Download Student Learning Targets

NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of a point, line, distance along a
line and distance around a circular arc.
Knowledge Learning Target(s)
DART Statements
1. I can identify the undefined notions used in geometry
1. I can identify the undefined notions used in geometry (point, line, plane, distance) and
(point, line, plane, distance) and describe their
describe their characteristics.
characteristics.
2. I can identify angles, circles, perpendicular lines, parallel lines, rays, and line segments.
2. I can identify angles, circles, perpendicular lines, parallel
3. I can define angles, circles, perpendicular lines, parallel lines, rays, and lines segments
lines, rays, and line segments.
precisely using the undefined terms and “if-then” and “iff” statements.
3.
I can define angles, circles, perpendicular lines, parallel
lines, rays, and lines segments precisely using the
undefined terms and “if-then” and “iff” statements.
G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane
as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)
Knowledge Learning Target(s)
DART Statements
1. I can draw transformations of reflections, rotations,
1. I can draw transformations of reflections, rotations, translations, and combinations of these using
translations, and combinations of these using graph paper,
graph paper, transparencies, and/or geometry software.
transparencies, and/or geometry software.
2. I can determine the coordinates for the image of a figure when a transformation rule is applied to
2. I can determine the coordinates for the image of a figure when the preimage.
a transformation rule is applied to the preimage.
Reasoning Learning Target(s)
3. I can distinguish between transformations that are rigid and
those that are not.
DART Statements
3. I can distinguish between transformations that are rigid and those that are not.
G.CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Reasoning Learning Target(s)
DART Statements
1. I can describe and illustrate how a figure is mapped onto itself 1. I can describe and illustrate how a figure is mapped onto itself using transformations.
using transformations.
2. I can calculate the number of lines of reflection symmetry and the degree of rotational symmetry
2. I can calculate the number of lines of reflection symmetry and of any regular polygon.
the degree of rotational symmetry of any regular polygon.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.CO.4 Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.
Performance Skill Learning Target(s)
DART Statements
1. I can construct the reflection definition by connecting any
1. I can construct the reflection definition by connecting any point on the preimage to its
point on the preimage to its corresponding point on the reflected corresponding point on the reflected image and describing the line segment’s relationship to the line
image and describing the line segment’s relationship to the line of of reflection
reflection
2. I can construct the translation definition by connecting any point on the preimage to its
2. I can construct the translation definition by connecting any
corresponding point on the translated image, and connecting a second point on the preimage to its
point on the preimage to its corresponding point on the
corresponding point on the translated image, and describing how the two segments are equal in
translated image, and connecting a second point on the preimage length, point the same direction, and are parallel.
to its corresponding point on the translated image, and
3. I can construct the rotation definition by connecting the center of rotation to any point on the
describing how the two segments are equal in length, point the
preimage and to its corresponding point on the rotated image, and describing the measure of the
same direction, and are parallel.
angle formed and the equal measures of the segments that formed the angle as part of the
definition..
3. I can construct the rotation definition by connecting the center
of rotation to any point on the preimage and to its corresponding
point on the rotated image, and describing the measure of the
angle formed and the equal measures of the segments that
formed the angle as part of the definition..
G.CO.5 Given a geometric figure and a rotation, reflection or translation, draw the transformed figure using, e.g. graph paper, tracing paper or geometry software.
Specify a sequence of transformations that will carry a given figure onto another.
Knowledge Learning Target(s)
DART Statements
1. I can draw specific transformations.
1. I can draw specific transformations.
Reasoning Learning Target(s)
2. I can predict and verify the sequence of transformations that
will map a figure onto another.
DART Statements
2. I can predict and verify the sequence of transformations that will map a figure onto another.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the
definition of congruence in terms of rigid motions to decide if they are congruent.
Knowledge Learning Target(s)
DART Statements
1. I can define rigid motions as reflections, rotations,
1. I can define rigid motions as reflections, rotations, translations, and combinations of these, all
translations, and combinations of these, all preserving distance
preserving distance and angle measure.
and angle measure.
2. I can define congruent figures as figures that have the same size and shape and state that a
2.I can define congruent figures as figures that have the same size composition of rigid motions will map one congruent figure onto another.
and shape and state that a composition of rigid motions will map
one congruent figure onto another.
Reasoning Learning Target(s)
3. I can determine if two figures are congruent by verifying if a
series of rigid motions will map one figure onto another.
DART Statements
3. I can determine if two figures are congruent by verifying if a series of rigid motions will map one
figure onto another.
4. I can predict the composition of transformations that will map
a figure onto a congruent figure.
4. I can predict the composition of transformations that will map a figure onto a congruent figure.
G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
Knowledge Learning Target(s)
DART Statements
1. I can define and classify a triangle.
1. I can define and classify a triangle.
2. I can identify corresponding sides and corresponding angles of
congruent triangles.
