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Texas digits Grade 6 Standards
use numerical or graphical representations to solve problems
use numerical or graphical representations to analyze problems
summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution.
summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution
use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution
represent numeric data graphically, including dot plots, stem-andleaf plots, histograms, and box plots
use coordinate geometry to identify locations on a plane
use equations and inequalities to solve problems
model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts
- How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths?
- How Do You Find the Area of a Rectangle?
- How Do You Solve an Equation Using Addition?
- How Do You Solve an Equation Using Division?
- How Do You Use Addition to Solve an Inequality Word Problem?
- What is a Solution to an Inequality?
- What is the Triangle Sum Theorem?
determine if the given value(s) make(s) one-variable, one-step equations or inequalities true.
use equations and inequalities to represent situations
write corresponding real-world problems given one-variable, onestep equations or inequalities.
represent solutions for one-variable, one-step equations and inequalities on number lines
write one-variable, one-step equations and inequalities to represent constraints or conditions within problems
- How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths?
- How Do You Find the Area of a Rectangle?
- How Do You Translate a Phrase with One Variable and Number Into a Mathematical Expression?
- How Do You Use Addition to Solve an Inequality Word Problem?
- What is the Triangle Sum Theorem?
- What's an Inequality?
use geometry to represent relationships and solve problems
determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers.
- How Do You Find the Area of a Rectangle?
- How Do You Find the Area of a Triangle?
- How Do You Multiply A Whole Number By A Fraction?
- How Do You Multiply Decimals?
- How Do You Multiply Mixed Numbers?
- What Does It Mean to Divide Fractions?
- What is the Formula for the Area of a Parallelogram?
- What is the Formula for the Area of a Trapezoid?
- What is the Formula for the Area of a Triangle?
- What is the Formula for the Volume of a Prism?
write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers
model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes
extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle
develop concepts of expressions and equations
generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties.
- How Do You Add Two Negative Numbers?
- How Do You Represent Real World Situations Using Integers?
- How Do You Turn a Fraction Into a Terminating Decimal?
- What are the Identity Properties of Addition and Multiplication?
- What Does It Mean to Divide Fractions?
- What is an Equation?
- What is the Associative Property of Addition?
- What is the Commutative Property of Addition?
- What is the Distributive Property?
determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations
distinguish between expressions and equations verbally, numerically, and algebraically
generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization
use multiple representations to describe algebraic relationships
represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b.
- How Do You Graph a Relationship Between Two Variables?
- How Do You Translate a Phrase with One Variable and Number Into a Mathematical Expression?
- How Do You Write a Rule for a Table?
- What Are Dependent and Independent Variables?
- What Are Numerical and Algebraic Expressions?
- What are the Identity Properties of Addition and Multiplication?
write an equation that represents the relationship between independent and dependent quantities from a table
identify independent and dependent quantities from tables and graphs
solve problems involving proportional relationships
use equivalent fractions, decimals, and percents to show equal parts of the same whole.
solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models
represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions
develop an understanding of proportional relationships in problem situations
convert units within a measurement system, including the use of proportions and unit rates.
generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money
represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers
represent ratios and percents with concrete models, fractions, and decimals
give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients
give examples of ratios as multiplicative comparisons of two quantities describing the same attribute
apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates
compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships
represent addition, subtraction, multiplication, and division while solving problems and justifying solutions
add, subtract, multiply, and divide integers fluently
represent integer operations with concrete models and connect the actions with the models to standardized algorithms
determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one
recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values
represent and use rational numbers in a variety of forms
multiply and divide positive rational numbers fluently
- How Do You Divide a Decimal by a Decimal?
- How Do You Divide Fractions?
- How Do You Multiply A Whole Number By A Fraction?
- How Do You Multiply Decimals?
- How Do You Multiply Mixed Numbers?
- How Do You Solve an Equation Using Division?
- How Do You Turn a Fraction Into a Terminating Decimal?
- What Does It Mean to Divide Fractions?
extend representations for division to include fraction notation such as a/b represents the same number as a รท b where b does not equal 0
order a set of rational numbers arising from mathematical and realworld contexts
locate, compare, and order integers and rational numbers using a number line
identify a number, its opposite, and its absolute value
classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers
acquire and demonstrate mathematical understanding
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
- How Do You Figure Out the Sign of a Product or Quotient?
- How Do You Find Equivalent Ratios by Making a Table?
- How Do You Find Equivalent Ratios?
- How Do You Find the Area of a Rectangle?
- How Do You Find the Area of a Triangle?
- How Do You Find the Range of a Data Set?
- How Do You Find the Surface Area of a Pyramid Using a Net?
- How Do You Multiply Mixed Numbers?
- How Do You Put the Sides of a Triangle in Order According to Size if You Know Two Angles of the Triangle?
- How Do You Turn a Fraction Into a Terminating Decimal?
- How Do You Use an Equation to Find a Part of a Whole?
- How Do You Write the Prime Factorization of a Number Using Exponents?
- What are Equivalent Ratios?
- What Are Numerical and Algebraic Expressions?
- What are Rates and Unit Rates?
- What is a Box-and-Whisker Plot?
- What is a Line Plot?
- What is a Stem-And-Leaf Plot?
- What is an Equation?
- What is the Associative Property of Addition?
- What is the Commutative Property of Addition?
- What is the Formula for the Volume of a Prism?
- What is the Interquartile Range?
- What is the Triangle Sum Theorem?
- What's a Percent?
- What's a Ratio?
- What's an Inequality?
- What's the Order of Operations?
analyze mathematical relationships to connect and communicate mathematical ideas
- How Do You Find Equivalent Ratios?
- How Do You Find the Area of a Rectangle in the Coordinate Plane?
- How Do You Find the Area of a Rectangle?
- How Do You Find the Area of a Triangle?
- How Do You Find the Range of a Data Set?
- How Do You Find the Surface Area of a Pyramid Using a Net?
- How Do You Find the Surface Area of a Rectangular Prism Using a Net?
- How Do You Graph a Rectangle on a Coordinate Plane?
- How Do You Graph a Relationship Between Two Variables?
- How Do You Multiply A Whole Number By A Fraction?
- How Do You Put Fractions and Decimals in Order?
- How Do You Put the Sides of a Triangle in Order According to Size if You Know Two Angles of the Triangle?
- How Do You Represent Real World Situations Using Integers?
- How Do You Solve an Equation Using Addition?
- How Do You Solve an Equation Using Division?
- How Do You Turn a Fraction Into a Terminating Decimal?
- How Do You Use an Equation to Find a Part of a Whole?
- How Do You Write a Rule for a Table?
- What are Equivalent Ratios?
- What are Rates and Unit Rates?
- What are the Identity Properties of Addition and Multiplication?
- What is a Stem-And-Leaf Plot?
- What is the Formula for the Area of a Parallelogram?
- What is the Formula for the Area of a Trapezoid?
- What is the Formula for the Area of a Triangle?
- What is the Formula for the Volume of a Prism?
- What is the Interquartile Range?
- What is the Mode of a Data Set?
- What is the Triangle Sum Theorem?
- What's a Ratio?
create and use representations to organize, record, and communicate mathematical ideas
- How Do You Find Equivalent Ratios by Making a Table?
- How Do You Find Equivalent Ratios?
- How Do You Find Percents Mentally Using Fractions?
- How Do You Find the Area of a Rectangle?
- How Do You Graph a Relationship Between Two Variables?
- How Do You Put Fractions and Decimals in Order?
- How Do You Solve an Equation Using Addition?
- How Do You Turn a Fraction Into a Terminating Decimal?
- How Do You Use an Equation to Find a Part of a Whole?
- How Do You Write a Rule for a Table?
- What are Equivalent Ratios?
- What Are Numerical and Algebraic Expressions?
- What are the Identity Properties of Addition and Multiplication?
- What is a Box-and-Whisker Plot?
- What is a Histogram?
- What is a Line Plot?
- What is a Stem-And-Leaf Plot?
- What is the Mode of a Data Set?
