Functions 
Define, evaluate, and compare
functions.

Understand that a function
is a rule that assigns to each input exactly one output. The graph of
a function is the set of ordered pairs consisting of an input and the
corresponding output.

Compare properties of two functions
each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For example,
given a linear function represented by a table of values and a linear
function represented by an algebraic expression, determine which
function has the greater rate of change.

Interpret the
equation y = mx + b as defining a linear function, whose graph
is a straight line; give examples of functions that are not linear.
For example, the function A = s^{2}
giving the area of a square as a function of its side length is not
linear because its graph contains the points (1,1), (2,4) and (3,9),
which are not on a straight line.

 Understand that a function is a rule
that assigns to each input exactly one output.
 Compare
properties of two functions each represented in a different way
 Interpret the
equation y = mx + b as defining a linear function, whose graph
is a straight line

Use functions to model relationships
between quantities.

Construct a
function to model a linear relationship between two quantities.
Determine the rate of change and initial value of the function from a
description of a relationship or from two (x, y) values,
including reading these from a table or from a graph. Interpret the rate
of change and initial value of a linear function in terms of the
situation it models, and in terms of its graph or a table of values.

Describe qualitatively the functional relationship between two
quantities by analyzing a graph (e.g., where the function is increasing
or decreasing, linear or nonlinear). Sketch a graph that exhibits the
qualitative features of a function that has been described verbally.

 Construct a function to model a
linear relationship between two quantities.

Describe qualitatively the functional relationship between two
quantities by analyzing a graph

Geometry

Understand congruence and similarity
using physical models, transparencies, or geometry software.
 Verify experimentally the properties
of rotations, reflections, and translations:
 Lines are taken to lines, and line segments
to line segments of the same length.
 Angles are taken to angles of the same
measure.
 Parallel lines are taken to parallel lines.
 Understand that a twodimensional figure is
congruent to another if the second can be obtained from the first by a
sequence of rotations, reflections, and translations; given two
congruent figures, describe a sequence that exhibits the congruence
between them.
 Describe the effect of dilations, translations,
rotations, and reflections on twodimensional figures using
coordinates.
 Understand that a twodimensional figure is
similar to another if the second can be obtained from the first by a
sequence of rotations, reflections, translations, and dilations; given
two similar twodimensional figures, describe a sequence that exhibits
the similarity between them.
 Use informal arguments to
establish facts about the angle sum and exterior angle of triangles,
about the angles created when parallel lines are cut by a transversal,
and the angleangle criterion for similarity of triangles.
For example, arrange three copies of the same triangle
so that the sum of the three angles appears to form a line, and give
an argument in terms of transversals why this is so.

 Verify experimentally the properties
of rotations, reflections, and translations:
Lines are taken to lines, and line segments
to line segments of the same length.
 Angles are taken to angles of the same
measure.
 Parallel lines are taken to parallel lines.
 Understand that a twodimensional
figure is congruent to another if the second can be obtained from
the first by a sequence of rotations
 Describe the effect of dilations, translations,
rotations, and reflections on twodimensional figures using
coordinates.
 Understand that a twodimensional
figure is similar to another
 Use informal arguments to establish
facts

Understand and apply the Pythagorean
Theorem.
 Explain a proof of the Pythagorean
Theorem and its converse.
 Apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in realworld and mathematical
problems in two and three dimensions.
 Apply the Pythagorean Theorem
to find the distance between two points in a coordinate system.

 Explain a proof of the Pythagorean
Theorem and its converse.
 Apply the Pythagorean Theorem to
determine unknown side
 Apply the Pythagorean Theorem
to find the distance between two points in a coordinate system.

Solve realworld and mathematical
problems involving volume of cylinders, cones, and spheres.
 Know the formulas for the volumes of
cones, cylinders, and spheres and use them to solve realworld and
mathematical problems.

 Know the formulas for the volumes of
cones, cylinders, and spheres and use them to solve realworld and
mathematical problems.

Statistics and Probability

Investigate patterns of association
in bivariate data.
 Construct and interpret scatter plots
for bivariate measurement data to investigate patterns of association
between two quantities. Describe patterns such as clustering,
outliers, positive or negative association, linear association, and
nonlinear association.
 Know that straight lines are widely used to
model relationships between two quantitative variables. For scatter
plots that suggest a linear association, informally fit a straight
line, and informally assess the model fit by judging the closeness of
the data points to the line.
 Use the equation of a linear model to solve
problems in the context of bivariate measurement data, interpreting
the slope and intercept. For example, in a linear model for a
biology experiment, interpret a slope of 1.5 cm/hr as meaning that an
additional hour of sunlight each day is associated with an additional
1.5 cm in mature plant height.
 Understand that patterns
of association can also be seen in bivariate categorical data by
displaying frequencies and relative frequencies in a twoway table.
Construct and interpret a twoway table summarizing data on two
categorical variables collected from the same subjects. Use relative
frequencies calculated for rows or columns to describe possible
association between the two variables. For
example, collect data from students in your class on whether or not
they have a curfew on school nights and whether or not they have
assigned chores at home. Is there evidence that those who have a
curfew also tend to have chores?

 Construct and interpret scatter
plots
 Use the equation of a linear model to solve
problems in the context of bivariate measurement data
 Understand that patterns of
association