Reasoning Learning Target(s)
3. I can explain that in a pair of congruent triangles,
corresponding sides are congruent and corresponding angles are
congruent.
4. I can demonstrate that when distance is preserved and angle
measure is preserved the triangles must also be congruent.
2. I can identify corresponding sides and corresponding angles of congruent triangles.
DART Statements
3. I can explain that in a pair of congruent triangles, corresponding sides are congruent and
corresponding angles are congruent.
4. I can demonstrate that when distance is preserved and angle measure is preserved the triangles
must also be congruent.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS) follow from the definition of congruence in terms of rigid motions.
Knowledge Learning Target(s)
DART Statements
1. I can define rigid motions as reflections, rotations,
1. I can define rigid motions as reflections, rotations, translations, and combinations of these, all of
translations, and combinations of these, all of which preserve
which preserve distance and angle measure.
distance and angle measure.
2. I can list the sufficient conditions to prove triangles are congruent.
2. I can list the sufficient conditions to prove triangles are
congruent.
Reasoning Learning Target(s)
3. I can map a triangle with one of the sufficient conditions onto
the original triangle and show that corresponding sides and
angles are congruent.
DART Statements
3. I can map a triangle with one of the sufficient conditions onto the original triangle and show that
corresponding sides and angles are congruent..
G.CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles
are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s
endpoints.
Knowledge Learning Target(s)
DART Statements
1. I can identify and use the properties of congruence and
1. I can identify and use the properties of congruence and equality (reflexive, symmetric, transitive)
equality (reflexive, symmetric, transitive) in my proofs.
in my proofs.
2. I can order statements based on the Law of Syllogism when
constructing my proof.
2. I can order statements based on the Law of Syllogism when constructing my proof.
3. I can correctly interpret geometric diagrams by identifying what can and cannot be assumed.
3. I can correctly interpret geometric diagrams by identifying
what can and cannot be assumed.
Reasoning Learning Target(s)
4. I can use theorems, postulates, or definitions to prove
theorems about lines, and angles, including:
DART Statements
4. I can use theorems, postulates, or definitions to prove theorems about lines, and angles,
including:
*Vertical angles are congruent
*Vertical angles are congruent
*a transversal with parallel lines creates congruent and
supplementary angles.
*a transversal with parallel lines creates congruent and supplementary angles.
*points on a perpendicular bisector of a line segment are exactly
those equidistant from the segment’s endpoint.
*points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoint.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent;
the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Reasoning Learning Target(s)
DART Statements
1. I can prove the following theorems about triangles:
1. I can prove the following theorems about triangles:
*Interior angles of a triangle sum to 180
*Interior angles of a triangle sum to 180
*Base angles of isosceles triangles are congruent
*Base angles of isosceles triangles are congruent
*Segment joining midpoints of two sides of a triangle is parallel to
the third side and ½ its length.
*Segment joining midpoints of two sides of a triangle is parallel to the third side and ½ its length.
*The medians of a triangle meet at one point.
*The medians of a triangle meet at one point.
G.CO.11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram
bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Reasoning Learning Target(s)
1. I can prove the following theorems.




Opposite sides of a parallelogram are congruent
Opposite angles of a parallelogram are congruent
Diagonals of a parallelogram bisect each other
Rectangles are parallelograms with congruent diagonals.
I can use properties of quadrilaterals to solve.
DART Statements
1. I can prove the following theorems.




Opposite sides of a parallelogram are congruent
Opposite angles of a parallelogram are congruent
Diagonals of a parallelogram bisect each other
Rectangles are parallelograms with congruent diagonals. I can use properties of
quadrilaterals to solve.
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular
bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Knowledge Learning Target(s)
DART Statements
1. I can identify the tools used in formal constructions.
1. I can identify the tools used in formal constructions.
Performance Skill Learning Target(s)
2. I can use tools and methods to precisely copy a segment, copy
an angle, bisect a segment, bisect and angle, construct
perpendicular lines and bisectors, and construct a line parallel to
a given line through a point not on the line.
3. I can informally perform the constructions listed above using
string, reflective devices, paper folding, or geometric software.
DART Statements
2. I can use tools and methods to precisely copy a segment, copy an angle, bisect a segment, bisect
and angle, construct perpendicular lines and bisectors, and construct a line parallel to a given line
through a point not on the line.
3. I can informally perform the constructions listed above using string, reflective devices, paper
folding, and/or geometric software.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.CO.13 Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.
Performance Skill Learning Target(s)
DART Statements
1. I can construct and explain the steps to construct the
1. I can construct and explain the steps to construct the following:
following:
* Equilateral triangle inscribed in a circle.
* Equilateral triangle inscribed in a circle.
* Square inscribed in a circle.
* Square inscribed in a circle.
* Hexagon inscribed in a circle.
* Hexagon inscribed in a circle.