- What is the Triangle Sum Theorem?
- What's a Percent?
- What's a Ratio?
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
- How Do You Add Two Negative Numbers?
- How Do You Compare Integers Using a Number Line?
- How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths?
- How Do You Divide a Decimal by a Decimal?
- How Do You Divide Fractions?
- How Do You Figure Out the Sign of a Product or Quotient?
- How Do You Find Equivalent Ratios by Making a Table?
- How Do You Find Percents Mentally Using Fractions?
- How Do You Find the Area of a Rectangle in the Coordinate Plane?
- How Do You Find the Area of a Rectangle?
- How Do You Find the Mean of a Data Set?
- How Do You Find the Range of a Data Set?
- How Do You Find the Surface Area of a Rectangular Prism Using a Net?
- How Do You Graph a Rectangle on a Coordinate Plane?
- How Do You Graph a Relationship Between Two Variables?
- How Do You Identify Points on a Graph?
- How Do You Multiply A Whole Number By A Fraction?
- How Do You Multiply Mixed Numbers?
- How Do You Put Fractions and Decimals in Order?
- How Do You Put the Sides of a Triangle in Order According to Size if You Know Two Angles of the Triangle?
- How Do You Represent Real World Situations Using Integers?
- How Do You Rewrite Subtraction as Addition?
- How Do You Turn a Fraction Into a Terminating Decimal?
- How Do You Use Addition to Solve an Inequality Word Problem?
- How Do You Use an Equation to Find a Part of a Whole?
- How Do You Write a Rule for a Table?
- How Do You Write the Prime Factorization of a Number Using Exponents?
- What Are Dependent and Independent Variables?
- What are Rates and Unit Rates?
- What are the Identity Properties of Addition and Multiplication?
- What Does Absolute Value Mean?
- What is a Box-and-Whisker Plot?
- What is a Histogram?
- What is a Line Plot?
- What is a Solution to an Inequality?
- What is a Stem-And-Leaf Plot?
- What is an Equation?
- What is the Associative Property of Addition?
- What is the Commutative Property of Addition?
- What is the Distributive Property?
- What is the Interquartile Range?
- What is the Mode of a Data Set?
- What is the Triangle Sum Theorem?
- What's a Percent?
- What's a Ratio?
- What's a Rational Number?
- What's an Inequality?
- What's the Order of Operations?
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
- How Do You Add Two Negative Numbers?
- How Do You Compare Integers Using a Number Line?
- How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths?
- How Do You Divide a Decimal by a Decimal?
- How Do You Divide Fractions?
- How Do You Evaluate an Algebraic Expression with One Variable?
- How Do You Figure Out the Sign of a Product or Quotient?
- How Do You Find the Area of a Rectangle in the Coordinate Plane?
- How Do You Find the Mean of a Data Set?
- How Do You Find the Range of a Data Set?
- How Do You Find the Surface Area of a Pyramid Using a Net?
- How Do You Find the Surface Area of a Rectangular Prism Using a Net?
- How Do You Identify Points on a Graph?
- How Do You Multiply A Whole Number By A Fraction?
- How Do You Multiply Decimals?
- How Do You Multiply Mixed Numbers?
- How Do You Put Fractions and Decimals in Order?
- How Do You Represent Real World Situations Using Integers?
- How Do You Rewrite Subtraction as Addition?
- How Do You Solve an Equation Using Addition?
- How Do You Solve an Equation Using Division?
- How Do You Turn a Fraction Into a Terminating Decimal?
- How Do You Use an Equation to Find a Part of a Whole?
- How Do You Write the Prime Factorization of a Number Using Exponents?
- What Does Absolute Value Mean?
- What Does It Mean to Divide Fractions?
- What is a Solution to an Inequality?
- What is an Equation?
- What's the Order of Operations?
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution
- How Do You Divide a Decimal by a Decimal?
- How Do You Multiply A Whole Number By A Fraction?
- How Do You Multiply Decimals?
- How Do You Multiply Mixed Numbers?
- How Do You Solve an Equation Using Addition?
- How Do You Solve an Equation Using Division?
- How Do You Use an Equation to Find a Part of a Whole?
- What Does It Mean to Divide Fractions?
- What is a Solution to an Inequality?
- What is the Associative Property of Addition?
apply mathematics to problems arising in everyday life, society, and the workplace
- How Do You Convert Gallons to Pints?
- How Do You Evaluate an Algebraic Expression with One Variable?
- How Do You Find the Area of a Rectangle?
- How Do You Find the Surface Area of a Pyramid Using a Net?
- How Do You Find the Surface Area of a Rectangular Prism Using a Net?
- How Do You Use an Equation to Find a Part of a Whole?
- What Does It Mean to Divide Fractions?
- What is a Line Plot?
- What's a Percent?
Texas digits Grade 7 Standards
develop an economic way of thinking and problem solving useful in ones life as a knowledgeable consumer and investor
use statistical representations to analyze data
compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads
use data from a random sample to make inferences about a population
compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations
solve one-variable equations and inequalities
model and solve one-variable, two-step equations and inequalities
- How Do You Find a Missing Angle in a Right Triangle?
- How Do You Solve a One-Step Inequality Using Subtraction?
- How Do You Solve a Two-Step Equation?
- How Do You Solve a Two-Step Inequality?
- How Do You Solve an Equation Using Addition?
- How Do You Write an Equation From a Word Problem?
- What are Acute, Obtuse, Right, and Straight Angles?
- What is a Circle?
determine if the given value(s) make(s) one-variable, two-step equations and inequalities true
write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships
use one-variable equations and inequalities to represent situations
solve geometric problems
solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids
determine the circumference and area of circles
determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles
solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shapes net
develop geometric relationships with volume
model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas
explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas
use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas
represent linear relationships using multiple representations
use probability and statistics to describe or solve problems involving proportional relationships
select and use different simulations to represent simple and compound events with and without technology
make predictions and determine solutions using experimental data for simple and compound events
represent sample spaces for simple and compound events using lists and tree diagrams
make predictions and determine solutions using theoretical probability for simple and compound events
find the probabilities of a simple event and its complement and describe the relationship between the two
solve problems using qualitative and quantitative predictions and comparisons from simple experiments
determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces
solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents
use geometry to describe or solve problems involving proportional relationships
represent and solve problems involving proportional relationships
represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt
- How Do You Find the Rate of Change Between Two Points on a Graph?
- What is the Formula for Compound Interest?
- What is the Formula for Simple Interest?
- What's the Constant of Variation?
- What's the Direct Variation or Direct Proportionality Formula?
- What's the Formula Connecting Distance, Speed, and Time?
- What's the Y-Intercept?
calculate unit rates from rates in mathematical and real-world problems
determine the constant of proportionality (k = y/x) within mathematical and real-world problems
solve problems involving ratios, rates, and percents, including multistep problems involving percent increase and percent decrease, and financial literacy problems
- How Do You Figure Out a Price Markup?
- How Do You Figure Out How Much Something is Marked Down?
- How Do You Figure Out Sales Tax?
- What are Equivalent Ratios?
- What are Rates and Unit Rates?
- What is a Scale Drawing?
- What is the Formula for Compound Interest?
- What is the Formula for Simple Interest?
- What is the Formula for the Area of a Circle?
- What is the Percent Equation?
- What's a Percent of Change?
- What's the Constant of Variation?
- What's the Direct Variation or Direct Proportionality Formula?
- What's the Formula Connecting Distance, Speed, and Time?
convert between measurement systems, including the use of proportions and the use of unit rates
add, subtract, multiply, and divide while solving problems and justifying solutions
add, subtract, multiply, and divide rational numbers fluently
- How Do You Add Two Negative Numbers?
- How Do You Convert a Temperature from Fahrenheit to Celsius?
- How Do You Figure Out Sales Tax?
- How Do You Figure Out the Sign of a Product or Quotient?
- How Do You Rewrite Subtraction as Addition?
- What is a Scale Drawing?
- What is the Percent Equation?
- What's a Rational Number?
- What's the Direct Variation or Direct Proportionality Formula?
