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MATH :
COURSE ONE
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The
Real Number System |
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STRAND:
Extend the properties of exponents to rational exponents. |
N-RN.1
Explain how the definition of the meaning of rational
exponents follows from extending the properties of integer
exponents to those values, allowing for a notation for
radicals in terms of rational exponents. For example, we
define to be the cube root of 5 because we want to hold,
so must equal 5. |
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MATH :
COURSE ONE
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The
Real Number System |
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STRAND:
Extend the properties of exponents to rational exponents. |
N-RN.2
Rewrite expressions involving radicals and rational
exponents using the properties of exponents. |
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MATH :
COURSE ONE
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Quantities |
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STRAND:
Reason quantitatively and use units to solve problems. |
N-Q.1 Use
units as a way to understand problems and to guide the
solution of multi-step problems; choose and interpret units
consistently in formulas; choose and interpret the scale and
the origin in graphs and data displays. |
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MATH :
COURSE ONE
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Quantities |
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STRAND:
Reason quantitatively and use units to solve problems. |
N-Q.3 Choose
a level of accuracy appropriate to limitations on
measurement when reporting quantities. |
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MATH :
COURSE ONE
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Seeing
Structure in Expressions |
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STRAND:
Interpret the structure of expressions. |
A-SSE 1
Interpret expressions that represent a quantity in terms of
its context.★
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Interpret parts of an
expression, such as terms, factors, and coefficients.
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Interpret complicated
expressions by viewing one or more of their parts as a
single entity. For example, interpret P(1+r)n as the
product
of P and a
factor not depending on P. |
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MATH :
COURSE ONE
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Seeing
Structure in Expressions |
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STRAND:
Interpret the structure of expressions. |
A-SSE 1
Interpret expressions that represent a quantity in terms of
its context.★
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Interpret parts of an
expression, such as terms, factors, and coefficients.
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Interpret complicated
expressions by viewing one or more of their parts as a
single entity. For example, interpret P(1+r)n as the
product
of P and a
factor not depending on P. |
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MATH :
COURSE ONE
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Seeing
Structure in Expressions |
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STRAND:
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).
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Interpret parts of an
expression, such as terms, factors, and coefficients.
-
Interpret complicated
expressions by viewing one or more of their parts as a
single entity. For example, interpret P(1+r)n as the
product
of P and a factor not depending on P. |
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MATH :
COURSE ONE
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Seeing
Structure in Expressions |
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STRAND:
Write expressions in
equivalent forms to solve problems.
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A-SSE
3. Choose and produce an equivalent form of an expression to
reveal and explain properties of the quantity represented by
the expression.★
a.
Factor a quadratic expression to reveal the zeros of the
function it defines.
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MATH :
COURSE ONE
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Arithmetic with Polynomials and Rational Expressions |
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STRAND:
Perform arithmetic
operations on polynomials
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A-APR.1
Understand that polynomials form a system analogous to the
integers, namely, they are closed under the operations of
addition, subtraction, and multiplication; add, subtract,
and multiply polynomials.
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MATH :
COURSE ONE
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Creating Equations* |
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STRAND:
Create equations that
describe numbers or relationships |
A-CED
1Create equations and inequalities in one variable and use
them to solve problems. Include equations arising from
linear and quadratic functions, and simple rational and
exponential functions.
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MATH :
COURSE ONE
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Creating Equations* |
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STRAND:
Create equations that
describe numbers or relationships |
A-CED
2. Create equations in two or more variables to represent
relationships between quantities; graph equations on
coordinate axes with labels and scales.
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MATH :
COURSE ONE
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Creating Equations* |
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STRAND:
Create equations that
describe numbers or relationships |
A-CED
3. Represent constraints by equations or inequalities, and
by systems of equations and/or inequalities, and interpret
solutions as viable or nonviable options in a modeling
context. For example, represent inequalities describing
nutritional and cost constraints on combinations of
different foods.
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MATH :
COURSE ONE
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Creating Equations* |
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STRAND:
Create equations that
describe numbers or relationships |
A-CED
4. Rearrange formulas to highlight a quantity of interest,
using the same reasoning as in solving equations. For
example, rearrange Ohm’s law
V = IR
to highlight resistance R.
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MATH :
COURSE ONE
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Reasoning with Equations and Inequalities |
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STRAND:
Understanding solving
equations as a process of reasoning and explain the
reasoning |
A-REI 1
Explain each step in solving a simple equation as following
from the equality of numbers asserted at the previous step,
starting from the assumption that the original equation has
a solution. Construct a viable argument to justify a
solution method.
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MATH :
COURSE ONE
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Reasoning with Equations and Inequalities |
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STRAND:
Solve systems of
equations.
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A-REI
6. Solve systems of linear equations exactly and
approximately (e.g., with graphs), focusing on pairs of
linear equations in two variables.