G.SRT.1a Verify experimentally the properties of dilations given by a center and a scale factor.
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Knowledge Learning Target(s)
DART Statements
1. I can define dilation.
1. I can define dilation.
Reasoning Learning Target(s)
2. I can perform a dilation with a given center and scale factor on
a figure in the coordinate system.
3. I can verify that when a side passes through the center of
dilation, the side and its image line on the same line.
4. I can verify that corresponding side of the preimage and
images are parallel.
5. I can verify that a side length of the image is equal to the scale
factor multiplied by the corresponding side length of the
preimage.
DART Statements
2. I can perform a dilation with a given center and scale factor on a figure in the coordinate system.
3. I can verify that when a side passes through the center of dilation, the side and its image line on
the same line.
4. I can verify that corresponding side of the preimage and images are parallel.
5. I can verify that a side length of the image is equal to the scale factor multiplied by the
corresponding side length of the preimage.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations
the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Knowledge Learning Target(s)
DART Statements
1. I can define similarity as a composition of rigid motions
1. I can define similarity as a composition of rigid motions followed by dilations in which angle
followed by dilations in which angle measure is preserved and
measure is preserved and side length is proportional.
side length is proportional.
2. I can identify corresponding sides and corresponding angles of similar triangles.
2. I can identify corresponding sides and corresponding angles of
similar triangles.
Reasoning Learning Target(s)
3. I can demonstrate that in a pair of similar triangles,
corresponding angles are congruent and sides are proportional.
DART Statements
3. I can demonstrate that in a pair of similar triangles, corresponding angles are congruent and sides
are proportional.
4. I can determine that two figure are similar by verifying that
4. I can determine that two figure are similar by verifying that angle measure is preserved and
angle measure is preserved and corresponding sides are
corresponding sides are proportional.
proportional.
G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Reasoning Learning Target(s)
DART Statements
1. I can show and explain that when two angle measures are
1. I can show and explain that when two angle measures are known the third angle measure is also
known the third angle measure is also known.
known.
2. I can conclude and explain that AA similarity is a sufficient
2. I can conclude and explain that AA similarity is a sufficient condition for two triangles to be
condition for two triangles to be similar.
similar.
G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.
Reasoning Learning Target(s)
DART Statements
1. I can prove the following:
1. I can prove the following:

A line parallel to one side of a triangle divides the other
two proportionally.
 If a line divides two sides of a triangle proportionally it is
parallel to the third side.
The Pythagorean Theorem proved using triangle similarity.
 A line parallel to one side of a triangle divides the other two proportionally.
 If a line divides two sides of a triangle proportionally it is parallel to the third side.
The Pythagorean Theorem proved using triangle similarity.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Knowledge Learning Target(s)
DART Statements
1. I can use triangle congruence and triangle similarity to solve
1. I can use triangle congruence and triangle similarity to solve problems.
problems.
Reasoning Learning Target(s)
2. I can use triangle congruence and triangle similarity to prove
relationships in geometric figures.
DART Statements
2. I can use triangle congruence and triangle similarity to prove relationships in geometric figures.
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute
angles.
Knowledge Learning Target(s)
DART Statements
3. I can define the trig ratios for acute angles in a right triangle.
3. I can define the trig ratios for acute angles in a right triangle.
Reasoning Learning Target(s)
1. I can demonstrate that within a right triangle, line segments
parallel to a leg create similar triangles by AA similarity.
DART Statements
1. I can demonstrate that within a right triangle, line segments parallel to a leg create similar
triangles by AA similarity.
2. I can use characteristics of similar figures to justify the trig.
ratios.
2. I can use characteristics of similar figures to justify the trig. ratios.
4. I can use division and the Pythagorean Theorem to prove that sin 2 + cos2 = 1
4. I can use division and the Pythagorean Theorem to prove that
sin2 + cos2 = 1
G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
Knowledge Learning Target(s)
1. I can define complementary angles.
1. I can define complementary angles.
DART Statements
Reasoning Learning Target(s)
2. I can calculate sine and cosine ratios for acute angles in a right
triangle when given two side lengths.
DART Statements
2. I can calculate sine and cosine ratios for acute angles in a right triangle when given two side
lengths.
3. I can use a diagram of a right triangle to explain that for a pair
of complementary angles A and B, the sine of A is equal to the
cosine of B and vice versa.
3. I can use a diagram of a right triangle to explain that for a pair of complementary angles A and B,
the sine of A is equal to the cosine of B and vice versa.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *(Modeling standard)
Reasoning Learning Target(s)
DART Statements
1. I can use angle measures to estimate side lengths.
1. I can use angle measures to estimate side lengths.
2. I can use side lengths to estimate angle measures.
2. I can use side lengths to estimate angle measures.
3. I can solve right triangles by finding the measures of all sides
and all angles.
3. I can solve right triangles by finding the measures of all sides and all angles.
4. I can use sine, cosine, tangent, and their inverses to solve for
the unknown side lengths and angle measures of a right triangle.