- What's the Formula Connecting Distance, Speed, and Time?
apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers
- How Do You Add Two Negative Numbers?
- How Do You Convert a Temperature from Fahrenheit to Celsius?
- How Do You Figure Out a Price Markup?
- How Do You Figure Out Sales Tax?
- How Do You Figure Out the Sign of a Product or Quotient?
- How Do You Find the Surface Area of a Pyramid Using a Net?
- How Do You Find the Surface Area of a Rectangular Prism Using a Net?
- How Do You Rewrite Subtraction as Addition?
- How Do You Solve an Equation Using Addition?
- What is a Scale Drawing?
- What is Circumference?
- What is the Formula for the Area of a Circle?
- What is the Formula for the Volume of a Prism?
- What is the Percent Equation?
- What's the Direct Variation or Direct Proportionality Formula?
- What's the Formula Connecting Distance, Speed, and Time?
represent and use rational numbers in a variety of forms
acquire and demonstrate mathematical understanding
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
- How Do You Add Two Negative Numbers?
- How Do You Convert a Temperature from Fahrenheit to Celsius?
- How Do You Convert Yards to Meters?
- How Do You Figure Out the Sign of a Product or Quotient?
- How Do You Find the Area of a Composite Figure?
- How Do You Find the Probability of a Simple Event?
- How Do You Find the Surface Area of a Pyramid Using a Net?
- How Do You Find the Surface Area of a Rectangular Prism Using a Net?
- How Do You Rewrite Subtraction as Addition?
- How Do You Solve a One-Step Inequality Using Subtraction?
- How Do You Solve a Two-Step Equation?
- How Do You Solve a Two-Step Inequality?
- How Do You Solve an Equation Using Addition?
- How Do You Use a Sample to Make Predictions About a Population?
- How Do You Use a Simulation to Solve a Problem?
- What are Acute, Obtuse, Right, and Straight Angles?
- What are Equivalent Ratios?
- What are Rates and Unit Rates?
- What are Supplementary Angles?
- What is a Circle?
- What is a Simulation?
- What is an Unbiased Sample?
- What is Circumference?
- What is Experimental Probability?
- What is the Distributive Property?
- What is the Formula for the Area of a Circle?
- What is the Formula for the Volume of a Prism?
- What is the Formula for the Volume of a Pyramid?
- What's a Percent of Change?
- What's a Rational Number?
- What's the Formula Connecting Distance, Speed, and Time?
apply mathematics to problems arising in everyday life, society, and the workplace
- How Do You Convert a Temperature from Fahrenheit to Celsius?
- How Do You Figure Out a Price Markup?
- How Do You Figure Out How Much Something is Marked Down?
- How Do You Figure Out Sales Tax?
- How Do You Find the Area of a Composite Figure?
- How Do You Find the Mean of a Data Set?
- How Do You Solve a Two-Step Equation by Distributing a Fraction First?
- How Do You Use a Sample to Make Predictions About a Population?
- How Do You Write an Equation From a Word Problem?
- What are Like Terms?
- What are Similar Figures?
- What is a Net?
- What is a Scale Drawing?
- What is an Unbiased Sample?
- What is the Distributive Property?
- What is the Formula for Compound Interest?
- What is the Formula for Simple Interest?
- What's a Percent of Change?
- What's the Direct Variation or Direct Proportionality Formula?
- What's the Formula Connecting Distance, Speed, and Time?
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution
- How Do You Convert Yards to Meters?
- How Do You Find the Surface Area of a Rectangular Prism Using a Net?
- How Do You Solve a One-Step Inequality Using Subtraction?
- How Do You Solve a Two-Step Inequality?
- What is the Formula for the Volume of a Prism?
- What's the Formula Connecting Distance, Speed, and Time?
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
- How Do You Add Two Negative Numbers?
- How Do You Determine Which Operations to Use in a Word Problem?
- How Do You Figure Out the Sign of a Product or Quotient?
- How Do You Find a Missing Angle in a Right Triangle?
- How Do You Find the Area of a Composite Figure?
- How Do You Find the Probability of a Simple Event?
- How Do You Find the Rate of Change Between Two Points on a Graph?
- How Do You Graph a Linear Equation by Making a Table?
- How Do You Rewrite Subtraction as Addition?
- How Do You Solve a One-Step Inequality Using Subtraction?
- How Do You Solve a Two-Step Equation by Distributing a Fraction First?
- How Do You Solve a Two-Step Inequality?
- How Do You Solve and Graph a Two-Step Inequality?
- How Do You Use a Sample to Make Predictions About a Population?
- How Do You Write an Equation From a Word Problem?
- What are Complementary Angles?
- What are Compound Events?
- What are Equivalent Ratios?
- What are Like Terms?
- What are Rates and Unit Rates?
- What are Similar Figures?
- What are Vertical Angles?
- What is a Circle Graph?
- What is a Net?
- What is a Sample Space?
- What is a Scale Drawing?
- What is an Unbiased Sample?
- What is Circumference?
- What is Experimental Probability?
- What is Probability?
- What is the Distributive Property?
- What is the Formula for Compound Interest?
- What is the Formula for Simple Interest?
- What is the Formula for the Area of a Circle?
- What is the Percent Equation?
- What's a Percent of Change?
- What's a Rational Number?
- What's the Constant of Variation?
- What's the Direct Variation or Direct Proportionality Formula?
- What's the Formula Connecting Distance, Speed, and Time?
- What's the Y-Intercept?
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
- How Do You Add Two Negative Numbers?
- How Do You Compare Two Data Sets Using Box-and-Whisker Plots?
- How Do You Determine Which Operations to Use in a Word Problem?
- How Do You Figure Out a Price Markup?
- How Do You Figure Out Sales Tax?
- How Do You Find a Missing Angle in a Right Triangle?
- How Do You Find the Area of a Composite Figure?
- How Do You Find the Mean of a Data Set?
- How Do You Find the Probability of a Simple Event?
- How Do You Find the Surface Area of a Pyramid Using a Net?
- How Do You Rewrite Subtraction as Addition?
- How Do You Solve a Two-Step Equation?
- How Do You Solve and Graph a Two-Step Inequality?
- How Do You Use a Sample to Make Predictions About a Population?
- How Do You Use a Tree Diagram to Count the Number of Outcomes in a Sample Space?
- What are Acute, Obtuse, Right, and Straight Angles?
- What are Complementary Angles?
- What are Like Terms?
- What are Rates and Unit Rates?
- What are Similar Figures?
- What are Supplementary Angles?
- What are Vertical Angles?
- What is a Circle Graph?
- What is a Sample Space?
- What is a Scale Drawing?
- What is an Unbiased Sample?
- What is Experimental Probability?
- What is the Formula for Compound Interest?
- What is the Formula for Simple Interest?
- What is the Percent Equation?
- What's a Percent of Change?
- What's a Rational Number?
- What's the Constant of Variation?
- What's the Direct Variation or Direct Proportionality Formula?
create and use representations to organize, record, and communicate mathematical ideas
- How Do You Compare Two Data Sets Using Box-and-Whisker Plots?
- How Do You Figure Out the Sign of a Product or Quotient?
- How Do You Find a Missing Angle in a Right Triangle?
- How Do You Find the Probability of Independent Events?
- How Do You Find the Surface Area of a Rectangular Prism Using a Net?
- How Do You Graph a Linear Equation by Making a Table?
- How Do You Solve a Two-Step Equation by Distributing a Fraction First?
- How Do You Use a Tree Diagram to Count the Number of Outcomes in a Sample Space?
- What are Acute, Obtuse, Right, and Straight Angles?
- What are Adjacent Angles?
- What are Complementary Angles?
- What are Supplementary Angles?
- What are Vertical Angles?
- What is a Circle?
- What is a Net?
- What is a Simulation?
- What is an Unbiased Sample?
- What is the Distributive Property?
- What is the Formula for Compound Interest?
- What is the Fundamental Counting Principle?
- What's the Constant of Variation?