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MATH :
COURSE ONE
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Reasoning with Equations and Inequalities |
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STRAND:
Represent and solve
equations and inequalities graphically.
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A-REI
10. Understand that the graph of an equation in two
variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a
line).
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MATH :
COURSE ONE
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Reasoning with Equations and Inequalities |
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STRAND:
Represent and solve
equations and inequalities graphically.
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A-REI
11. Explain why the x-coordinates of the points where the
graphs of the equations y = f(x) and y = g(x) intersect are
the solutions of the equation f(x) = g(x); find the
solutions approximately, e.g., using technology to graph the
functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are
linear, polynomial, rational, absolute value, exponential,
and logarithmic functions.★
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MATH :
COURSE ONE
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Reasoning with Equations and Inequalities |
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STRAND:
Represent and solve
equations and inequalities graphically.
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A-REI
12. Graph the solutions to a linear inequality in two
variables as a halfplane (excluding the boundary in the case
of a strict inequality), and graph the solution set to a
system of linear inequalities in two variables as the
intersection of the corresponding half-planes.
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MATH :
COURSE ONE
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Interpreting Functions |
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STRAND:
Understand the
Concept of a Function and use Function Notation. |
F-IF 1.
Understand that a function from one set (called the domain)
to another set (called the range) assigns to each element of
the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x)
denotes the output of f corresponding to the input x. The
graph of f is the graph of the equation y = f(x).
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MATH :
COURSE ONE
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Interpreting Functions |
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STRAND:
Understand the
Concept of a Function and use Function Notation. |
F-IF 2.
Use function notation, evaluate functions for inputs in
their domains, and interpret statements that use function
notation in terms of a context.
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MATH :
COURSE ONE
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Interpreting Functions |
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STRAND:
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.
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MATH :
COURSE ONE
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Interpreting Functions |
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STRAND:
Interpret functions
that arise in applications in terms of the context.
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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.★
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MATH :
COURSE ONE
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Interpreting Functions |
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STRAND:
Interpret functions
that arise in applications in terms of the context.
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F-IF 5.
Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes.
For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory,
then the positive integers would be an appropriate domain
for the function.★
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MATH :
COURSE ONE
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Interpreting Functions |
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STRAND:
Interpret functions
that arise in applications in terms of the context. |
F-IF 6.
Calculate and interpret the average rate of change of a
function (presented symbolically or as a table) over a
specified interval. Estimate the rate of change from a
graph.★
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MATH :
COURSE ONE
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Interpreting Functions |
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STRAND:
Analyze functions
using different representations.
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F-IF 7.
Graph functions expressed symbolically and show key features
of the graph, by hand in simple cases and using technology
for more complicated cases.★
a.
Graph linear and quadratic functions and show intercepts,
maxima, and minima.
b.
Graph exponential and logarithmic functions, showing
intercepts and end behavior, and trigonometric functions,
showing period, midline, and amplitude. At this level, for
part e, focus on exponential functions only |
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MATH :
COURSE ONE
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Interpreting Functions |
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STRAND:
Analyze functions
using different representations.
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F-IF 8.
Write a function defined by an expression in different but
equivalent forms to reveal and explain different properties
of the function.
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.
b. Use
the properties of exponents to interpret expressions for
exponential functions. For example, identify percent rate of
change in functions such as y = (1.02)t, y = (0.97)t, y =
(1.01)12t, y = (1.2)t/10, and classify them as representing
exponential growth or decay. |
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MATH :
COURSE ONE
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Interpreting Functions |
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STRAND:
Analyze functions
using different representations.
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F-IF 9.
Compare properties of two functions each represented in a
different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). For example, given a
graph of one quadratic function and an algebraic expression
for another, say which has the larger maximum.
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MATH :
COURSE ONE
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Building Functions |
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STRAND:
Build a Function that
Models a Relationship Between two Quantities.
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BF 1.
Write a function that describes a relationship between two
quantities.★
a.
Determine an explicit expression, a recursive process, or
steps for calculation from a context.
b.
Combine standard function types using arithmetic operations.
For example, build a function that models the temperature of
a cooling body by adding a constant function to a decaying
exponential, and relate these functions to the model.
c. (+)
Compose functions. For example, if T(y) is the temperature
in the atmosphere as a function of height, and h(t) is the
height of a weather balloon as a function of time, then
T(h(t)) is the temperature at the location of the weather
balloon as a function of time.
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MATH :
COURSE ONE
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Linear and Exponential Models |
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STRAND:
Construct and compare
linear and exponential models and solve problems.
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F-LE 1.
Distinguish between situations that can be modeled with
linear functions and with exponential functions.
a.
Prove that linear functions grow by equal differences over
equal intervals, and that exponential functions grow by
equal factors over equal intervals.
b.
