Teach To One Roadmaps - Math Skills
Algebra
Target the precise skills and concepts each student needs.
We’ve developed a system of organizing the 300 skills a student must learn cumulatively in order to be Algebra-ready. The skills and concepts covered in Teach to One Roadmaps allow students to gain unlearned, prerequisite skills while still advancing at grade level.
Browse the skills and concepts covered in each grade level below.
Grade 9
Complex Linear Equations & Inequalities
- I will solve multi-step inequalities and graph the solution set of an inequality on a number line.
- I will write algebraic equations or inequalities that represent a situation.
- I will solve literal equations for a given variable.
- I will analyze and solve verbal problems whose solution requires solving a linear inequality in one variable.
Polynomial Operations
- I will add and subtract polynomials.
- I will multiply a binomial by a monomial or a binomial.
- I will identify polynomials and represent them in standard form.
- I will multiply and divide monomial expressions with a common base.
Linear Function Analysis
- I will write the equation of a line, given its slope and the coordinates of a point on the line.
- I will determine the slope of a line, given its equation in any form.
- I will use function notation and identify the domain and range of functions.
- I will calculate and interpret the average rate of change of a function over a specified interval.
Advanced Functions & Sequences
- I will identify the effects of transformations on equations and graphs of quadratic functions.
- I will compare properties of two functions each represented in a different way.
- I will recognize geometric sequences are functions and write them both recursively and explicitly.
- I will recognize arithmetic sequences are functions and write them both recursively and explicitly.
Advanced Linear Functions
- I will determine if two lines are parallel, given their equations in any form.
- I will explore the concept of inverse functions and find inverses of linear functions.
- I will graph piecewise-defined functions including step functions and absolute value functions.
Advanced Systems of Functions
- I will solve systems of linear and quadratic equations graphically.
- I will solve a system of one linear and one quadratic equation in two variables algebraically.
- I will graph linear inequalities in two variables.
- I will graph and solve systems of linear inequalities with rational coefficients in two variables.
Exponential Functions
- I will calculate compound interest and solve real world and mathematical problems involving interest.
- I will analyze and solve verbal problems that involve exponential growth and decay.
- I will identify and graph exponential functions.
- I will distinguish between situations that can be modeled with linear and exponential functions.
Factoring Polynomials
- I will factor polynomial expressions using the greatest common factor (GCF) of the terms.
- I will factor quadratic expressions with three terms.
- I will identify and factor the difference of two perfect squares.
- I will factor algebraic expressions completely.
- I will factor trinomials where the leading coefficient is not equal to 1.
Graphing Quadratics
- I will find the roots, vertex, and axis of symmetry of a parabola given its graph.
- I will determine the vertex and axis of symmetry of a parabola, given its equation.
- I will graph quadratic relationships from equations or tables of values.
Solving Quadratics
- I will analyze and solve verbal problems that involve quadratic equations.
- I will understand and apply the multiplication property of zero to solve quadratic equations by factoring.
- I will solve quadratic equations by completing the square.
- I will derive the quadratic formula and use it to solve quadratic equations.
- I will complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Advanced Data in Two Variables
- I will distinguish between correlation and causation.
- I will compute and interpret the correlation coefficient of a linear fit.
- I will interpret relative frequencies in two-way tables in the context of the data and recognize possible associations and trends in the data.
- I will use residuals to analyze how well a function fits data.
Advanced Single Variable Data
- I will summarize, represent, and interpret data in histograms and cumulative frequency histograms.
- I will summarize, represent, and interpret data in box plots, find percentiles, and use a five number summary.
- I will find the standard deviation of a data set and use it describe and compare data sets.
Radical Expressions
- I will simplify radical terms.
- I will perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form.
- I will explore and explain properties of sums and products of rational and irrational numbers.
- I will explain how the system of integer exponents extends to rational number exponents, including representing radicals in terms of rational exponents.
