[F]
Overview
CONCEPTUAL CATEGORY: Functions
Interpreting Functions
Model periodic phenomena with
trigonometric functions.
Interpret functions that arise in
applications in terms of the context.
Extend the domain of trigonometric
functions using the unit c
Grade 6
(3) Students understand the use of variables in mathematical expressions. They write expressions
and equations that correspond to given situations, evaluate expressions, and use expressions and
formulas to solve problems. Students understand that
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: inter
Summarize, represent, and interpret data on two categorical and quantitative variables. 1
5.
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies
in the context of the data (including joint, marginal, a
Understand congruence in terms of rigid motions.
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
[]
CONCEPTUAL CATEGORY: Modeling
Graphing utilities, spreadsheets, computer algebra systems, and dynamic geometry software are powerful
tools that can be used to model purely mathematical phenomena (e.g., the behavior of polynomials) as
well as physical p
Content Standards
Seeing Structure in Expressions
A-SSE
Interpret the structure of expressions.
1.
Interpret expressions that represent a quantity in terms of its context.
a.
Interpret parts of an expression, such as terms, factors, and coefficients.
b.
5.
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different
proportional relationships represented in different ways. For example, compare a distance-time graph to a
distance-time equation to determine
Prove theorems involving similarity.1
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.
5.
Use con
[G]
CONCEPTUAL CATEGORY: Geometry
Overview
Congruence
Expressing Geometric Properties with
Experiment with transformations in the
Equations
plane.
Understand congruence in terms of rigid
description and the equation for a conic
motions.
section.
Prove geo
[N]
CONCEPTUAL CATEGORY: Number and Quantity
Overview
The Real Number System
Extend the properties of exponents to
Perform operations on matrices and use
matrices in applications.
rational exponents.
Use properties of rational and irrational
STANDARDS FOR
Arithmetic with Polynomials and Rational Expressions
A-APR
Perform arithmetic operations on polynomials.
1.
Understand that polynomials form a system analogous to the integers, namely, they are closed under the
operations of addition, subtraction, and mul
Introduction: High School Content Standards/CONCEPTUAL CATEGORIES
The star symbol () following the standards in the illustration indicates those are also Modeling
standards. Modeling is best interpreted not as a collection of isolated topics but in relati
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 exponent
MODEL INTEGRATED PATHWAY: Model Mathematics II
(4) Building on probability concepts that began in the middle grades, students use the language
of set theory to expand their ability to compute and interpret theoretical and experimental
probabilities for co
Grade 7
by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures
below zero), students explain and interpret the rules for adding, subtracting, multiplying, and
dividing with negative numbers. They use the arithmetic o
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 wh
Perform arithmetic operations on polynomials.
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.
MA.1.
MODEL INTEGRATED PATHWAY: Model Mathematics III
Overview
Number and Quantity
process of reasoning and explain the
The Complex Number System
reasoning.
Use complex numbers in polynomial
identities and equations.
Understand solving equations as a
Represent
Content Standards
Number and Quantity
The Real Number System
N-RN
Extend the properties of exponents to rational exponents.
1.
Explain how the definition of the meaning of rational exponents follows from extending the properties of
integer exponents to th
MODEL TRADITIONAL PATHWAY: Model Algebra II
(4) Students see how the visual displays and summary statistics they learned in earlier grades
relate to different types of data and to probability distributions. They identify different ways
of collecting datai
Introduction
The fundamental purpose of the Model Geometry course is to formalize and extend students geometric
experiences from the middle grades. This course is comprised of standards selected from the high school
conceptual categories, which were writt
12.
(+) Work with 2 2 matrices as transformations of the plane, and interpret the absolute value of the
determinant in terms of area.
Algebra
Seeing Structure in Expressions
A-SSE
Interpret the structure of expressions.
1.
Interpret expressions that repre
Content Standards
Number and Quantity
The Complex Number System
N-CN
Perform arithmetic operations with complex numbers.
3.
(+)
Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex
numbers.
Represent complex numbe
[S]
CONCEPTUAL CATEGORY: Statistics and Probability
Introduction
Decisions or predictions are often based on datanumbers in context. These decisions or predictions
would be easy if the data always sent a clear message, but the message is often obscured by
2.
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile,
BTUs per cubic foot).
3.
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy
physical constraints
Using Probability to Make Decisions
S-MD
Use probability to evaluate outcomes of decisions.1
6.
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
7.
(+) Analyze decisions and strategies using probabili
[A]
CONCEPTUAL CATEGORY: Algebra
A spreadsheet or a computer algebra system (CAS) can be used to experiment with algebraic expressions,
perform complicated algebraic manipulations, and understand how algebraic manipulations behave.
Equations and Inequalit
Content Standards
Ratios and Proportional Relationships
6.RP
Understand ratio concepts and use ratio reasoning to solve problems.
1.
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two
quantities. For exam
Grade 8
The Standards for Mathematical Practice complement the content standards so that students increasingly engage
with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle, and
high school years.
Ove
1
Application to Students with Disabilities
The Common Core State Standards articulate rigorous grade-level expectations in the areas of
mathematics and English language arts. These standards identify the knowledge and skills students need
in order to be
MODEL ADVANCED COURSE: Model Precalculus
Introduction
Precalculus combines the trigonometric, geometric, and algebraic techniques needed to prepare students
for the study of calculus, and strengthens students conceptual understanding of problems and
mathe
MODEL TRADITIONAL PATHWAY: Model Algebra I
Overview
Number and Quantity
process of reasoning and explain the
The Real Number System
Quantities
Solve equations and inequalities in one
variable.
Use properties of rational and irrational
numbers.
reasoning.
MODEL TRADITIONAL PATHWAY: Model Geometry
Overview
circles.
Number and Quantity
Quantities
Expressing Geometric Properties with Equations
Geometry
section.
Experiment with transformations in the
plane.
Understand congruence in terms of rigid
motions.
Prov
Introduction:
High School Content Standards/MODEL PATHWAYS AND MODEL COURSES
mathematics, for building their understanding of mathematics, and for preparing them for future success.
Development of the Model Pathways into instructional programs will requir