Recognize situations in which one quantity changes at a
constant rate per unit interval relative to another.
c.
Recognize situations in which a quantity grows or decays by
a constant percent rate per unit interval relative to
another.
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MATH :
COURSE ONE
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Linear and Exponential Models |
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STRAND:
Construct and compare
linear and exponential models and solve problems.
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F-LE
2. Construct linear and exponential functions, including
arithmetic and geometric sequences, given a graph, a
description of a relationship, or two input-output pairs
(include reading these from a table). |
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MATH :
COURSE ONE
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Linear and Exponential Models |
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STRAND:
Construct and compare
linear and exponential models and solve problems.
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F-LE
3. Observe using graphs and tables that a quantity
increasing exponentially eventually exceeds a quantity
increasing linearly, quadratically, or (more generally) as a
polynomial function.
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MATH :
COURSE ONE
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Linear and Exponential Models |
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STRAND:
Interpret expressions
for functions in terms of the situation they model. |
F-LE.5
Interpret the parameters in a linear or exponential function
in terms of a context.
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MATH :
COURSE ONE
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Congruence |
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STRAND:
Experiment with
transformation 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. |
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Video |
Vertical & Supplementary Angles
Reviewing Angles, Arcs, & Sectors
The Basics of Angles: Rays, Endpoints, Sides, & Vertices
How to Measure Angles
What Are Angles?
Section A: Angles Defined
Circles: An Introduction
Defining Circles
Perpendicular Lines
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Math
Explanation |
Grades 07-08: Naming, Measuring, and Drawing Angles
Grades 07-08: Naming, Measuring, and Drawing Angles:
Complementary, Supplementary, and Congruent
Grades 07-08: Parallel and Perpendicular Lines
Grades 07-08: Parallel and Perpendicular Lines: Identifying
Parallel Lines
Grades 07-08: Parallel and Perpendicular Lines: Lines
Intersected by a Transversal |
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MATH :
COURSE ONE
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Expressing Geometric Properties with Equations |
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STRAND:
Use Coordinates to
Prove Simple Geometric Theorems Algebraically
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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 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). |
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MATH :
COURSE ONE
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Congruence |
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STRAND:
Experiment with
transformation in the plane. |
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).
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MATH :
COURSE ONE
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Geometric Measurement and Dimension |
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STRAND:
Explain Volume
Formulas and Use Them to Solve Problems |
G-MD 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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MATH :
COURSE ONE
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Geometric Measurement and Dimension |
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STRAND:
Explain Volume
Formulas and Use Them to Solve Problems |
G-MD 3.
Use volume formulas for cylinders, pyramids, cones, and
spheres to solve problems.★ |
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MATH :
COURSE ONE
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Interpreting Categorical and Quantitative Data |
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STRAND:
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S-ID
1.Represent data with plots on the real number line (dot
plots, histograms, and box plots). |
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MATH :
COURSE ONE
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Interpreting Categorical and Quantitative Data |
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STRAND:
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S-ID 3.
Interpret differences in shape, center, and spread in the
context of the data sets, accounting for possible effects of
extreme data points (outliers).
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MATH :
COURSE ONE
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Interpreting Categorical and Quantitative Data |
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STRAND:
Summarize, Represent,
and Interpret Data on Two Categorical and Quantitative
Variables.
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S-ID 5.
Summarize categorical data for two categories in two-way
frequency tables. Interpret relative frequencies in the
context of the data (including joint, marginal, and
conditional relative frequencies). Recognize possible
associations and trends in the data. |
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MATH :
COURSE ONE
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Interpreting Categorical and Quantitative Data |
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STRAND:
Summarize, Represent,
and Interpret Data on Two Categorical and Quantitative
Variables.
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S-ID 6.
Represent data on two quantitative variables on a scatter
plot, and describe how the variables are related.
a. Fit
a function to the data; use functions fitted to data to
solve problems in the context of the data. Use given
functions or choose a function suggested by the context.
Emphasize linear, quadratic, and exponential models.
b.
Informally assess the fit of a function by plotting and
analyzing residuals.
c. Fit
a linear function for a scatter plot that suggests a linear
association.
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MATH :
COURSE ONE
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Interpreting Categorical and Quantitative Data |
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STRAND:
Interpret Linear
Models
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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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MATH :
COURSE ONE
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Interpreting Categorical and Quantitative Data |
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STRAND:
Interpret Linear
Models
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S-ID
8. Compute (using technology) and interpret the correlation
coefficient of a linear fit. |
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MATH :
COURSE ONE
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Interpreting Categorical and Quantitative Data |
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STRAND:
Interpret Linear
Models
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S-ID
8. Compute (using technology) and interpret the correlation
coefficient of a linear fit. |
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