Academic standards list

Integrated Math 3 — 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.

Quantities

TSS.Math.M3.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.  
 

Seeing Structure in Expressions

TSS.Math.M3.A.SSE  —  Conceptual Category: Algebra
 
Interpret the structure of expressions.
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 1 components within this standard.
Recognize a finite geometric series (when the common ratio is not 1), and know and use the sum formula to solve problems in context.

Arithmetic with Polynomials and Rational Expressions

TSS.Math.M3.A.APR  —  Conceptual Category: Algebra
 
Understand the relationship between zeros and factors of polynomials.
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x -
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the
Use polynomial identities to solve problems.
Know and use polynomial identities to describe numerical relationships.  
 
Rewrite rational expressions.
Rewrite rational expressions in different forms.  
 

Creating Equations

TSS.Math.M3.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.M3.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 rational and radical equations in one variable, and identify extraneous solutions when they exist.
 
Represent and solve equations graphically.
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) =

Interpreting Functions

TSS.Math.M3.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
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 representations.
Graph functions expressed symbolically and show key features of the graph, by hand and using technology.  
     There are 4 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.M3.F.BF  —  Conceptual Category: Functions
 
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  
 
Find inverse functions.  
     There are 1 components within this standard.
 

Linear, Quadratic, and Exponential Models

TSS.Math.M3.F.LE  —  Conceptual Category: Functions
 
Construct and compare linear, quadratic, and exponential models and solve problems.
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more  
 
For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the  
 

Trigonometric Functions

TSS.Math.M3.F.TF  —  Conceptual Category: Functions
 
Extend the domain of trigonometric functions using the unit circle.
Understand and use radian measure of an angle.  
     There are 2 components within this standard.
 
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures  
 
Prove and apply trigonometric identities.
Use trigonometric identities to find values of trig functions.  
     There are 2 components within this standard.
 

Congruence

TSS.Math.M3.G.CO  —  Conceptual Category: Geometry
 
Make geometric constructions.
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic  
 

Circles

TSS.Math.M3.G.C  —  Conceptual Category: Geometry
 
Understand and apply theorems about circles.
Recognize that all circles are similar.  
 
Identify and describe relationships among inscribed angles, radii, and chords.  
 
Construct the incenter and circumcenter of a triangle and use their properties to solve problems in context.  
 
Find areas of sectors of circles.
Find the area of a sector of a circle in a real-world context.  
 

Expressing Geometric Properties with Equations

TSS.Math.M3.G.GPE  —  Conceptual Category: Geometry
 
Translate between the geometric description and the equation for a circle.
Know and write the equation of a circle of given center and radius using the Pythagorean Theorem.  
 
Use coordinates to prove simple geometric theorems algebraically.
Use coordinates to prove simple geometric theorems algebraically.
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Know and use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Modeling with Geometry

TSS.Math.M3.G.MG  —  Conceptual Category: Geometry
 
Apply geometric concepts in modeling situations.
Use geometric shapes, their measures, and their properties to describe objects.
Apply geometric methods to solve real-world problems.

Interpreting Categorical and Quantitative Data

TSS.Math.M3.S.ID  —  Conceptual Category: Statistics and Probability
 
Summarize, represent, and interpret data on a single count or measurement variable.
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.  
 
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 2 components within this standard.
 

Making Inferences and Justify Conclusions

TSS.Math.M3.S.IC  —  Conceptual Category: Statistics and Probability
 
Understand and evaluate random processes underlying statistical experiments.
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
 
Decide if a specified model is consistent with results from a given datagenerating process (e.g., using simulation).
 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
 
Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context.
 
 
♦  Academic Standards marked with a diamond are "Supporting Content" within the grade level or course.
 
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