Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - Student Outcomes
Visualize cross-sections of three-dimensional objects.
Have an understanding of how a 3D printer works and its relation to Cavalieri’s principle.
Jan 26, 2016 - 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.
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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×...
Jan 26, 2016 - 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...
Jan 26, 2016 - Student Outcomes
Students understand the definitions of a general prism and a cylinder and the distinction between a cross-section and a slice.
Jan 26, 2016 - Students study the basic properties of two-dimensional and three-dimensional space, noting how ideas shift between the dimensions. They learn that general cylinders are the parent category for...
Jan 26, 2016 - 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.
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - Students begin their work with 3-dimensions by first developing a stronger sense of area in two dimensions. They find approximated areas of curved figures by “squeezing” them between inscribed and...
Jan 26, 2016 - Student Outcomes
Students develop an understanding of how to determine a missing angle in a right triangle diagram and applythis to real world situations.
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - Student Outcomes
Students prove that the area of a triangle is one-half times the product of two side lengths times the sine of the included angle and solve problems using this formula.
Students find...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
