# 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

## Multi-Step Equations

8

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

## Multi-Step Equations

8

I will solve multistep equations with rational numbers.

## 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 use similar triangles to explain constant slope and derive equations to describe lines.

## Analyzing Linear Functions

8

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

## 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.

## Linear Relationships

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.

## Linear Relationships

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 Relationships

8

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

## Systems of Linear Equations

8

I will solve systems of two linear equations graphically.

## 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.

## Systems of Linear Equations

8

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

## Understanding Functions

8

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

## Understanding Functions

8

I will determine function rules of functions represented in tables.

## Understanding Functions

8

I will use graphs to represent linear functions given by equations or linear data from a table.

## 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.

## Data in 2 Variables

8

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

## Dilations

7

I will solve real world and mathematical problems using similar triangles or other similar shapes.

## Dilations

8

I will draw the image of a figure under a dilation on a coordinate plane.

## Dilations

8

I will understand similarity and describe a sequence of transformations that exhibits similarity between two figures.

## Rigid Motion

8

I will verify experimentally the properties of rotations, reflections, and translations.

## Rigid Motion

8

I will draw the image of a figure under a translation on a coordinate plane.

## Rigid Motion

8

I will draw the image of a figure under a reflection on a coordinate plane.

## Rigid Motion

8

I will draw the image of a figure under a rotation on a coordinate plane.

## Rigid Motion

8

I will use transformations to map a figure onto a congruent figure.

## Angle Relationships

7

I will use angle relationships of intersecting lines to solve mathematical and real world problems.

## Angle Relationships

8

I will determine angle relationships when two lines (parallel or not) are cut by a transversal and use angle relationships to solve real world and mathematical problems.

## Angle Relationships

8

I will establish facts about the angle sum and exterior angles of triangles.

## Angle Relationships

8

I will explore and explain triangle similarity, especially the angle angle criterion.

## 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 understand and simplify expressions containing integer exponents.

## Laws of Exponents

8

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

## Scientific Notation

8

I will use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

## Scientific Notation

8

I will write and compare numbers in scientific notation.

## Scientific Notation

8

I will solve real world and mathematical problems involving numbers in scientific notation.

## Rational and 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.

## Rational and Irrational Numbers

8

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

## Rational and 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.

## Rational and 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.

## Pythagorean Theorem

8

I will explore and explain the Pythagorean Theorem.

## Pythagorean Theorem

8

I will use the Pythagorean Theorem to determine the unknown length of a side of a right triangle and explore Pythagorean triples.

## Pythagorean Theorem

8

I will solve real world and mathematical problems using the Pythagorean Theorem.

## Pythagorean Theorem

8

I will use and explain the distance formula on a coordinate plane.

## Circular Volume

8

I will develop and use a formula to determine the volume of cylinders.

## Circular Volume

8

I will develop and use a formula to determine the volume of cones.

## Circular Volume

8

I will develop and use a formula to determine the volume of spheres.

## Operations with Rational Numbers

7

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

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

## Solving 2-Step Equations

7

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

## Solving 2-Step Equations

7

I will solve two-step equations.

## Solving 2-Step Equations

7

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

## Solving 2-Step Equations

7

I will solve algebraic equations using the distributive property.

## Solving 2-Step Equations

7

I will add and subtract linear algebraic expressions.

## Proportional Thinking

7

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

## Proportional Thinking

7

I will represent proportional relationships by equations.

## Proportional Thinking

7

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

## Proportional Thinking

7

I will represent fractions as terminating or repeating decimals.

## Proportional Thinking

7

I will represent rational numbers in multiple ways.

## Circles

7

I will explore the relationship between the circumference and diameter of a circle in order to determine the circumference of a circle.

## Circles

7

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

## 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.

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

## Algebraic Expressions

6

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

## Algebraic Expressions

6

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

## Algebraic Expressions

6

I will use substitution to evaluate algebraic expressions or formulas 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.

## Numerical Expressions

6

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

## Solving Simple Equations

6

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

## Solving Simple Equations

6

I will solve one-step algebraic equations.

## Solving Simple Equations

6

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

## Standard Algorithm Operations

6

I will fluently multiply multi-digit decimals using the standard algorithm.

## Standard Algorithm Operations

6

I will fluently divide multi-digit decimals using the standard algorithm.

## Ratio Thinking

6

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

## 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 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.

## Ratio Thinking

6

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

## Ratio Thinking

6

I will determine percents from ratios.

## Area of Triangles and Quadrilaterals

5

I will classify and draw triangles by their angles and sides.

## Area of Triangles and Quadrilaterals

6

I will develop and use an area formula in order to determine the area of any triangle.

## Area of Triangles and Quadrilaterals

6

I will develop and use an area formula in order to determine the area of any parallelogram.

## Decimal Place Value

4

I will compare decimals using models.

## Decimal Place Value

5

I will understand the value of a single digit in a multi-digit number and explain the relationship between the digits.

## Decimal Place Value

5

I will read and write decimal numbers using base ten numerals, number names, and expanded form.

## Decimal Place Value

5

I will compare and order decimals using the math symbols <, >, and =.

## Decimal Place Value

5

I will use rounding rules to round numbers to the ones place and decimal place values.

## 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.

## 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.

## Advanced Whole Number Operations

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.

## Advanced Whole Number Operations

5

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

## 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.

## Powers of 10

5

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

## Decimal Operations

5

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

## Decimal Operations

5

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

## Decimal Operations

5

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

## Decimal Operations

5

I will divide a decimal by a decimal using multiple strategies.

## Fraction Operations

5

I will simplify fractions to lowest terms.

## Fraction Operations

5

I will multiply whole numbers by fractions.

## Fraction Operations

5

I will interpret multiplication as scaling.

## Volume

5

I will understand volume and measure it using unit cubes.

## Volume

5

I will develop and use a formula for finding the volume of rectangular prisms.

## Missing Equation Values

2

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

## Missing Equation Values

3

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

## Multiplying & Dividing

3

I will multiply one-digit whole numbers by multiples of 10.

## Multiplying & Dividing

4

I will calculate and list multiples of whole numbers.

## Multiplying & Dividing

4

I will make sense of multiplicative comparisons.

## 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.

## Understanding 2-D Objects

4

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

## Understanding 2-D Objects

4

I will understand angles measured in degrees as a fraction of a circle.

## Understanding 2-D Objects

4

I will draw and measure angles and classify angles as acute, obtuse, right, and straight.

## Understanding 2-D Objects

4

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

## Understanding 2-D Objects

4

I will solve addition and subtraction problems to find unknown angles.

## Understanding 2-D Objects

5

I will classify and draw quadrilaterals by their angles and sides.

## Understanding Area

3

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

## Understanding Area

3

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

## Understanding Fractions

4

I will create equivalent fractions and explain fraction equivalence.

## Understanding Fractions

4

I will understand decimals are part of a whole and express decimals as fractions to tenths or hundredths.

## Understanding Fractions

4

I will understand a fraction as a multiple of a unit fraction.

## Understanding Fractions

4

I will recognize and generate equivalent products of fractions and whole numbers.

## Whole Numbers

4

I will read and write whole numbers up to millions using base-ten numerals, number names, and expanded form.

## Whole Numbers

4

I will round whole numbers to the nearest ten, hundred, or thousand.

## Whole Numbers

4

I will compare whole numbers up to millions.

## Basic Algebraic Thinking

3

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

## Basic Algebraic Thinking

4

I will solve word problems involving operations with whole numbers.

## 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.