5. I can use the Pythagorean theorem to solve for an unknown
side length of a right triangle.
6. I can draw right triangles that describe real world problems
and label the sides and angles with their given measures.
4. I can use sine, cosine, tangent, and their inverses to solve for the unknown side lengths and angle
measures of a right triangle.
5. I can use the Pythagorean theorem to solve for an unknown side length of a right triangle.
6. I can draw right triangles that describe real world problems and label the sides and angles with
their given measures.
7. I can solve application problems involving right triangles. Including angle of elevation and
depression, navigation, and surveying.
7. I can solve application problems involving right triangles.
Including angle of elevation and depression, navigation, and
surveying.
G.SRT.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
Knowledge Learning Target(s)
DART Statements
1. I can understand that two right triangles are created when an
1. I can understand that two right triangles are created when an altitude is drawn from a vertex.
altitude is drawn from a vertex.
Reasoning Learning Target(s)
DART Statements
2. I can find the length of a triangle’s altitude by using the sine
2. I can find the length of a triangle’s altitude by using the sine function.
function.
3. I can use the traditional area formula of a triangle A = ½(base)(height) and the sine function to
3. I can use the traditional area formula of a triangle A =
generate an equivalent area formula A = ½ (a)(b)sinC.
½(base)(height) and the sine function to generate an equivalent
area formula A = ½ (a)(b)sinC.
4. I can Solve for the area of a triangle using the above formula.
4. I can Solve for the area of a triangle using the above formula.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.SRT.10(+) Prove the Laws of Sines and Cosines and use them to solve problems.
Reasoning Learning Target(s)
1. I can derive the Law of Sines.
1. I can derive the Law of Sines.
DART Statements
2. I can use the Law of Sines to solve real world problems.
2. I can use the Law of Sines to solve real world problems.
3. I can derive the Law of Cosines.
3. I can derive the Law of Cosines.
4. I can use the Law of Cosines to solve real world problems.
4. I can use the Law of Cosines to solve real world problems.
G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems,
resultant forces).
Reasoning Learning Target(s)
DART Statements
1. I can use the triangle inequality and side/angle relationships to 1. I can use the triangle inequality and side/angle relationships to estimate the measures of
estimate the measures of unknown sides and angles.
unknown sides and angles.
2. I can distinguish between situations that require the Law of
Sines and situations that require the Law of Cosines.
2. I can distinguish between situations that require the Law of Sines and situations that require the
Law of Cosines.
3. I can apply the Law of Sines to find unknown side lengths and
unknown angle measures in right and non-right triangles.
3. I can apply the Law of Sines to find unknown side lengths and unknown angle measures in right
and non-right triangles.
4. I can use the Law of Sines to determine if two given side
lengths and a given non-adjacent angle measures make two
triangles, one triangle, or no triangle.
4. I can use the Law of Sines to determine if two given side lengths and a given non-adjacent angle
measures make two triangles, one triangle, or no triangle.
5. I can apply the Law of cosines to find unknown side lengths
and unknown angle measures in right and non-right triangles.
6. I can represent real world problems with diagrams of right and
non-right triangles and use them to solve for unknown side
lengths and angle measures.
G.C.1 Prove that all circles are similar.
Reasoning Learning Target(s)
1. I can prove that all circles are similar by showing that
for a dilation centered at the center of a circle, the
preimage and the image have equal central angle
measures.
5. I can apply the Law of cosines to find unknown side lengths and unknown angle measures in right
and non-right triangles.
6. I can represent real world problems with diagrams of right and non-right triangles and use them
to solve for unknown side lengths and angle measures.
DART Statements
1. I can prove that all circles are similar by showing that for a dilation centered at the
center of a circle, the preimage and the image have equal central angle measures.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles;
inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Knowledge Learning Target(s)
DART Statements
1. I can identify central angles, inscribed angles,
1. I can identify central angles, inscribed angles, circumscribed angles, diameters, radii,
circumscribed angles, diameters, radii, chords, and
tangents.
6. I can recognize that the radius of a circle is
perpendicular to the tangent where the radius intersects
the circle.
Reasoning Learning Target(s)
2. I can describe the relationship between a central
angle and the arc it intercepts.
3. I can describe the relationship between and inscribed
angle and the arc it intercepts.
4. I can describe the relationship between a
circumscribed angle and the arcs it intercepts.
5. I can recognize that an inscribed angle whose sides
intersect the endpoints of the diameter of a circle is a
right angle.
chords, and tangents.
6. I can recognize that the radius of a circle is perpendicular to the tangent where the
radius intersects the circle.
DART Statements
2. I can describe the relationship between a central angle and the arc it intercepts.
3. I can describe the relationship between and inscribed angle and the arc it
intercepts.
4. I can describe the relationship between a circumscribed angle and the arcs it
intercepts.
