[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
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 an
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 descr
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
i
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 figu
[]
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
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 ex
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 distan
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 Pythagore
[G]
CONCEPTUAL CATEGORY: Geometry
Overview
Congruence
Expressing Geometric Properties with
Experiment with transformations in the
Equations
plane.
Understand congruence in terms of rigid
description a
[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.
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
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 interpret
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 proper
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 inte
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
di
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 f
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 multipl
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
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 f
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 distribu
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
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 struct
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 an
[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 sen
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
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).
[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
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 describ
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 throug