# Academic standards list

### Integrated Math 1 — 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.M1.N.Q — Conceptual Category: Number and Quantity

Reason quantitatively and use units to solve problems.

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… ♦

Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling. ♦

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. ♦

### Seeing Structure in Expressions

TSS.Math.M1.A.SSE — Conceptual Category: Algebra

Interpret the structure of expressions.

Interpret expressions that represent a quantity in terms of its context.

*There are 2 components within this standard*.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*.### Creating Equations

TSS.Math.M1.A.CED — Conceptual Category: Algebra

Create equations that describe numbers or relationships

Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with…

Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable…

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

### Reasoning with Equations and Inequalities

TSS.Math.M1.A.REI — Conceptual Category: Algebra

Solve equations and inequalities in one variable.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Solve systems of equations.

Represent and solve equations and inequalities graphically.

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…

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) =…

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the…

### Interpreting Functions

TSS.Math.M1.F.IF — Conceptual Category: Functions

Understand the concept of a function and use function notation.

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…

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

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 representations.

Graph functions expressed symbolically and show key features of the graph, by hand and using technology. ♦

*There are 1 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.M1.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 1 components within this standard*.Write arithmetic and geometric sequences with an explicit formula and use them to model situations.

### Linear and Exponential Models

TSS.Math.M1.F.LE — Conceptual Category: Functions

Construct and compare linear and exponential models and solve problems.

Distinguish between situations that can be modeled with linear functions and with exponential functions. ♦

*There are 3 components within this standard*.Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or… ♦

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.

Interpret expressions for functions in terms of the situation they model.

### Congruence

TSS.Math.M1.G.CO — Conceptual Category: Geometry

Experiment with transformations in the plane.

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, plane,… ♦

Represent transformations in the plane in multiple ways, including technology. Describe transformations as functions that take points in the plane… ♦

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry the shape onto itself. ♦

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. ♦

Given a geometric figure and a rigid motion, draw the image of the figure in multiple ways, including technology. Specify a sequence of rigid motions… ♦

Understand congruence in terms of rigid motions.

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 motions to show that two triangles are congruent if and only if corresponding pairs of sides and…

Explain how the criteria for triangle congruence (ASA, SAS, AAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Prove geometric theorems.

### Interpreting Categorical and Quantitative Data

TSS.Math.M1.S.ID — Conceptual Category: Statistics and Probability

Summarize, represent, and interpret data on a single count or measurement variable.

Represent single or multiple data sets with dot plots, histograms, stem plots (stem and leaf), and box plots. ♦

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of… ♦

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). ♦

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*.Interpret linear models.

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

♦ Academic Standards marked with a diamond are "

*Supporting Content*" within the grade level or course.

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