- What's the Direct Variation or Direct Proportionality Formula?
analyze mathematical relationships to connect and communicate mathematical ideas
- How Do You Compare Two Data Sets Using Box-and-Whisker Plots?
- How Do You Convert a Temperature from Fahrenheit to Celsius?
- How Do You Determine Which Operations to Use in a Word Problem?
- How Do You Find a Missing Angle in a Right Triangle?
- How Do You Find the Area of a Composite Figure?
- How Do You Find the Probability of a Simple Event?
- How Do You Find the Probability of Independent Events?
- How Do You Find the Rate of Change Between Two Points on a Graph?
- How Do You Graph a Linear Equation by Making a Table?
- How Do You Use a Sample to Make Predictions About a Population?
- How Do You Use a Simulation to Solve a Problem?
- How Do You Use a Tree Diagram to Count the Number of Outcomes in a Sample Space?
- What are Compound Events?
- What are Similar Figures?
- What is a Circle Graph?
- What is a Sample Space?
- What is a Simulation?
- What is an Unbiased Sample?
- What is Circumference?
- What is Experimental Probability?
- What is Probability?
- What is the Distributive Property?
- What is the Formula for Simple Interest?
- What is the Formula for the Area of a Circle?
- What is the Formula for the Volume of a Prism?
- What is the Formula for the Volume of a Pyramid?
- What is the Fundamental Counting Principle?
- What is the Percent Equation?
- What's the Y-Intercept?
Texas digits Grade 8 Standards
develop an economic way of thinking and problem solving useful in ones life as a knowledgeable consumer and investor
use statistical procedures to describe data
construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data
determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points
develop transformational geometry concepts
generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane
differentiate between transformations that preserve congruence and those that do not
explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90, 180, 270, and 360 dgrees as applied to two-dimensional shapes on a coordinate plane using an algebraic representation
model the effect on linear and area measurements of dilated two-dimensional shapes
use multiple representations to develop foundational concepts of simultaneous linear equations
use one-variable equations or inequalities in problem situations
write a corresponding real-world problem when given a onevariable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants
model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants
use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle- angle criterion for similarity of triangles
use geometry to solve problems
solve problems involving the volume of cylinders, cones, and spheres
use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders
use the Pythagorean Theorem and its converse to solve problems
determine the distance between two points on a coordinate plane using the Pythagorean Theorem
write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants
develop mathematical relationships and make connections to geometric formulas
use proportional and relationships to develop foundational concepts of functions
contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation
use a trend line that approximates the linear relationship between bivariate sets of data to make predictions
represent linear proportional situations with tables, graphs, and equations in the form of y = kx
represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b does not equal 0
solve problems involving direct variation
identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems
write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations
distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b does not equal 0
identify functions using sets of ordered pairs, tables, mappings, and graphs
explain proportional and non-proportional relationships involving slope
graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship
use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems
- How Do You Find the Rate of Change Between Two Points on a Graph?
- How Do You Solve a Word Problem Using the Direct Variation Formula?
- How Do You Write and Use a Prediction Equation?
- What Does Direct Variation Look Like on a Graph?
- What Does the Slope of a Line Mean?
- What is a Linear Function?
- What's Slope-Intercept Form of a Linear Equation?
- What's the Y-Intercept?
use proportional relationships to describe dilations
generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation
compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane
use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation
represent and use real numbers in a variety of forms
extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers
approximate the value of an irrational number, including pi and square roots of numbers less than 225, and locate that rational number approximation on a number line
convert between standard decimal notation and scientific notation
order a set of real numbers arising from mathematical and real-world contexts
acquire and demonstrate mathematical understanding
select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
- How Can You Tell if a Relation is Not a Function?
- How Do You Convert From Decimal Notation to Scientific Notation?
- How Do You Estimate the Square Root of a Non-Perfect Square?
- How Do You Find a Value for x that Makes Two Lines Parallel?
- How Do You Find the Length of a Leg of a Right Triangle?
- How Do You Make a Scatter Plot?
- How Do You Multiply Two Numbers Using Scientific Notation?
- How Do You Put Real Numbers in Order?
- How Do You Solve a System of Equations Using the Elimination by Addition Method?
- How Do You Solve a System of Equations Using the Elimination by Subtraction Method?
- How Do You Solve a Two-Step Equation?
- How Do You Solve an Equation with Variables on Both Sides?
- How Do You Use a Scatter Plot to Find a Line of Fit?
- How Do You Write and Use a Prediction Equation?
- What Does the Slope of a Line Mean?
- What is a Reflection?
- What is a Rotation?
- What is a Translation?
- What is a Transversal?
- What is an Unbiased Sample?
- What is the Angle-Angle Postulate for Triangle Similarity?
- What is the Converse of the Pythagorean Theorem?
- What Is the Distance Formula?
- What is the Distributive Property?
- What is the Formula for the Surface Area of a Cylinder?
- What is the Formula for the Volume of a Cone?
- What is the Formula for the Volume of a Cylinder?
- What is the Formula for the Volume of a Sphere?
- What is the Mean of a Data Set?
- What is the Pythagorean Theorem?
- What is the Triangle Sum Theorem?
- What's a Scatter Plot?
- What's an Irrational Number?
- What's Positive Correlation?
- What's Scientific Notation?
- What's the Product of Powers Rule?
- What's the Quotient of Powers Rule?
apply mathematics to problems arising in everyday life, society, and the workplace
- How Do You Convert From Decimal Notation to Scientific Notation?
- How Do You Multiply Two Numbers Using Scientific Notation?
- How Do You Put Real Numbers in Order?
- How Do You Solve a System of Equations by Graphing?
- How Do You Solve a System of Equations Using the Elimination by Addition Method?
- How Do You Solve a System of Equations Using the Elimination by Subtraction Method?
- How Do You Solve a Two-Step Equation?
- How Do You Use the Formula for Simple Interest?
- What Does Direct Variation Look Like on a Graph?
- What is an Unbiased Sample?
- What is the Formula for the Surface Area of a Prism?
- What is the Mean of a Data Set?
use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
- How Can You Tell if a Relation is Not a Function?
- How Can You Tell When a System of Equations Has Infinitely Many Solutions?
- How Do You Convert From Decimal Notation to Scientific Notation?
- How Do You Estimate the Square Root of a Non-Perfect Square?
- How Do You Evaluate an Algebraic Expression by Plugging In Values?
- How Do You Find the Rate of Change Between Two Points on a Graph?
- How Do You Make a Scatter Plot?
- How Do You Multiply Two Numbers Using Scientific Notation?
- How Do You Solve a System of Equations by Graphing?
- How Do You Solve a System of Equations Using the Elimination by Addition Method?
- How Do You Solve a System of Equations Using the Elimination by Subtraction Method?
- How Do You Solve a Two-Step Equation?
- How Do You Solve a Word Problem Using the Direct Variation Formula?
- How Do You Solve an Equation with Variables on Both Sides?
- How Do You Solve an Inequality With Variables on Both Sides?
- How Do You Use a Scatter Plot to Find a Line of Fit?
- How Do You Use the Formula for Simple Interest?
- How Do You Write and Use a Prediction Equation?
- What are Similar Figures?
- What Does Congruent Mean?
- What Does Direct Variation Look Like on a Graph?
- What Does the Slope of a Line Mean?
- What is a Dilation?
- What is a Linear Function?
- What is a Reflection?
- What is a Rotation?
- What is a Translation?
- What is an Identity Equation?
- What is an Unbiased Sample?
- What Is the Distance Formula?
- What is the Distributive Property?
- What is the Formula for the Surface Area of a Cylinder?
- What is the Formula for the Surface Area of a Prism?
- What is the Formula for the Volume of a Cone?
- What is the Formula for the Volume of a Cylinder?
- What is the Mean of a Data Set?
- What's a Function?
- What's a Scatter Plot?
- What's a System of Linear Equations?
- What's an Irrational Number?
- What's Positive Correlation?
- What's Scientific Notation?
- What's Slope-Intercept Form of a Linear Equation?
- What's the Product of Powers Rule?
- What's the Quotient of Powers Rule?
