# Fill in the gaps with grade level roadmaps

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.

## Roadmap Skill Cluster

## Grade

## Description

## Complex Linear Equations & Inequalities

9

I will solve multi-step inequalities and graph the solution set of an inequality on a number line.

## Complex Linear Equations & Inequalities

9

I will write algebraic equations or inequalities that represent a situation.

## Complex Linear Equations & Inequalities

9

I will solve literal equations for a given variable.

## Complex Linear Equations & Inequalities

9

I will analyze and solve verbal problems whose solution requires solving a linear inequality in one variable.

## Polynomial Operations

9

I will add and subtract polynomials.

## Polynomial Operations

9

I will multiply a binomial by a monomial or a binomial.

## Polynomial Operations

9

I will identify polynomials and represent them in standard form.

## Polynomial Operations

9

I will multiply and divide monomial expressions with a common base.

## Linear Function Analysis

9

I will write the equation of a line, given its slope and the coordinates of a point on the line.

## Linear Function Analysis

9

I will determine the slope of a line, given its equation in any form.

## Linear Function Analysis

9

I will use function notation and identify the domain and range of functions.

## Linear Function Analysis

9

I will calculate and interpret the average rate of change of a function over a specified interval.

## Advanced Functions & Sequences

9

I will identify the effects of transformations on equations and graphs of quadratic functions.

## Advanced Functions & Sequences

9

I will compare properties of two functions each represented in a different way.

## Advanced Functions & Sequences

9

I will recognize geometric sequences are functions and write them both recursively and explicitly.

## Advanced Functions & Sequences

9

I will recognize arithmetic sequences are functions and write them both recursively and explicitly.

## Advanced Linear Functions

9

I will determine if two lines are parallel, given their equations in any form.

## Advanced Linear Functions

9

I will explore the concept of inverse functions and find inverses of linear functions.

## Advanced Linear Functions

9

I will graph piecewise-defined functions including step functions and absolute value functions.

## Advanced Systems of Functions

9

I will solve systems of linear and quadratic equations graphically.

## Advanced Systems of Functions

9

I will solve a system of one linear and one quadratic equation in two variables algebraically.

## Advanced Systems of Functions

9

I will graph linear inequalities in two variables.

## Advanced Systems of Functions

9

I will graph and solve systems of linear inequalities with rational coefficients in two variables.

## Exponential Functions

9

I will calculate compound interest and solve real world and mathematical problems involving interest.

## Exponential Functions

9

I will analyze and solve verbal problems that involve exponential growth and decay.

## Exponential Functions

9

I will identify and graph exponential functions.

## Exponential Functions

9

I will distinguish between situations that can be modeled with linear and exponential functions.

## Factoring Polynomials

9

I will factor polynomial expressions using the greatest common factor (GCF) of the terms.

## Factoring Polynomials

9

I will factor quadratic expressions with three terms.

## Factoring Polynomials

9

I will identify and factor the difference of two perfect squares.

## Factoring Polynomials

9

I will factor algebraic expressions completely.

## Factoring Polynomials

9

I will factor trinomials where the leading coefficient is not equal to 1.

## Graphing Quadratics

9

I will find the roots, vertex, and axis of symmetry of a parabola given its graph.

## Graphing Quadratics

9

I will determine the vertex and axis of symmetry of a parabola, given its equation.

## Graphing Quadratics

9

I will graph quadratic relationships from equations or tables of values.

## Solving Quadratics

9

I will analyze and solve verbal problems that involve quadratic equations.

## Solving Quadratics

9

I will understand and apply the multiplication property of zero to solve quadratic equations by factoring.

## Solving Quadratics

9

I will solve quadratic equations by completing the square.

## Solving Quadratics

9

I will derive the quadratic formula and use it to solve quadratic equations.

## Solving Quadratics

9

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

9

I will distinguish between correlation and causation.

## Advanced Data in Two Variables

9

I will compute and interpret the correlation coefficient of a linear fit.

## Advanced Data in Two Variables

9

I will interpret relative frequencies in two-way tables in the context of the data and recognize possible associations and trends in the data.

## Advanced Data in Two Variables

9

I will use residuals to analyze how well a function fits data.

## Advanced Single Variable Data

9

I will summarize, represent, and interpret data in histograms and cumulative frequency histograms.

## Advanced Single Variable Data

9

I will summarize, represent, and interpret data in box plots, find percentiles, and use a five number summary.

## Advanced Single Variable Data

9

I will find the standard deviation of a data set and use it describe and compare data sets.