- I will explain how the system of integer exponents extends to rational number exponents, including representing radicals in terms of rational exponents.
Grade 8
Multi-Step Equations
- I will solve multistep equations with rational numbers.
- I will solve equations by moving variables to one side of an equation.
- I will give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
Analyzing Linear Functions
- I will create graphs to match given descriptions of situations involving a relationship between two variables or describe situations that could match given graphs.
- I will distinguish between linear and non-linear relationships.
- I will represent, analyze, and compare linear relationships in graphs, equations, and tables.
- I will determine the slope and the equation of a line given the coordinates of two points on the line.
Linear Functions
- I will determine the slope and y-intercept of a line from a graph, and explain what slope and y-intercept mean in real world and mathematical problems.
- I will construct a function to model a linear relationship and describe the rate of change and initial value.
- I will graph proportional relationships, interpreting the unit rate as the slope of the graph and compare two different proportional relationships represented in different ways.
Understanding Functions
- I will graph proportional relationships, interpreting the unit rate as the slope of the graph and compare two different proportional relationships represented in different ways.
- I will determine function rules of functions represented in tables.
- I will define and identify functions in tables, graphs, and ordered pairs.
Systems of Linear Equations
- I will solve systems of two linear equations graphically.
- I will analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables.
- I will solve systems of two linear equations in two variables algebraically.
- I will recognize systems of linear equations that have one solution, no solution, or infinitely many solutions.
- I will solve systems of linear equations by eliminating variables.
Data in 2-Variables
- I will make and use lines of best fit on scatterplots and their equations to analyze data.
- I will make and use two-way tables to understand and interpret bivariate data.
- I will make and use scatterplots to analyze associations in bivariate data.
Irrational Numbers
- I will recognize and state the value of the square root of a perfect square and estimate square roots of other whole numbers.
- I will compare irrational numbers by approximating their value and placing them on a number line and estimate the value of expressions involving irrational numbers.
- I will know that the numbers that are not rational are called irrational and understand the decimal expansions of different kinds of numbers, including converting repeating decimals into fractions.
- I will calculate or estimate square and cube roots of numbers and understand the inverse relationship of powers and roots.
Laws of Exponents
- I will develop and apply the laws of exponents for multiplication and division to generate equivalent numerical expressions.
- I will generate equivalent expressions in which an exponent is raised to another exponent.
- I will understand and simplify expressions containing integer exponents.
Grade 7
Operations with Rational Numbers
- I will multiply and divide integers and other rational numbers.
- I will subtract integers and other rational numbers with and without the use of a number line.
- I will add integers and other rational numbers with and without the use of a number line.
- I will make sense of situations where an integer is combined with its opposite.
Operations with Linear Expressions
- I will add and subtract linear algebraic expressions.
- I will expand linear expressions.
- I will factor linear algebraic expressions
Two Step Equations & Inequalities
- I will solve one and two-step inequalities and graph the solution set of an inequality on a number line.
- I will solve two-step equations.
- I will translate verbal sentences into algebraic inequalities.
- I will translate real world situations into algebraic expressions and equations.
- I will solve algebraic equations using the distributive property.
- I will solve two-step equations with positive and negative numbers.
Proportional Reasoning
- I will graph a proportional relationship and explain what a point (x, y) on the graph means in terms of a situation.
- I will use ratio reasoning to decide if two quantities are in a proportional relationship.
- I will represent proportional relationships by equations.
Applying Percents
- I will represent fractions as terminating or repeating decimals.
- I will solve real world and mathematical problems about simple interest.
- I will represent rational numbers in multiple ways.
Grade 6
Positive & Negative Numbers on Number Line
- I will identify and plot points in all four quadrants of a coordinate plane.
- I will find and interpret the absolute value of positive and negative rational numbers in mathematical and real world situations.
- I will write, interpret, and explain statements of order for rational numbers on the number line and in real world contexts.