- What's the Y-Intercept?
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
- How Can You Tell if a Function is Linear or Nonlinear From a Graph?
- How Can You Tell if a Relation is Not a Function?
- How Do You Convert From Decimal Notation to Scientific Notation?
- How Do You Estimate the Square Root of a Non-Perfect Square?
- How Do You Evaluate an Algebraic Expression by Plugging In Values?
- How Do You Find the Length of a Leg of a Right Triangle?
- How Do You Find the Rate of Change Between Two Points on a Graph?
- How Do You Multiply Two Numbers Using Scientific Notation?
- How Do You Put Real Numbers in Order?
- How Do You Solve a System of Equations Using the Substitution Method?
- How Do You Use a Scatter Plot to Find a Line of Fit?
- How Do You Use the Formula for Simple Interest?
- What are Interior and Exterior Angles of a Polygon?
- What are Similar Figures?
- What Does Congruent Mean?
- What Does the Slope of a Line Mean?
- What is a Dilation?
- What is a Linear Function?
- What is a Transversal?
- What is an Unbiased Sample?
- What is the Angle-Angle Postulate for Triangle Similarity?
- What is the Converse of the Pythagorean Theorem?
- What Is the Distance Formula?
- What is the Distributive Property?
- What is the Formula for the Volume of a Cylinder?
- What is the Formula for the Volume of a Sphere?
- What is the Triangle Sum Theorem?
- What's a System of Linear Equations?
- What's the Product of Powers Rule?
- What's the Quotient of Powers Rule?
- What's the Y-Intercept?
create and use representations to organize, record, and communicate mathematical ideas
- How Can You Tell if a Function is Linear or Nonlinear From a Graph?
- How Can You Tell if a Relation is Not a Function?
- How Do You Find the Rate of Change Between Two Points on a Graph?
- How Do You Make a Scatter Plot?
- How Do You Solve a System of Equations by Graphing?
- How Do You Solve a System of Equations Using the Elimination by Subtraction Method?
- How Do You Solve a Word Problem Using the Direct Variation Formula?
- How Do You Solve an Inequality With Variables on Both Sides?
- What Does the Slope of a Line Mean?
- What is a Linear Function?
- What is a Transversal?
- What is an Identity Equation?
- What is an Unbiased Sample?
- What Is the Distance Formula?
- What is the Distributive Property?
- What is the Formula for the Surface Area of a Prism?
- What's a Function?
- What's a System of Linear Equations?
- What's Positive Correlation?
- What's Slope-Intercept Form of a Linear Equation?
- What's the Y-Intercept?
analyze mathematical relationships to connect and communicate mathematical ideas
- How Do You Find a Value for x that Makes Two Lines Parallel?
- How Do You Find the Length of a Leg of a Right Triangle?
- How Do You Multiply Two Numbers Using Scientific Notation?
- How Do You Solve a System of Equations by Graphing?
- How Do You Solve a System of Equations Using the Elimination by Addition Method?
- How Do You Solve a System of Equations Using the Elimination by Subtraction Method?
- How Do You Solve a System of Equations Using the Substitution Method?
- How Do You Solve an Inequality With Variables on Both Sides?
- How Do You Write and Use a Prediction Equation?
- What are Interior and Exterior Angles of a Polygon?
- What are Similar Figures?
- What Does Congruent Mean?
- What is a Rotation?
- What is a Transversal?
- What is an Unbiased Sample?
- What is the Angle-Angle Postulate for Triangle Similarity?
- What is the Distributive Property?
- What is the Formula for the Surface Area of a Cylinder?
- What is the Formula for the Surface Area of a Prism?
- What is the Formula for the Volume of a Cone?
- What is the Formula for the Volume of a Cylinder?
- What is the Mean of a Data Set?
- What is the Pythagorean Theorem?
- What is the Triangle Sum Theorem?
- What's a Function?
- What's Slope-Intercept Form of a Linear Equation?
- What's the Product of Powers Rule?
Texas Algebra 1 Standards
Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.
Decide whether relations represented verbally, tabularly, graphically, and symbolically define a function
Identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes
Evaluate functions, expressed in function notation, given one or more elements in their domains
- How Do You Find f(x) If You Have a Value For x?
- How Do You Find the Common Difference in an Arithmetic Sequence?
- How Do You Graph an Exponential Function Using a Table?
- How Do You Write a Quadratic Equation in Vertex Form if You Have the Vertex and Another Point?
- How Do You Write a Rule for a Geometric Sequence?
- What is Function Notation?
- What's an Arithmetic Sequence?
- What's an Exponential Function?
Solve mathematic and scientific formulas, and other literal equations, for a specified variable
- How Do You Solve a Formula For a Variable?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- How Do You Use the Formula for Direct Variation?
- How Do You Use the Square Root Method to Solve a Quadratic Equation with Two Solutions?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- What is a Literal Equation?
- What's Point-Slope Form of a Linear Equation?
- What's the Direct Variation or Direct Proportionality Formula?
Write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms
Linear functions, equations, and inequalities. The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations.
Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems
- How Do You Find the Slope of a Line from a Graph?
- How Do You Make a Scatter Plot?
- How Do You Make an Approximate Graph From a Word Problem?
- How Do You Use the Formula for Direct Variation?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- How Do You Write and Use a Prediction Equation?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- What's Point-Slope Form of a Linear Equation?
- What's Slope-Intercept Form of a Linear Equation?
- What's the Direct Variation or Direct Proportionality Formula?
- What's the Formula for Slope?
Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, ax + by = c, and y - y1 = m(x - x1)
- How Do You Find the Slope of a Line from a Graph?
- How Do You Graph a Linear Equation by Making a Table?
- How Do You Know if Two Lines are Parallel?
- How Do You Know if Two Lines Are Perpendicular?
- How Do You Make a Scatter Plot?
- How Do You Use the Formula for Direct Variation?
- How Do You Use the Graph of a Linear Equation to Solve a Word Problem?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- How Do You Write and Use a Prediction Equation?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- What's a Function?
- What's a Function?
- What's Point-Slope Form of a Linear Equation?
- What's Slope-Intercept Form of a Linear Equation?
- What's Standard Form of a Linear Equation?
- What's the Direct Variation or Direct Proportionality Formula?
- What's the Formula for Slope?
Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems
- How Do You Graph a Linear Equation by Making a Table?
- How Do You Use the Formula for Direct Variation?
- How Do You Use the Graph of a Linear Equation to Solve a Word Problem?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- What's Point-Slope Form of a Linear Equation?
- What's Slope-Intercept Form of a Linear Equation?
- What's Standard Form of a Linear Equation?
- What's the Direct Variation or Direct Proportionality Formula?
Graph the solution set of linear inequalities in two variables on the coordinate plane
Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane
Estimate graphically the solutions to systems of two linear equations with two variables in real-world problems
Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist
Linear functions, equations, and inequalities. The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.
Write linear equations in two variables in various forms, including y = mx + b, ax + by = c, and y - y1 = m(x - x1), given one point and the slope and given two points
- How Do You Know if Two Lines are Parallel?
- How Do You Know if Two Lines Are Perpendicular?
- How Do You Make a Scatter Plot?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- How Do You Write and Use a Prediction Equation?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- What's Point-Slope Form of a Linear Equation?
- What's Slope-Intercept Form of a Linear Equation?
- What's Standard Form of a Linear Equation?
Write the equation of a line that contains a given point and is parallel to a given line
Determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities
- How Do You Find f(x) If You Have a Value For x?
- How Do You Graph a Linear Equation by Making a Table?
- How Do You Use the Graph of a Linear Equation to Solve a Word Problem?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
- What is Function Notation?
- What's Standard Form of a Linear Equation?
Write linear equations in two variables given a table of values, a graph, and a verbal description
- How Do You Know if Two Lines are Parallel?
- How Do You Know if Two Lines Are Perpendicular?
- How Do You Make a Scatter Plot?
- How Do You Use the Formula for Direct Variation?
- How Do You Use X- and Y-Intercepts To Graph a Line In Standard Form?
- How Do You Write an Equation from a Word Problem?