5. I can recognize that an inscribed angle whose sides intersect the endpoints of the
diameter of a circle is a right angle.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Knowledge Learning Target(s)
DART Statements
1. I can define the terms: inscribed, circumscribed,
1. I can define the terms: inscribed, circumscribed, angle bisector, and perpendicular
angle bisector, and perpendicular bisector.
bisector.
Reasoning Learning Target(s)
4. I can apply the Arc Addition Postulate to solve for
missing arc measures.
DART Statements
4. I can apply the Arc Addition Postulate to solve for missing arc measures.
5. I can prove that opposite angles in an inscribed quadrilateral are supplementary.
5. I can prove that opposite angles in an inscribed
quadrilateral are supplementary.
Performance Skill Learning Target(s)
2. I can construct the inscribed circle whose center is
DART Statements
2. I can construct the inscribed circle whose center is the point of intersection of the
the point of intersection of the angle bisectors.
angle bisectors. (incenter)
(incenter)
3. I can construct the circumscribed circle whose
3. I can construct the circumscribed circle whose center is the pint of intersection of
the perpendicular bisectors of each side of the triangle. (circumcenter)
center is the pint of intersection of the perpendicular
bisectors of each side of the triangle. (circumcenter)
G.C. 4 (+) Construct a tangent line from a point outside a given circle to the circle.
Knowledge Learning Target(s)
DART Statements
1. I can define and identify a tangent line.
1. I can define and identify a tangent line.
Performance Skill Learning Target(s)
2. I can construct a tangent line from a point outside the circle to
the circle using construction tools of computer software.
DART Statements
2. I can construct a tangent line from a point outside the circle to the circle using construction tools
of computer software.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.C. 5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the
constant of proportionality; derive the formula for the area of a sector.
Knowledge Learning Target(s)
DART Statements
2. I can define the radian measure of an angle as the
2. I can define the radian measure of an angle as the ratio of an arc length to its radius
ratio of an arc length to its radius and calculate a radian
measure when given an arc length and its radius.
and calculate a radian measure when given an arc length and its radius.
4. I can define and calculate the area of a sector of a circle.
4. I can define and calculate the area of a sector of a
circle.
Reasoning Learning Target(s)
1. I can use similarity to calculate the length of an arc.
DART Statements
1. I can use similarity to calculate the length of an arc.
3. I can convert degrees to radians using the constant
3. I can convert degrees to radians using the constant of proportionality.
of proportionality.
G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given
by an equation.
Knowledge Learning Target(s)
DART Statements
1. I can identify the center and radius of a circle given
1. I can identify the center and radius of a circle given its equation.
its equation.
2. I can draw a right triangle with a horizontal leg, a
2. I can draw a right triangle with a horizontal leg, a vertical leg, and the radius of a
circle as its hypotenuse.
vertical leg, and the radius of a circle as its hypotenuse.
Reasoning Learning Target(s)
3. I can use the distance formula, the coordinates of a
DART Statements
3. I can use the distance formula, the coordinates of a circle’s center and the circle’s
circle’s center and the circle’s radius to write the
radius to write the equation of the circle.
equation of the circle.
4. I can convert an equation of a circle in general form
to standard form by completing the square.
5. I can identify the center and radius of a circle given
its equation.
4. I can convert an equation of a circle in general form to standard form by completing
the square.
5. I can identify the center and radius of a circle given its equation.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.GPE.2 Derive the equation of a parabola given a focus and directrix.
Knowledge Learning Target(s)
1. I can define a parabola.
1. I can define a parabola.
Reasoning Learning Target(s)
2. I can find the distance from a point on the parabola
to the directrix.
3. I can find the distance from a point on the parabola
to the focus using the distance formula.
4. I can equate the two distance expressions for a
parabola to write its equation.
DART Statements
DART Statements
2. I can find the distance from a point on the parabola to the directrix.
3. I can find the distance from a point on the parabola to the focus using the distance
formula.
4. I can equate the two distance expressions for a parabola to write its equation.
5. I can identify the focus and directrix of a parabola when given its equation.
5. I can identify the focus and directrix of a parabola
when given its equation.
G.GPE.3(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum of difference of distances from the foci is constant.
Knowledge Learning Target(s)
DART Statements
1. I can define an ellipse and a hyperbola.
1. I can define an ellipse and a hyperbola.
2. I can define and identify the foci of an ellipse and a hyperbola.
Reasoning Learning Target(s)
3. I can use the distance formula to write an expression for the sum
of the distances from a point on the ellipse or hyperbola to each
focus and equate it to the given constant sum.
2. I can define and identify the foci of an ellipse and a hyperbola.
DART Statements
3. I can use the distance formula to write an expression for the sum of the distances from a point
on the ellipse or hyperbola to each focus and equate it to the given constant sum.