## Radical Expressions

9

I will simplify radical terms.

## Radical Expressions

9

I will perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form.

## Radical Expressions

9

I will explore and explain properties of sums and products of rational and irrational numbers.

## Radical Expressions

9

I will explain how the system of integer exponents extends to rational number exponents, including representing radicals in terms of rational exponents.

## Radical Expressions

9

I will explain how the system of integer exponents extends to rational number exponents, including representing radicals in terms of rational exponents.

## Multi-Step Equations

8

I will solve multistep equations with rational numbers.

## Multi-Step Equations

8

I will solve equations by moving variables to one side of an equation.

## Multi-Step Equations

8

I will give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

## Analyzing Linear Functions

8

I will create graphs to match given descriptions of situations involving a relationship between two variables or describe situations that could match given graphs.

## Analyzing Linear Functions

8

I will distinguish between linear and non-linear relationships.

## Analyzing Linear Functions

8

I will represent, analyze, and compare linear relationships in graphs, equations, and tables.

## Analyzing Linear Functions

8

I will determine the slope and the equation of a line given the coordinates of two points on the line.

## Linear Functions

8

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.

## Linear Functions

8

I will construct a function to model a linear relationship and describe the rate of change and initial value.

## Linear Functions

8

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

8

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

8

I will determine function rules of functions represented in tables.

## Understanding Functions

8

I will define and identify functions in tables, graphs, and ordered pairs.

## Systems of Linear Equations

8

I will solve systems of two linear equations graphically.

## Systems of Linear Equations

8

I will analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables.

## Systems of Linear Equations

8

I will solve systems of two linear equations in two variables algebraically.

## Systems of Linear Equations

8

I will recognize systems of linear equations that have one solution, no solution, or infinitely many solutions.

## Systems of Linear Equations

8

I will solve systems of linear equations by eliminating variables.

## Data in 2-Variables

8

I will make and use lines of best fit on scatterplots and their equations to analyze data.

## Data in 2-Variables

8

I will make and use two-way tables to understand and interpret bivariate data.

## Data in 2-Variables

8

I will make and use scatterplots to analyze associations in bivariate data.

## Irrational Numbers

8

I will recognize and state the value of the square root of a perfect square and estimate square roots of other whole numbers.

## Irrational Numbers

8

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.

## Irrational Numbers

8

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.

## Irrational Numbers

8

I will calculate or estimate square and cube roots of numbers and understand the inverse relationship of powers and roots.

## Laws of Exponents

8

I will develop and apply the laws of exponents for multiplication and division to generate equivalent numerical expressions.

## Laws of Exponents

8

I will generate equivalent expressions in which an exponent is raised to another exponent.

## Laws of Exponents

8

I will understand and simplify expressions containing integer exponents.

## Operations with Rational Numbers

7

I will multiply and divide integers and other rational numbers.

## Operations with Rational Numbers

7

I will subtract integers and other rational numbers with and without the use of a number line.

## Operations with Rational Numbers

7

I will add integers and other rational numbers with and without the use of a number line.

## Operations with Rational Numbers

7

I will make sense of situations where an integer is combined with its opposite.

## Operations with Linear Expressions

7

I will add and subtract linear algebraic expressions.

## Operations with Linear Expressions

7

I will expand linear expressions.

## Operations with Linear Expressions

7

I will factor linear algebraic expressions

## Two Step Equations & Inequalities

7

I will solve one and two-step inequalities and graph the solution set of an inequality on a number line.

## Two Step Equations & Inequalities

7

I will solve two-step equations.

## Two Step Equations & Inequalities

7

I will translate verbal sentences into algebraic inequalities.

## Two Step Equations & Inequalities

7

I will translate real world situations into algebraic expressions and equations.

## Two Step Equations & Inequalities

7

I will solve algebraic equations using the distributive property.

## Two Step Equations & Inequalities

7

I will solve two-step equations with positive and negative numbers.

## Proportional Reasoning

7

I will graph a proportional relationship and explain what a point (x, y) on the graph means in terms of a situation.

## Proportional Reasoning

7

I will use ratio reasoning to decide if two quantities are in a proportional relationship.

## Proportional Reasoning

7

I will represent proportional relationships by equations.

## Applying Percents

7

I will represent fractions as terminating or repeating decimals.

## Applying Percents

7

I will solve real world and mathematical problems about simple interest.

## Applying Percents

7

I will represent rational numbers in multiple ways.

## Positive & Negative Numbers on Number Line

6

I will identify and plot points in all four quadrants of a coordinate plane.

