Academic standards list

Integrated Math 2 — Mathematics

Introduction

Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

The Real Number System

TSS.Math.M2.N.RN  —  Conceptual Category: Number and Quantity
 
Extend the properties of exponents to rational exponents.
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for
Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Quantities

TSS.Math.M2.N.Q  —  Conceptual Category: Number and Quantity
 
Reason quantitatively and use units to solve problems.
Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling.  
 

The Complex Number System

TSS.Math.M2.N.CN  —  Conceptual Category: Number and Quantity
 
Perform arithmetic operations with complex numbers.
Know there is a complex number i such that r^2 = -1, and every complex number has the form a + bi with a and b real.  
 
Know and use the relation r^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.  
 
Use complex numbers in polynomial identities and equations.
Solve quadratic equations with real coefficients that have complex solutions.  
 

Seeing Structure in Expressions

TSS.Math.M2.A.SSE  —  Conceptual Category: Algebra
 
Interpret the structure of expressions.
Interpret expressions that represent a quantity in terms of its context.
     There are 1 components within this standard.
 
Use the structure of an expression to identify ways to rewrite it.
 
Write expressions in equivalent forms to solve problems.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
     There are 2 components within this standard.

Arithmetic with Polynomials and Rational Expressions

TSS.Math.M2.A.APR  —  Conceptual Category: Algebra
 
Perform arithmetic operations on polynomials.
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and
 

Creating Equations

TSS.Math.M2.A.CED  —  Conceptual Category: Algebra
 
Create equations that describe numbers or relationships.
Create equations and inequalities in one variable and use them to solve problems.
Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Reasoning with Equations and Inequalities

TSS.Math.M2.A.REI  —  Conceptual Category: Algebra
 
Understand solving equations as a process of reasoning and explain the reasoning.
Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the
Solve equations and inequalities in one variable.
Solve quadratic equations and inequalities in one variable.
     There are 2 components within this standard.
Solve systems of equations.
Write and solve a system of linear equations in context.  
 
Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.  
 

Interpreting Functions

TSS.Math.M2.F.IF  —  Conceptual Category: Functions
 
Interpret functions that arise in applications in terms of the context.
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
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
Analyze functions using different representation.
Graph functions expressed symbolically and show key features of the graph, by hand and using technology.  
     There are 3 components within this standard.
 
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.  
     There are 2 components within this standard.
 
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).  
 

Building Functions

TSS.Math.M2.F.BF  —  Conceptual Category: Functions
 
Build a function that models a relationship between two quantities.
Write a function that describes a relationship between two quantities.
     There are 2 components within this standard.
Build new functions from existing functions.
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find  
 

Similarity, Right Triangles, And Trigonometry

TSS.Math.M2.G.SRT  —  Conceptual Category: Geometry
 
Understand similarity in terms of similarity transformations.
Verify informally the properties of dilations given by a center and a scale factor.
 
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
 
Prove theorems involving similarity.
Prove theorems about similar triangles.
 
Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.
Define trigonometric ratios and solve problems involving triangles.
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric
Explain and use the relationship between the sine and cosine of complementary angles.
Solve triangles.
     There are 2 components within this standard.

Geometric Measurement and Dimension

TSS.Math.M2.G.GMD  —  Conceptual Category: Geometry
 
Explain volume and surface area formulas and use them to solve problems.
Give an informal argument for the formulas for the circumference of a circle and the volume and surface area of a cylinder, cone, prism, and pyramid.  
 
Know and use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems.  
 

Interpreting Categorical and Quantitative Data

TSS.Math.M2.S.ID  —  Conceptual Category: Statistics and Probability
 
Summarize, represent, and interpret data on two categorical and quantitative variables.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.  
     There are 1 components within this standard.
 

Conditional Probability and the Rule of Probability.

TSS.Math.M2.S.CP  —  Conceptual Category: Statistics and Probability
 
Understand independence and conditional probability and use them to interpret data.
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or  
 
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this   
 
Know and understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional  
 
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.  
 
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A and interpret the answer in terms of the model.  
 
Know and 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.  
 
 
♦  Academic Standards marked with a diamond are "Supporting Content" within the grade level or course.
 
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