4. I can use algebra to convert the derived equation for an ellipse or hyperbola to standard form.
4. I can use algebra to convert the derived equation for an ellipse
or hyperbola to standard form.
5. I can identify the center, foci, and axes of an ellipse or hyperbola
when given the standard form equation.
5. I can identify the center, foci, and axes of an ellipse or hyperbola when given the standard form
equation.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate
plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
Reasoning Learning Target(s)
DART Statements
1. I can represent the vertices of a figure in the coordinate plane
1. I can represent the vertices of a figure in the coordinate plane using variables.
using variables.
2. I can use coordinates to prove or disprove a claim about a figure.
2. I can use coordinates to prove or disprove a claim about a
*slope to determine parallel or perpendicular
figure.
*slope to determine parallel or perpendicular
*distance for congruence
*distance for congruence
*midpoint for bisectors
*midpoint for bisectors
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
Reasoning Learning Target(s)
DART Statements
1. I can determine if lines are parallel using their slopes.
1. I can determine if lines are parallel using their slopes.
2. I can write an equation of a parallel line through a specific
point.
3. I can determine if lines are perpendicular using their slopes.
2. I can write an equation of a parallel line through a specific point.
3. I can determine if lines are perpendicular using their slopes.
4. I can write an equation of a perpendicular line through a specific point.
4. I can write an equation of a perpendicular line through a
specific point.
G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Reasoning Learning Target(s)
DART Statements
1. I can calculate the point(s) on a directed line segment whose
1. I can calculate the point(s) on a directed line segment whose endpoints are (x1,y1) and
endpoints are (x1,y1) and (x2,y2) that partitions the segment into
(x2,y2) that partitions the segment into a given ration, r1 to r2 using a formula.
a given ration, r1 to r2 using a formula.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.GPE.7 Use coordinates to compute perimeters of polygons and area of triangles and rectangles, e.g., using the distance formula.*(Modeling standard)
Reasoning Learning Target(s)
DART Statements
1. I can use the coordinates of the vertices of a polygon graphed
1. I can use the coordinates of the vertices of a polygon graphed in the coordinate plane and use the
in the coordinate plane and use the distance formula to compute distance formula to compute the perimeter.
the perimeter.
2. I can use coordinates of the vertices of triangles and rectangles graphed in the coordinate plane to
2. I can use coordinates of the vertices of triangles and rectangles compute area.
graphed in the coordinate plane to compute area.
G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection
arguments, Cavalieri’s Principle, and informal limit arguments.
Knowledge Learning Target(s)
DART Statements
1. I can define Pi as the ration of a circle’s circumference to its
1. I can define Pi as the ration of a circle’s circumference to its diameter.
diameter.
2. I can use algebra to demonstrate that circumference = pi * d
2. I can use algebra to demonstrate that circumference = pi * d
7. I can identify the base for prisms, cylinders, pyramids, and cones.
7. I can identify the base for prisms, cylinders, pyramids, and
8. I can calculate the area of the base for prisms, cylinders, pyramids, and cones.
cones.
8. I can calculate the area of the base for prisms, cylinders,
pyramids, and cones.
Reasoning Learning Target(s)
3. I can find the area of a circle.
3. I can find the area of a circle.
4. I can break a regular polygon into triangles to find its area.
4. I can break a regular polygon into triangles to find its area.
5. I can use the Area formula for a regular polygon
5. I can use the Area formula for a regular polygon
6. I can explain that as a polygon increases its number of sides it
approaches the area of a circle.
6. I can explain that as a polygon increases its number of sides it approaches the area of a circle.
9. I can develop the formula for the volume of a prism and
cylinder, I can compare the two formulas and defend that they
are the same.
10. I can explain and use the property that a pyramid and cone
are 1/3 the volume of a prism and cylinder.
DART Statements
9. I can develop the formula for the volume of a prism and cylinder, I can compare the two formulas
and defend that they are the same.
11. I can explain and use the property that a pyramid and cone are 1/3 the volume of a prism and
cylinder.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.GMD.2(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figure.
Knowledge Learning Target(s)
DART Statements
1. I can state that if two solid figures have the same total height
1. I can state that if two solid figures have the same total height and their cross-sectional areas are
and their cross-sectional areas are identical at every level, the
identical at every level, the figures have the same volume.
figures have the same volume.
Reasoning Learning Target(s)
2. I can use a deck of cards to demonstrate.
DART Statements
2. I can use a deck of cards to demonstrate.
3. I can find cross sectional area using Pythagorean theorem and
area formulas.
3. I can find cross sectional area using Pythagorean theorem and area formulas.
4. I can develop the formula for the volume of a sphere.
4. I can develop the formula for the volume of a sphere.
G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Reasoning Learning Target(s)
1. I can calculate the volume of a cylinder and use the volume
formula to solve problems.
2. I can calculate the volume of a pyramid and use the volume
formula to solve problems.