- How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?
- How Do You Write and Use a Prediction Equation?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- What's a Function?
- What's a Function?
- What's Point-Slope Form of a Linear Equation?
- What's Slope-Intercept Form of a Linear Equation?
- What's Standard Form of a Linear Equation?
- What's the Direct Variation or Direct Proportionality Formula?
Write and solve equations involving direct variation
- How Do You Find Missing Measurements of Similar Figures Using a Proportion?
- How Do You Solve a Proportion Using Cross Products?
- How Do You Solve a Proportion Using the Multiplication Property of Equality?
- How Do You Use the Formula for Direct Variation?
- What are Similar Figures?
- What's the Direct Variation or Direct Proportionality Formula?
Write systems of two linear equations given a table of values, a graph, and a verbal description
- How Do You Graph a System of Equations With No Solution?
- How Do You Solve a System of Equations by Graphing?
- How Do You Solve a System of Equations Using the Elimination by Addition Method?
- How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
- How Do You Solve a System of Equations Using the Substitution Method?
- How Do You Solve a Word Problem Using the Elimination by Subtraction Method?
- How Do You Solve a Word Problem Using Two Equations?
- How Do You Solve Two Equations with Two Variables?
Write linear inequalities in two variables given a table of values, a graph, and a verbal description
Write an equation of a line that is parallel or perpendicular to the x or y axis and determine whether the slope of the line is zero or undefined
Write the equation of a line that contains a given point and is perpendicular to a given line
Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.
Simplify numerical radical expressions involving square roots
Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents
- How Do You Find the Product of Powers?
- What are Rational Exponents?
- What Do You Do With a Negative Exponent?
- What Do You Do With a Zero Exponent?
- What's the Power of a Power Rule?
- What's the Power of a Product Rule?
- What's the Power of a Quotient Rule?
- What's the Product of Powers Rule?
- What's the Quotient of Powers Rule?
Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.
Determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend
Add and subtract polynomials of degree one and degree two
Multiply polynomials of degree one and degree two
- How Do You Factor a 4-Term Polynomial by Grouping?
- How Do You Factor the Greatest Common Factor out of a Polynomial?
- How Do You Figure Out What Factoring Strategy to Use?
- How Do You Multiply a Monomial by a Polynomial?
- How Do You Multiply Binomials Using FOIL?
- How Do You Use the Formula for the Product of a Sum and a Difference?
- What's the Formula for the Square of a Sum?
- What's the Grid Method of FOILing?
Factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two
- How Do You Divide Two Polynomials by Factoring and Canceling?
- How Do You Factor a 4-Term Polynomial by Grouping?
- How Do You Factor a Polynomial by Guessing and Checking?
- How Do You Factor a Polynomial Using Difference of Squares?
- How Do You Factor a Polynomial Using the A-C Method?
- How Do You Factor a Trinomial?
- How Do You Figure Out a Template for Factoring a Trinomial?
- How Do You Figure Out What Factoring Strategy to Use?
- How Do You Find Excluded Values?
- How Do You Use a Shortcut to Factor a Perfect Square Trinomial?
Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial
Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property
- How Do You Divide Two Polynomials by Factoring and Canceling?
- How Do You Factor a 4-Term Polynomial by Grouping?
- How Do You Factor a Polynomial by Guessing and Checking?
- How Do You Factor a Polynomial Using the A-C Method?
- How Do You Factor the Greatest Common Factor out of a Polynomial?
- How Do You Figure Out What Factoring Strategy to Use?
- How Do You Find Excluded Values?
- How Do You Multiply a Monomial by a Polynomial?
- How Do You Multiply Binomials Using FOIL?
- What's the Grid Method of FOILing?
Linear functions, equations, and inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.
Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides
- How Do You Find Missing Measurements of Similar Figures Using a Proportion?
- How Do You Solve a Multi-Step Equation Using the Distributive Property?
- How Do You Solve a Multi-Step Equation with Fractions by Multiplying Away the Fraction?
- How Do You Solve a Proportion Using Cross Products?
- How Do You Solve a Proportion Using the Multiplication Property of Equality?
- How Do You Solve an Equation with Variables on Both Sides?
- How Do You Solve an Identity Equation?
- What are Similar Figures?
Solve systems of two linear equations with two variables for mathematical and real-world problems
- How Do You Graph a System of Equations With No Solution?
- How Do You Solve a System of Equations by Graphing?
- How Do You Solve a System of Equations Using the Elimination by Addition Method?
- How Do You Solve a System of Equations Using the Elimination by Multiplication Method?
- How Do You Solve a System of Equations Using the Substitution Method?
- How Do You Solve a Word Problem Using the Elimination by Subtraction Method?
- How Do You Solve a Word Problem Using Two Equations?
- How Do You Solve Two Equations with Two Variables?
Solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides
Quadratic functions and equations. The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations.
Determine the domain and range of quadratic functions and represent the domain and range using inequalities
Write quadratic functions when given real solutions and graphs of their related equations
Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)2+ k), and rewrite the equation from vertex form to standard form (f(x) = ax2+ bx + c)
Exponential functions and equations. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
Determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities
Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay
- How Can You Tell if a Function is Linear or Nonlinear From a Graph?
- How Can You Tell if a Function is Linear or Nonlinear From a Table?
- How Do You Graph an Exponential Function Using a Table?
- What Do You Do With a Negative Exponent?
- What Do You Do With a Zero Exponent?
- What is exponential decay?
- What is Exponential Growth?
- What's an Exponential Function?
Interpret the meaning of the values of a and b in exponential functions of the form f(x) = abx in real-world problems
Graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems
Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula
- How Do You Solve a Quadratic Equation by Completing the Square?
- How Do You Solve a Quadratic Equation by Factoring?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- How Do You Use the Square Root Method to Solve a Quadratic Equation with Two Solutions?
- What is the Converse of the Pythagorean Theorem?
- What is the Discriminant?
- What is the Pythagorean Theorem?
- What is the Quadratic Formula?
- What's the Zero Product Property?
Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems
Linear functions, equations, and inequalities. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.
Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association
Write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems
Compare and contrast association and causation in real-world problems
Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.
Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry
- How Do You Find the Axis of Symmetry for a Quadratic Function?
- How Do You Graph a Quadratic Function?
- How Do You Graph the Parent Quadratic Function y=x2?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- How Do You Use the Square Root Method to Solve a Quadratic Equation with Two Solutions?
- How Do You Write a Quadratic Equation in Vertex Form if You Have the Vertex and Another Point?
- What is a Quadratic Function?
Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d
Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions
Texas Geometry Standards
Probability. The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events.
Develop strategies to use permutations and combinations to solve contextual problems
Identify whether two events are independent and compute the probability of the two events occurring together with or without replacement
Determine probabilities based on area to solve contextual problems
Apply independence in contextual problems
Apply conditional probability in contextual problems
Two-dimensional and three-dimensional figures. The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures.
Identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes
Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change
- How Do You Find the Area of a Sector of a Circle?
- How Do You Find the Lateral and Surface Areas of a Cone?
- How Do You Find the Lateral and Surface Areas of a Cylinder?
- How Do You Find the Lateral and Surface Areas of a Rectangular Prism?
- How Do You Find the Lateral and Surface Areas of a Regular Pyramid?
- How Do You Find the Surface Area of a Sphere?
- How Do You Find the Volume of a Cone?
- How Do You Find the Volume of a Sphere?
- How Do You Use Similar Figures to Find the Area of a Polygon?
- What is a Circle?
- What is Circumference?
- What is the Formula for the Area of a Circle?
- What is the Formula for the Volume of a Pyramid?
- What is the Relationship Between the Surface Areas of Similar Solids?
Circles. The student uses the process skills to understand geometric relationships and apply theorems and equations about circles.
Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems
- How Do You Determine Whether a Line is Tangent to a Circle?
- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- How Do You Find Missing Measures of Angles in Quadrilaterals Inscribed in Circles?
- How Do You Find the Measure of an Angle Created by Intersecting Chords in a Circle?
- How Do You Find The Measure of an Inscribed Angle When You Know the Measure of the Intercepted Arc?
