High School Mathematics Standards
Traditional
Sequence |
Integrated Sequence |
Performance Expectation |
Algebra 1 |
Math 1 |
Math 2 |
Math 3 |
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G.1.A |
M1.4.A |
G.1.A |
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Distinguish between inductive and
deductive reasoning. |
G.1.B |
M1.4.B |
G.1.B |
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Use inductive reasoning to make
conjectures, to test the plausibility of a geometric statement, and to
help find a counterexample. |
G.1.C |
M1.4.C |
G.1.C |
M2.3.A |
G.1.C |
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Use deductive reasoning to prove that
a valid geometric statement is true. |
G.1.D |
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M2.3.B |
G.1.D |
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Write the converse, inverse, and
contrapositive of a valid proposition and determine their validity. |
G.1.E |
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M2.3.C |
G.1.E |
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Identify errors or gaps in a
mathematical argument and develop counterexamples to refute invalid
statements about geometric relationships. |
G.1.F |
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M2.3.D |
G.1.F |
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Distinguish between definitions and
undefined geometric terms and explain the role of definitions, undefined
terms, postulates (axioms), and theorems. |
G.2.A |
M1.4.E |
G.2.A |
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Know, prove, and apply theorems about
parallel and perpendicular lines. |
G.2.B |
M1.4.F |
G.2.B |
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Know, prove, and apply theorems about
angles, including angles that arise from parallel lines intersected by a
transversal. |
G.2.C |
M1.4.G |
G.2.C |
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Explain and perform basic compass and
straightedge constructions related to parallel and perpendicular lines. |
G.2.D |
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M3.5.A |
G.2.D |
Describe the intersections of lines
in the plane and in space, of lines and planes, and of planes in space. |
G.3.A |
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M2.3.E |
G.3.A |
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Know, explain, and apply
basic postulates and theorems about
triangles and the special lines, line segments, and rays associated with
a triangle |
G.3.B |
M1.4.D |
G.3.B |
M2.3.F |
G.3.B |
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Determine and prove triangle
congruence, triangle similarity, and other properties of triangles . |
G.3.C |
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M2.3.I |
G.3.C |
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Use the properties of special right
triangles (30°–60°–90° and 45°– 45°–90°) to solve problems . |
G.3.D |
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M2.3.G |
G.3.D |
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Know, prove, and apply the
Pythagorean Theorem and its converse. |
G.3.E |
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M2.3.H |
G.3.E |
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Solve problems involving the basic
trigonometric ratios of sine, cosine, and tangent. |
G.3.F |
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M2.3.J |
G.3.F |
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Know, prove, and apply basic theorems
about parallelograms. |
G.3.G |
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M2.3.K |
G.3.G |
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Know, prove, and apply theorems about
properties of quadrilaterals and other polygons. |
G.3.H |
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M3.7.A |
G.3.H |
Know, prove, and apply basic theorems
relating circles to tangents , chords, radii, secants, and inscribed
angles. |
G.3.I |
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M3.7.C |
G.3.I |
Explain and perform constructions
related to the circle. |
G.3.J |
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M3.5.B |
G.3.J |
Describe prisms, pyramids,
parallelepipeds, tetrahedra, and regular polyhedra in terms of their
faces, edges, vertices, and properties. |
G.3.K |
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M3.5.C |
G.3.K |
Analyze cross-sections of cubes,
prisms, pyramids, and spheres and identify the resulting shapes. |
G.4.A |
M1.3.H |
G.4.A |
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Determine the equation of a line in
the coordinate plane that is described geometrically, including a line
through two given points, a line through a given point parallel to a
given line, and a line through a given point perpendicular to a given
line. |
G.4.B |
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M2.3.L |
G.4.B |
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Determine the coordinates of a point
that is described geometrically. |
G.4.C |
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M2.3.M |
G.4.C |
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Verify and apply
properties of triangles and quadrilaterals in the coordinate plane. |
G.4.D |
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M3.7.B |
G.4.D |
Determine the equation of a circle
that is described geometrically in the coordinate plane and, given
equations for a circle and a line, determine the coordinates of their
intersection(s). |
G.5.A |
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M3.2.A |
G.5.A |
Sketch results of transformations and
compositions of
transformations for a given two-dimensional figure on the coordinate
plane, and describe the rule (s) for performing translations or for
performing reflections about the coordinate axes or the line y = x. |
G.5.B |
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M3.2.B |
G.5.B |
Determine and apply properties of
transformations. |
G.5.C |
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M3.2.C |
G.5.C |
Given two congruent or similar
figures in a coordinate plane, describe a composition of translations,
reflections, rotations, and dilations that superimposes one figure on
the other. |
G.5.D |
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M3.2.D |
G.5.D |
Describe the symmetries of
two-dimensional figures and describe transformations, including
reflections across a line and rotations about a point. |
G.6.A |
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M3.7.D |
G.6.A |
Derive and apply formulas for arc
length and area of a sector of a circle. |
G.6.B |
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M3.5.F |
G.6.B |
Analyze distance and angle measures
on a sphere and apply these measurements to the geometry of the earth. |
G.6.C |
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M3.5.D |
G.6.C |
Apply formulas for surface area and
volume of three-dimensional figures to solve problems. |
G.6.D |
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M3.5.E |
G.6.D |
Predict and verify the effect that
changing one, two, or three linear dimensions has on perimeter, area,
volume, or surface area of two-and three-dimensional figures. |
G.6.E |
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M2.5.B |
G.6.E |
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Use different degrees of precision in
measurement, explain the reason for using a certain degree of precision,
and apply estimation strategies to obtain reasonable measurements with
appropriate precision for a given purpose. |
G.6.F |
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M2.5.C |
G.6.F |
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Solve problems involving measurement
conversions within and
between systems , including those involving derived units, and analyze
solutions in terms of reasonableness of solutions and appropriate units. |
G.7.A |
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M2.6.A |
G.7.A |
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Analyze a problem situation and
represent it mathematically. |
G.7.B |
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M2.6.B |
G.7.B |
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Select and apply strategies to solve
problems. |
G.7.C |
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M2.6.C |
G.7.C |
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Evaluate a solution for
reasonableness, verify its accuracy, and interpret the solution in the
context of the original problem. |
G.7.D |
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M2.6.D |
G.7.D |
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Generalize a solution strategy for a
single problem to a class of related problems, and apply a strategy for
a class of related problems to solve specific problems. |
G.7.E |
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M2.6.E |
G.7.E |
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Read and interpret diagrams, graphs ,
and text containing the
symbols , language, and conventions of mathematics. |
G.7.F |
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M2.6.F |
G.7.F |
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Summarize mathematical ideas with
precision and efficiency for a given audience and purpose. |
G.7.G |
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M2.6.G |
G.7.G |
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Use inductive reasoning to make
conjectures, and use deductive reasoning to prove or disprove
conjectures. |
G.7.H |
M1.8.H |
G.7.H |
M2.6.H |
G.7.H |
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Synthesize information to draw
conclusions and evaluate the
arguments and conclusions of others. |
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