3. I can calculate the volume of a cone and use the volume
formula to solve problems.
DART Statements
1. I can calculate the volume of a cylinder and use the volume formula to solve problems.
2. I can calculate the volume of a pyramid and use the volume formula to solve problems.
3. I can calculate the volume of a cone and use the volume formula to solve problems.
4. I can calculate the volume of a sphere and use the volume formula to solve problems.
4. I can calculate the volume of a sphere and use the volume
formula to solve problems.
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of twodimensional objects.
Knowledge Learning Target(s)
DART Statements
1. I can identify the shapes of two-dimensional cross-sections of
1. I can identify the shapes of two-dimensional cross-sections of three-dimensional objects.
three-dimensional objects.
Reasoning Learning Target(s)
2. I can rotate a 2-D figure and identify the 3-D object that is
formed.
DART Statements
2. I can rotate a 2-D figure and identify the 3-D object that is formed.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* (Modeling
standard)
Reasoning Learning Target(s)
DART Statements
1. I can model real world figures with mathematical properties.
1. I can model real world figures with mathematical properties.
2. I can estimate measures of real-world objects using
comparable geometric shapes or three-dimensional figures.
2. I can estimate measures of real-world objects using comparable geometric shapes or threedimensional figures.
3. I can apply the properties of geometric figures to comparable
real-world objects.
3. I can apply the properties of geometric figures to comparable real-world objects.
G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*(Modeling standard)
Reasoning Learning Target(s)
DART Statements
1. I can decide whether it is best to calculate or estimate the area 1. I can decide whether it is best to calculate or estimate the area or volume of a geometric figure
or volume of a geometric figure and perform the calculation or
and perform the calculation or estimation.
estimation.
2. I can break composite geometric figures into manageable pieces.
2. I can break composite geometric figures into manageable
3. I can convert units of measure.
pieces.
3. I can convert units of measure.
4. I can apply area and volume to situation involving density.
4. I can apply area and volume to situation involving density.
G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with
typographic grid systems based on ratios).* (Modeling standard)
Reasoning Learning Target(s)
DART Statements
2. I can solve design problems using a geometric model.
2. I can solve design problems using a geometric model.
Performance Skill Learning Target(s)
1. I can create a visual representation of a design problem.
DART Statements
1. I can create a visual representation of a design problem.
3. I can interpret the results and make conclusions based on the
geometric model.
3. I can interpret the results and make conclusions based on the geometric model.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or
complements of other events (“or”, “and”, “not”).
Knowledge Learning Target(s)
DART Statements
1. I can define event and sample space.
1. I can define event and sample space.
3. I can define union, intersection, and complement.
3. I can define union, intersection, and complement.
Reasoning Learning Target(s)
2. I can establish events as subsets of a sample space.
DART Statements
2. I can establish events as subsets of a sample space.
4. I can establish events as subsets of a sample space
4. I can establish events as subsets of a sample space based on the union, intersection,
based on the union, intersection, and/or complement of
and/or complement of other events.
other events.
S.CP 2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this
characterization to determine if they are independent.
Knowledge Learning Target(s)
DART Statements
1. I can define and identify independent events.
1. I can define and identify independent events.
Reasoning Learning Target(s)
2. I can explain and provide an example to illustrate that
DART Statements
2. I can explain and provide an example to illustrate that for two independent events,
for two independent events, the probability of the
the probability of the events occurring together is the product of the probability of
events occurring together is the product of the
each event.
probability of each event.
3. I can calculate the probability of an event.
4. I can predict if two events are independent, explain
my reasoning, and check my statement by calculating
P(AandB) and P(A)xP(B)
3. I can calculate the probability of an event.
4. I can predict if two events are independent, explain my reasoning, and check my
statement by calculating P(AandB) and P(A)xP(B)
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
S.CP 3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A
given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
Knowledge Learning Target(s)
DART Statements
1. I can define dependent events and conditional
1. I can define dependent events and conditional probability.
probability.
Reasoning Learning Target(s)
2. I can explain that conditional probability is the
DART Statements
2. I can explain that conditional probability is the probability of an event occurring
probability of an event occurring given the occurrence of
given the occurrence of some other event and give examples that illustrate conditional
some other event and give examples that illustrate
probability.
conditional probability.
3. I can explain that for two events A and B, the
probability of event A occurring give the occurrence of
event B is P(A|B)= P(AandB)/P(B) and give examples.
3. I can explain that for two events A and B, the probability of event A occurring give
the occurrence of event B is P(A|B)= P(AandB)/P(B) and give examples.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
S.CP. 4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a
sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your
school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given
that the student is in 10th grade. Do the same for other subjects and compare the results.
Reasoning Learning Target(s)
DART Statements
1. I can determine when a two-way frequency table is an
1. I can determine when a two-way frequency table is an appropriate display for a set
appropriate display for a set of data.
of data.
