High School

Outcomes

The Real Number System
- Extend The Properties Of Exponents To Rational Exponents.
  - N.RN.2
    Rewrite expressions involving radicals and rational exponents using the properties of exponents.
    
    Play Activities 7
    
    Examples
The Complex Number System
- Represent Complex Numbers And Their Operations On The Complex Plane.
  - N.CN.6
    (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
    
    Play Activities 2
    
    Examples
Seeing Structure In Expressions
- Interpret The Structure Of Expressions
  - A.SSE.2
    Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
    
    Play Activities 4
    
    Examples
- Write Expressions In Equivalent Forms To Solve Problems
  - A.SSE.3.c
    Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t _ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
    
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    Examples
Interpreting Functions
- Understand The Concept Of A Function And Use Function Notation
  - F.IF.3
    Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n _ 1.
    
    Play Activities 2
    
    Examples
- Interpret Functions That Arise In Applications In Terms Of The Context
  - F.IF.4
    For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity._
    
    Play Activities 6
    
    Examples
- Analyze Functions Using Different Representations
  - F.IF.7.a
    Graph linear and quadratic functions and show intercepts, maxima, and minima.
    
    Play Activities 7
    
    Examples
  - F.IF.8.a
    Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
    
    Play Activities 3
    
    Examples
Congruence
- Experiment With Transformations In The Plane
  - G.CO.1
    Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
    
    Play Activities 11
    
    Examples
  - 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.
    
    Play Activities 33
    
    Examples
- Understand Congruence In Terms Of Rigid Motions
  - 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.
    
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    Examples
  - 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.
    
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    Examples
- Prove Geometric Theorems
  - 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.
    
    Play Activities 13
    
    Examples
  - G.CO.10
    Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; 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.
    
    Play Activities 6
    
    Examples
  - 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.
    
    Play Activities 4
    
    Examples
Similarity, Right Triangles, And Trigonometry
- Understand Similarity In Terms Of Similarity Transformations
  - G.SRT.3
    Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
    
    Play Activities 2
    
    Examples
- Prove Theorems Involving Similarity
  - 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.
    
    Play Activities 3
    
    Examples
Circles
- Understand And Apply Theorems About Circles
  - 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.
    
    Play Activities 5
    
    Examples
  - G.C.3
    Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
    
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    Examples
  - G.C.4
    (+) Construct a tangent line from a point outside a given circle to the circle.
    
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    Examples
- Find Arc Lengths And Areas Of Sectors Of Circles
  - 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.
    
    Play Activities 1
    
    Examples
Expressing Geometric Properties With Equations
- Use Coordinates To Prove Simple Geometric Theorems Algebraically
  - G.GPE.7
    Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula._
    
    Play Activities 2
    
    Examples
Geometric Measurement And Dimension
- Explain Volume Formulas And Use Them To Solve Problems
  - 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.
    
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    Examples
  - G.GMD.3
    Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems._
    
    Play Activities 13
    
    Examples
Interpreting Categorical And Quantitative Data
- Summarize, Represent, And Interpret Data On A Single Count Or Measurement Variable
  - S.ID.4
    Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
    
    Play Activities 2
    
    Examples
- Interpret Linear Models
  - S.ID.7
    Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
    
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    Examples
Conditional Probability And The Rules Of Probability
- Use The Rules Of Probability To Compute Probabilities Of Compound Events In A Uniform Probability Model
  - S.CP.7
    Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
    
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    Examples
  - 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.
    
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    Examples
  - S.CP.9
    (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
    
    Play Activities 3
    
    Examples