- How Do You Use Intersecting Chords to Find Arc Measures in a Circle?
- What is a Tangent Line to a Circle?
Apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems
Apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems
Show that the equation of a circle with center at the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)2 + (y - k)2 =r2
Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity).
Describe and perform transformations of figures in a plane using coordinate notation
- How Do You Graph a Glide Reflection?
- How Do You Identify a Congruence Transformation?
- How Do You Identify a Similarity Transformation?
- How Do You Identify Corresponding Parts in Congruent Triangles?
- How Do You Make a Figure Larger Using a Dilation?
- How Do You Rotate a Figure 180 Degrees Around the Origin?
- How Do You Use a Graph to Reflect a Figure Over the Y-Axis?
- How Do You Use a Graph to Translate a Figure Diagonally?
- What is a Congruence Transformation, or Isometry?
- What is a Dilation?
- What is a Reflection?
- What is a Rotation?
- What is a Translation?
Identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane
- How Do You Identify a Congruence Transformation?
- How Do You Identify a Similarity Transformation?
- How Do You Identify Corresponding Parts in Congruent Triangles?
- How Do You Rotate a Figure 180 Degrees Around the Origin?
- How Do You Use a Graph to Translate a Figure Diagonally?
- What is a Rotation?
- What is a Translation?
Determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane
- How Do You Graph a Glide Reflection?
- How Do You Identify a Congruence Transformation?
- How Do You Identify a Similarity Transformation?
- How Do You Identify Corresponding Parts in Congruent Triangles?
- How Do You Make a Figure Larger Using a Dilation?
- What is a Congruence Transformation, or Isometry?
- What is a Dilation?
Identify and distinguish between reflectional and rotational symmetry in a plane figure
Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures.
Apply the formula for the area of regular polygons to solve problems using appropriate units of measure
- How Do You Find the Area of a Regular Polygon When You Know the Length of the Apothem?
- How Do You Find the Area of a Sector of a Circle?
- How Do You Use Similar Figures to Find the Area of a Polygon?
- What is the Formula for the Area of a Circle?
- What is the Formula for the Area of a Parallelogram?
- What is the Formula for the Area of a Triangle Using Sines?
- What is the Formula for the Area of a Triangle?
Apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure
- How Do You Find the Lateral and Surface Areas of a Cone?
- How Do You Find the Lateral and Surface Areas of a Cylinder?
- How Do You Find the Lateral and Surface Areas of a Rectangular Prism?
- How Do You Find the Lateral and Surface Areas of a Regular Pyramid?
- How Do You Find the Surface Area of a Sphere?
- How Do You Find the Volume of a Sphere?
Determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure
Apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure
Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures.
Determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint
Determine an equation of a line parallel or perpendicular to a given line that passes through a given point
Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines
- How Do You Find the Distance Between Two Points?
- How Do You Know if Two Lines are Parallel?
- How Do You Know if Two Lines Are Perpendicular?
- How Do You Write a Coordinate Proof?
- How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
- What are Equilateral, Isosceles, and Scalene Triangles?
- What are Parallel Lines?
- What are Skew Lines?
- What is a Circle?
- What Is the Distance Formula?
- What's Slope-Intercept Form of a Linear Equation?
- What's the Midpoint Formula?
Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures.
Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools
- How Do You Determine if Triangles on the Coordinate Plane are Congruent?
- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- How Do You Find Missing Angles in a Transversal Diagram?
- How Do You Find Missing Angles in a Triangle With Variables?
- How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?
- How Do You Find Missing Angles in an Isosceles Triangle?
- How Do You Find the Measure of an Angle Created by Intersecting Chords in a Circle?
- How Do You Find the Sum of the Interior Angles of a Polygon?
- How Do You Use Intersecting Chords to Find Arc Measures in a Circle?
- How Do You Use the Diagonals of a Rectangle to Find the Value of a Variable?
- How Do You Use the Triangle Proportionality Theorem to Find Missing Lengths in a Diagram?
- What are Parallel Lines?
- What are Skew Lines?
- What is a Rectangle?
- What is a Trapezoid?
- What is Inductive Reasoning?
- What is the Circumcenter of a Triangle?
- What is the Corresponding Angles Postulate?
- What is the Incenter of a Triangle?
- What is the Side-Angle-Side Postulate for Triangle Congruence?
- What is the Triangle Sum Theorem?
Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships
- How Can You Tell if a Point is on the Perpendicular Bisector of a Line Segment?
- How Do You Construct a Perpendicular Bisector?
- How Do You Determine if Triangles on the Coordinate Plane are Congruent?
- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- How Do You Find a Value for x that Makes Two Lines Parallel?
- How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?
- How Do You Find Missing Angles in an Isosceles Triangle?
- What are Perpendicular Lines?
- What are Supplementary Angles?
- What are Vertical Angles?
- What is the Circumcenter of a Triangle?
- What is the Converse of the Corresponding Angles Postulate?
- What is the Incenter of a Triangle?
- What is the Side-Angle-Side Postulate for Triangle Congruence?
Construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge
Verify the triangle inequality theorem using constructions and apply the theorem to solve problems
Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships.
Distinguish between undefined terms, definitions, postulates, conjectures, and theorems
Verify that a conjecture is false using a counterexample
Identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse
Compare geometric relationships between euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle
Proof and congruence. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.
Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems
- How Can You Tell if a Point is on the Perpendicular Bisector of a Line Segment?
- How Do You Determine Whether a Line is Tangent to a Circle?
- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- How Do You Find a Value for x that Makes Two Lines Parallel?
- How Do You Find Missing Angles in a Transversal Diagram?
- How Do You Find the Measure of an Angle Created by Intersecting Chords in a Circle?
- How Do You Use Intersecting Chords to Find Arc Measures in a Circle?
- How Do You Use Parallel and Perpendicular Theorems to Prove a Relationship Between Two Lines?
- How Do You Write an Indirect Proof?
- What are Parallel Lines?
- What are Skew Lines?
- What are Supplementary Angles?
- What are Vertical Angles?
- What is a Tangent Line to a Circle?
- What is a Theorem?
- What is the Circumcenter of a Triangle?
- What is the Converse of the Corresponding Angles Postulate?
- What is the Corresponding Angles Postulate?
- What is the Incenter of a Triangle?
Apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles
- How Do You Graph a Glide Reflection?
- How Do You Identify a Congruence Transformation?
- How Do You Identify Corresponding Parts in Congruent Triangles?
- How Do You Rotate a Figure 180 Degrees Around the Origin?
- How Do You Use a Graph to Translate a Figure Diagonally?
- What is a Congruence Transformation, or Isometry?
- What is a Rotation?
- What is a Translation?
- What is the Distributive Property?
- What is the Substitution Property of Equality?
Prove two triangles are congruent by applying the side-angle-side, angle-side-angle, side-side-side, angle-angle-side, and hypotenuse-leg congruence conditions
- How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?
- How Do You Find Missing Angles in an Isosceles Triangle?
- How Do You Identify Common Parts in Overlapping Triangles?
- How Do You Prove that Two Overlapping Triangles are Congruent?
- How Do You Show that Corresponding Parts of Congruent Triangles are Congruent?
- How Do You Use a Congruence Postulate to Prove Triangles are Congruent?
- How Do You Use the Law of Detachment to Draw a Valid Conclusion?
- What are the Legs and Hypotenuse of a Right Triangle?
- What is CPCTC?
- What is the Angle-Side-Angle Postulate for Triangle Congruence?
- What is the Distributive Property?
- What is the Hypotenuse-Leg Congruence Theorem?
- What is the Law of Syllogism?
- What is the Substitution Property of Equality?
Prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems
- How Do You Find the Distance Between Two Points?
- How Do You Find the Value for a Variable in the Angles of a Quadrilateral To Make it a Rhombus?
- How Do You Find Values for Variables in the Angles of a Quadrilateral To Make it a Parallelogram?
- How Do You Use the Law of Detachment to Draw a Valid Conclusion?