2. I can collect data from a random sample.
2. I can collect data from a random sample.
3. I can construct a two-way frequency table for the
3. I can construct a two-way frequency table for the data using the appropriate
data using the appropriate categories for each variable.
categories for each variable.
4. I can decide if events are independent of each other
4. I can decide if events are independent of each other by comparing P(B|A) and P(B)
by comparing P(B|A) and P(B) or P(A|B) and P(A).
or P(A|B) and P(A).
5. I can calculate the conditional probability of A given
5. I can calculate the conditional probability of A given B using the formula
B using the formula P(A|B)=P(AandB)\P(B)
P(A|B)=P(AandB)\P(B)
Performance Skill Learning Target(s)
6. I can pose a question for which a two-way frequency
DART Statements
6. I can pose a question for which a two-way frequency is appropriate, use statistical
is appropriate, use statistical techniques to sample the
techniques to sample the population, and design a n appropriate product to summarize
population, and design a n appropriate product to
the process and report the results.
summarize the process and report the results.
S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the
chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
Reasoning Learning Target(s)
DART Statements
1. I can illustrate the concept of a conditional
1. I can illustrate the concept of a conditional probability using everyday examples of
probability using everyday examples of dependent
events.
2. I can illustrate the concept of independence using
everyday examples of independent events.
dependent events.
2. I can illustrate the concept of independence using everyday examples of independent
events.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A and interpret the answer in terms of the model.
Reasoning Learning Target(s)
DART Statements
1. I can calculate the probability of the intersection of
1. I can calculate the probability of the intersection of two events.
two events.
2. I can calculate the conditional probability of A given
B.
2. I can calculate the conditional probability of A given B.
3. I can interpret probability based on the context of the given problem.
3. I can interpret probability based on the context of
the given problem.
S.CP.7 Apply the Additional Rule, P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in terms of the model.
Reasoning Learning Target(s)
DART Statements
1. I can apply the Apply the Addition Rule to determine
1. I can apply the Apply the Addition Rule to determine the probability of the union of
the probability of the union of two events using the
formula.
P(A or B)=P(A) + P(B) – P(A and B)
2. I can interpret the probability of unions and
intersections based on the context of the given problem.
two events using the formula.
P(A or B)=P(A) + P(B) – P(A and B)
2. I can interpret the probability of unions and intersections based on the context of
the given problem.
S.CP.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
Reasoning Learning Target(s)
DART Statements
1. I can apply the general Multiplication Rule to calculate the
1. I can apply the general Multiplication Rule to calculate the probability of the intersection of two
probability of the intersection of two events using the formula.
events using the formula.
2. I can interpret conditional probability based on the context of
the given problem.
2. I can interpret conditional probability based on the context of the given problem.
NLHS- State Geometry Standards
Last Reviewed: 5/16/2012
S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
Knowledge Learning Target(s)
DART Statements
2. I can define factorial, permutation, combination, and
2. I can define factorial, permutation, combination, and compound event.
compound event.
Reasoning Learning Target(s)
DART Statements
1. I can apply the fundamental counting principle to find the total 1. I can apply the fundamental counting principle to find the total number of possible outcomes in a
number of possible outcomes in a sample space.
sample space.
3. I can distinguish between situations that require permutations
and those that require combinations.
3. I can distinguish between situations that require permutations and those that require
combinations.
4. I can apply the permutation formula to determine the number
of outcomes in an event.
4. I can apply the permutation formula to determine the number of outcomes in an event.
5. I can apply the combination formula to determine the number of outcomes in an event.
5. I can apply the combination formula to determine the number
of outcomes in an event.
6. I can compute the probabilities of compound events.
6. I can compute the probabilities of compound events.
7. I can solve problems involving permutations and combinations.
7. I can solve problems involving permutations and
combinations.
8. I can write and solve original problems involving compound events, permutations, and/or
combinations.
8. I can write and solve original problems involving compound
events, permutations, and/or combinations.
S.MD.6: (+) Use probabilities to make fair decisions (e.g. drawing by lots, using a random number generator.)
This unit sets the stage for work in Algebra II, where the ideas of statistical inference are introduced. Evaluating the risks associated with conclusions drawn from
sample data (i.e. incomplete information) requires an understanding of probability concepts.
Reasoning Learning Target(s)
DART Statements
1. I can use probability to create a method for making a fair
1. I can use probability to create a method for making a fair decision.
decision.
2. I can use probability to analyze the results of a process and decide if it resulted in a fair decision.
2. I can use probability to analyze the results of a process and
decide if it resulted in a fair decision.
S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game.)
Reasoning Learning Target(s)
DART Statements
1. I can analyze data to determine whether or not the best
1. I can analyze data to determine whether or not the best decision was made.
decision was made.
2. I can analyze the available strategies, recommend a strategy, and defend my choice.
2. I can analyze the available strategies, recommend a strategy,
and defend my choice.