## Positive & Negative Numbers on Number Line

6

I will find and interpret the absolute value of positive and negative rational numbers in mathematical and real world situations.

## Positive & Negative Numbers on Number Line

6

I will write, interpret, and explain statements of order for rational numbers on the number line and in real world contexts.

## Positive & Negative Numbers on Number Line

6

I will use integers and other rational numbers to represent numerical situations and place them on a number line.

## Algebraic Expressions

6

I will use substitution to evaluate algebraic expressions or formulas using the order of operations, including parentheses and exponents.

## Algebraic Expressions

6

I will substitute values into algebraic expressions and evaluate the expressions.

## Algebraic Expressions

6

I will use variables to represent numbers and write expressions to represent a real world or mathematical problem.

## Numerical Expressions

6

I will evaluate numerical expressions using the order of operations, including parentheses and exponents.

## Numerical Expressions

6

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.

## Numerical Expressions

6

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

6

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.

## Simple Equations and Inequalities

6

I will solve one-step algebraic equations.

## Simple Equations and Inequalities

6

I will solve problems by writing, solving, and interpreting one-step equations.

## Simple Equations and Inequalities

6

I will understand solving an equation as finding the values for the variable that make the equation true.

## Ratio Thinking

6

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.

## Ratio Thinking

6

I will know how ratios work and express ratios in different forms using ratio language.

## Ratio Thinking

6

I will understand the concept of rate and calculate and compare unit rates.

## Ratio Thinking

6

I will represent linear relationships in tables, equations, and graphs in the first quadrant of the coordinate plane.

## Percents

6

I will determine percents from ratios.

## Percents

6

I will solve real world and mathematical problems involving percents, including finding the whole, given a part and percent.

## Percents

6

I will represent percents as decimals to hundredths, fractions out of 100, and on a 100 grid.

## Understanding the Coordinate Plane

4

I will identify and draw intersecting, perpendicular, and parallel lines.

## Understanding the Coordinate Plane

4

I will identify and classify lines, line segments, rays, and angles.

## Understanding the Coordinate Plane

5

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.

## Understanding the Coordinate Plane

5

I will use a pair of perpendicular lines, called axes, to define a coordinate system and locate points using coordinates.

## Understanding the Coordinate Plane

5

I will solve real-world problems by plotting and interpreting points in the first quadrant of the coordinate plane.

## Fraction and Decimal Thinking

4

I will create equivalent fractions and explain fraction equivalence.

## Fraction and Decimal Thinking

5

I will simplify fractions to lowest terms.

## Fraction and Decimal Thinking

5

I will multiply whole numbers by fractions.

## Fraction and Decimal Thinking

5

I will multiply whole numbers by fractions.

## Fraction and Decimal Thinking

5

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.

## Fraction and Decimal Thinking

5

I will multiply a decimal by a whole number using a variety of strategies.

## Fraction and Decimal Thinking

5

I will divide a decimal by a whole number using a variety of strategies.

## Powers of 10

5

I will explain patterns about multiplying or dividing decimal numbers by powers of ten.

## Powers of 10

5

I will explain patterns in the number of zeros in the products when multiplying whole numbers by 10; 100; and 1,000.

## Missing Values in Equations

2

I will determine an unknown whole number in an addition or subtraction equation.

## Missing Values in Equations

3

I will determine an unknown whole number in a multiplication or division equation.

## Multiplying & Dividing

3

I will develop and use a formula for finding the area of rectangles.

## Multiplying & Dividing

3

I will understand the concept of area and find area of figures by counting square units.

## Multiplying & Dividing

4

I will identify and use the distributive property of multiplication over addition, relating it to area models.

## Multiplying & Dividing

4

I will identify all the factors of a given whole number and identify prime and composite numbers.

## Multiplying & Dividing

4

I will calculate and list multiples of whole numbers.

## Multiplying & Dividing

4

I will multiply 2-digit by 2-digit numbers using area models to represent partial products.

## Multiplying & Dividing

4

I will make sense of multiplicative comparisons.

## Basic Algebraic Thinking

4

I will generate a number or shape pattern that follows a given rule and identify features of the pattern.

## Basic Algebraic Thinking

4

I will define, identify, and use the commutative and associative properties of addition and multiplication.

## Basic Algebraic Thinking

4

I will solve word problems involving operations with whole numbers.

## Basic Algebraic Thinking

4

I will solve two-step word problems using all four operations.

## Basic Algebraic Thinking

5

I will use the order of operations, including parentheses, to evaluate numerical expressions involving whole numbers.