- I will use integers and other rational numbers to represent numerical situations and place them on a number line.
Algebraic Expressions
- I will use substitution to evaluate algebraic expressions or formulas using the order of operations, including parentheses and exponents.
- I will substitute values into algebraic expressions and evaluate the expressions.
- I will use variables to represent numbers and write expressions to represent a real world or mathematical problem.
Numerical Expressions
- I will evaluate numerical expressions using the order of operations, including parentheses and exponents.
- I will find common factors and the greatest common factor (GCF) of two or more whole numbers and rewrite expressions using common factors and the distributive property.
- I will translate between repeated multiplication and exponential form and find the value of a whole number raised to a power.
Simple Equations and Inequalities
- I will write a simple inequality to represent a condition or constraint in a real world or mathematical problem and represent solutions to inequalities on number line diagrams.
- I will solve one-step algebraic equations.
- I will solve problems by writing, solving, and interpreting one-step equations.
- I will understand solving an equation as finding the values for the variable that make the equation true.
Ratio Thinking
- I will make tables of equivalent ratios, find missing values in the tables, plot the pairs of values on a coordinate plane, and use tables to compare ratios.
- I will know how ratios work and express ratios in different forms using ratio language.
- I will understand the concept of rate and calculate and compare unit rates.
- I will represent linear relationships in tables, equations, and graphs in the first quadrant of the coordinate plane.
Percents
- I will determine percents from ratios.
- I will solve real world and mathematical problems involving percents, including finding the whole, given a part and percent.
- I will represent percents as decimals to hundredths, fractions out of 100, and on a 100 grid.
Grade 5
Understanding the Coordinate Plane
- I will generate two numerical patterns using two given rules, graph ordered pairs of corresponding terms on a coordinate plane, and identify apparent relationships between corresponding terms.
- I will use a pair of perpendicular lines, called axes, to define a coordinate system and locate points using coordinates.
- I will solve real-world problems by plotting and interpreting points in the first quadrant of the coordinate plane.
Fraction and Decimal Thinking
- I will simplify fractions to lowest terms.
- I will multiply whole numbers by fractions.
- I will interpret fractions as division of the numerator by the denominator and solve whole number division problems leading to answers in the form of fractions or mixed numbers.
- I will multiply a decimal by a whole number using a variety of strategies.
- I will divide a decimal by a whole number using a variety of strategies.
Powers of 10
- I will explain patterns about multiplying or dividing decimal numbers by powers of ten.
- I will explain patterns in the number of zeros in the products when multiplying whole numbers by 10; 100; and 1,000.
Basic Algebraic Thinking
- I will use the order of operations, including parentheses, to evaluate numerical expressions involving whole numbers.
Grade 4
Understanding the Coordinate Plane
- I will identify and draw intersecting, perpendicular, and parallel lines.
- I will identify and classify lines, line segments, rays, and angles.
Fraction and Decimal Thinking
- I will create equivalent fractions and explain fraction equivalence.
Multiplying & Dividing
- I will identify and use the distributive property of multiplication over addition, relating it to area models.
- I will identify all the factors of a given whole number and identify prime and composite numbers.
- I will calculate and list multiples of whole numbers.
- I will multiply 2-digit by 2-digit numbers using area models to represent partial products.
- I will make sense of multiplicative comparisons.
Basic Algebraic Thinking
- I will generate a number or shape pattern that follows a given rule and identify features of the pattern.
- I will define, identify, and use the commutative and associative properties of addition and multiplication.
- I will solve word problems involving operations with whole numbers.
- I will solve two-step word problems using all four operations.
Grade 3
Missing Values in Equations
- I will determine an unknown whole number in a multiplication or division equation.
Multiplying & Dividing
- I will develop and use a formula for finding the area of rectangles.
- I will understand the concept of area and find area of figures by counting square units.
Grade 2
Missing Values in Equations
- I will determine an unknown whole number in an addition or subtraction equation.