- What are Equilateral, Isosceles, and Scalene Triangles?
- What is a Parallelogram?
- What is the Distributive Property?
- What is the Law of Syllogism?
- What is the Substitution Property of Equality?
Verify theorems about the relationships in triangles, including proof of the pythagorean theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems
- How Do You Determine Whether a Triangle Can Be Formed Given Three Side Lengths?
- How Do You Find Missing Angles in a Triangle With Variables?
- How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?
- How Do You Find Missing Angles in an Isosceles Triangle?
- How Do You Find the Sum of the Interior Angles of a Polygon?
- How Do You Find the Value for a Variable in the Angles of a Quadrilateral To Make it a Rhombus?
- How Do You Put the Sides of a Triangle in Order According to Size if You Know Two Angles of the Triangle?
- How Do You Use the Centroid to Find Segment Lengths in a Triangle?
- How Do You Use the Diagonals of a Rectangle to Find the Value of a Variable?
- How Do You Use the Hinge Theorem to Compare Side Lengths in Two Triangles?
- How Do You Use the Law of Detachment to Draw a Valid Conclusion?
- How Do You Write a Coordinate Proof?
- How Do You Write an Indirect Proof?
- What are Acute, Obtuse, Right, and Straight Angles?
- What are Supplementary Angles?
- What are Vertical Angles?
- What is a 30-60-90 Degree Triangle?
- What is a 45รยฐ-45รยฐ-90รยฐ Triangle?
- What is a Median of a Triangle?
- What is a Rectangle?
- What is an Angle?
- What is the Circumcenter of a Triangle?
- What is the Converse of the Pythagorean Theorem?
- What is the Distributive Property?
- What is the Hinge Theorem?
- What is the Incenter of a Triangle?
- What is the Law of Syllogism?
- What is the Pythagorean Theorem?
- What is the Substitution Property of Equality?
- What is the Triangle Midsegment Theorem?
- What is the Triangle Sum Theorem?
Similarity, proof, and trigonometry. The student uses the process skills to understand and apply relationships in right triangles.
Determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems
Apply the relationships in special right triangles 30ยฐ-60ยฐ-90ยฐ and 45ยฐ-45ยฐ-90ยฐ and the pythagorean theorem, including pythagorean triples, to solve problems
- How Do You Determine Whether a Line is Tangent to a Circle?
- How Do You Determine Whether Two Chords are Equidistant From the Center of a Circle?
- How Do You Find the Area of a Regular Polygon When You Know the Length of the Apothem?
- How Do You Find the Area of a Sector of a Circle?
- How Do You Find the Area of a Trapezoid?
- How Do You Find the Lateral and Surface Areas of a Cone?
- How Do You Find the Lateral and Surface Areas of a Regular Pyramid?
- What is a 30-60-90 Degree Triangle?
- What is a 45รยฐ-45รยฐ-90รยฐ Triangle?
- What is a Tangent Line to a Circle?
- What is the Converse of the Pythagorean Theorem?
- What is the Formula for the Area of a Circle?
- What is the Formula for the Area of a Trapezoid?
- What is the Pythagorean Theorem?
Similarity, proof, and trigonometry. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.
Similarity, proof, and trigonometry. The student uses the process skills in applying similarity to solve problems.
Texas Algebra 2 Standards
Exponential and logarithmic functions and equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.
Determine the effects on the key attributes on the graphs of f(x) = bx and f(x) = logb(x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d
Rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations
Formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation
Determine the reasonableness of a solution to a logarithmic equation
Solve exponential equations of the form y = abx where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions
Systems of equations and inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions.
Solve systems of three linear equations in three variables by using gaussian elimination, technology with matrices, and substitution
Formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic
Solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation
Formulate systems of at least two linear inequalities in two variables
Solve systems of two or more linear inequalities in two variables
Determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables
Determine possible solutions in the solution set of systems of two or more linear inequalities in two variables
Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.
Graph the functions f(x)=โx, f(x)=1/x, f(x)=x3, f(x)= 3โx, f(x)=bx, f(x)=|x|, and f(x)=logb (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval
- How Do You Convert From Exponential Form to Logarithmic Form?
- How Do You Convert From Exponential Form to Natural Logarithmic Form?
- How Do You Find the Degree of a Polynomial?
- How Do You Graph a Square Root Function Using a Table?
- How Do You Graph an Absolute Value Function?
- How Do You Graph the Natural Base Exponential Function?
- How Do You Translate a Function?
- What Does the Constant 'k' do in y = |x|+k?
- What is a Cubic Function?
- What is a Logarithm?
- What is a Natural Logarithm?
- What is an Absolute Value Function?
- What is Domain?
- What is Exponential Growth?
- What is the Natural Base Exponential Function?
- What's an Exponential Function?
Describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range
Graph and write the inverse of a function using notation such as f -1 (x)
Use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other
Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions.
Determine the effect on the graph of f(x) = โx when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d
Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening
Write the quadratic function given three specified points in the plane
Formulate quadratic and square root equations using technology given a table of data
Transform a quadratic function f(x) = ax2 + bx + c to the form f(x) = a(x - h)2 + k to identify the different attributes of f(x)
Solve quadratic and square root equations
- How Do You Add Complex Numbers?
- How Do You Convert a Quadratic from Standard Form to Vertex Form by Completing the Square?
- How Do You Solve a Quadratic Equation by Completing the Square?
- How Do You Solve a Quadratic Equation by Factoring?
- How Do You Solve a Quadratic Equation by Using the Quadratic Formula?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- How Do You Solve a Radical Equation?
- What is the Discriminant?
- What is the Imaginary Unit i?
Solve quadratic inequalities
Identify extraneous solutions of square root equations
Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions.
Analyze data to select the appropriate model from among linear, quadratic, and exponential models
Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models
Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data
Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.
Determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two
Add, subtract, and multiply polynomials
Add, subtract, and multiply complex numbers
- How Can You Tell if a Relation is Not a Function?
- How Do You Add Complex Numbers?
- How Do You Convert From Exponential Form to Logarithmic Form?
- How Do You Find All the Rational Zeros of a Polynomial Function?
- How Do You Graph a Quadratic Function?
- How Do You Graph the Natural Base Exponential Function?
- How Do You Solve a Quadratic Equation by Factoring?
- How Do You Solve a Quadratic Equation with Two Solutions by Graphing?
- How Do You Translate a Function?
- What is a Logarithm?
- What is an Absolute Value Function?
- What is Domain?
- What is Exponential Growth?
- What is the Imaginary Unit i?
- What is the Natural Base Exponential Function?
- What is the Standard Form of a Quadratic?
- What's a Function?
- What's an Exponential Function?
- What's the Inverse of a Relation?
Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping
- How Do You Factor a Polynomial Using Sum of Cubes?
- How Do You Factor a Polynomial Using the A-C Method?
- How Do You Factor a Trinomial?
- How Do You Find All the Rational Zeros of a Polynomial Function?
- How Do You Graph a Square Root Function Using a Table?
- What is the Factor Theorem?
- What is the Fundamental Theorem of Algebra?
Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods
Determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two
Solve equations involving rational exponents
Rewrite radical expressions that contain variables to equivalent forms
Cubic, cube root, absolute value and rational functions, equations, and inequalities. The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions.
Analyze the effect on the graphs of f(x) = |x| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d
Analyze the effect on the graphs of f(x) = x3 and f(x) = 3โx when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d
Solve absolute value linear equations
Solve absolute value linear inequalities
Determine the reasonableness of a solution to a rational equation
Formulate rational equations that model real-world situations
- How Do You Add Two Rational Expressions with Different Denominators?
- How Do You Divide Two Polynomials by Factoring and Canceling?
- How Do You Find the Least Common Denominator of Two Rational Expressions?
- How Do You Multiply Two Rational Expressions?
- How Do You Solve a Rational Equation by Adding Fractions?
- How Do You Solve a Rational Equation by LCD Multiplication?
- How Do You Use the Formula for Inverse Variation to Write an Equation?
- What's the Inverse Variation or Indirect Proportionality Formula?