomes Students complete the square in order to write the equation of a circle in center-radius form. Students recognize when a quadratic in x and y is the equation for a circle.
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- Student Outcomes Students write the equation for a circle in center-radius form, (x - a)2 (y - b)2 = r2 using the Pythagorean theorem or the distance formula. Students write the equation of a circle...
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- Topic D brings in coordinate geometry to establish the equation of a circle. Students solve problems to find the equations of specific tangent lines or the coordinates of specific points of contact...
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- Student Outcomes Students find “missing lengths” in circle-secant or circle-secant-tangent diagrams.
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- Student Outcomes Students find the measures of angle/arcs and chords in figures that include two secant lines meeting outside a circle, where the measures must be inferred from other data.
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- Student Outcomes Students understand that an angle whose vertex lies in the interior of a circle intersects the circle in two points and that the edges of the angles are contained within two secant...