Teach To One Roadmaps - Math Skills
8th Grade
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 8
Multi-Step Equations
- I will solve equations by moving variables to one side of an equation.
- I will solve multistep equations with rational numbers.
- I will give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
Analyzing Linear Functions
- I will use similar triangles to explain constant slope and derive equations to describe lines.
- I will represent, analyze, and compare linear relationships in graphs, equations, and tables.
- 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.
Linear Relationships
- 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 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 determine the slope and the equation of a line given the coordinates of two points on the line.
Systems of Linear Equations
- I will solve systems of two linear equations graphically.
- 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.
- I will analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables.
Understanding Functions
- I will define and identify functions in tables, graphs, and ordered pairs.
- I will determine function rules of functions represented in tables.
- I will use graphs to represent linear functions given by equations or linear data from a table.
Data in 2-Variables
- 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.
- I will make and use lines of best fit on scatterplots and their equations to analyze data.
Dilations
- I will draw the image of a figure under a dilation on a coordinate plane.
- I will understand similarity and describe a sequence of transformations that exhibits similarity between two figures.
Rigid Motion
- I will verify experimentally the properties of rotations, reflections, and translations.
- I will draw the image of a figure under a translation on a coordinate plane.
- I will draw the image of a figure under a reflection on a coordinate plane.
- I will draw the image of a figure under a rotation on a coordinate plane.
- I will use transformations to map a figure onto a congruent figure.
Angle Relationships
- 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.
- I will establish facts about the angle sum and exterior angles of triangles.
- I will explore and explain triangle similarity, especially the angle angle criterion.
Laws of Exponents
- I will develop and apply the laws of exponents for multiplication and division to generate equivalent numerical expressions.
- I will understand and simplify expressions containing integer exponents.
- I will generate equivalent expressions in which an exponent is raised to another exponent.
Scientific Notation
- 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.
- I will write and compare numbers in scientific notation.
- I will solve real world and mathematical problems involving numbers in scientific notation.
Rational and 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 calculate or estimate square and cube roots of numbers and understand the inverse relationship of powers and roots.
- 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 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
- I will explore and explain the Pythagorean Theorem.
- I will use the Pythagorean Theorem to determine the unknown length of a side of a right triangle and explore Pythagorean triples.
- I will solve real world and mathematical problems using the Pythagorean Theorem.
- I will use and explain the distance formula on a coordinate plane.
Circular Volume
- I will develop and use a formula to determine the volume of cylinders.
- I will develop and use a formula to determine the volume of cones.
- I will develop and use a formula to determine the volume of spheres.
Grade 7
Dilations
- I will solve real world and mathematical problems using similar triangles or other similar shapes.
Angle Relationships
- I will use angle relationships of intersecting lines to solve mathematical and real world problems.
Operations with Rational Numbers
- I will make sense of situations where an integer is combined with its opposite.
- I will add integers and other rational numbers with and without the use of a number line.
- 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 subtract integers and other rational numbers with and without the use of a number line.
Solving 2-Step Equations
- I will translate real world situations into algebraic expressions and equations.
- I will solve two-step equations.
- I will solve two-step equations with positive and negative numbers.
- I will solve algebraic equations using the distributive property.
- I will add and subtract linear algebraic expressions.
Proportional Thinking
- I will graph a proportional relationship and explain what a point (x, y) on the graph means in terms of a situation.
- I will represent proportional relationships by equations.
- I will use ratio reasoning to decide if two quantities are in a proportional relationship.
- I will translate real world situations into algebraic expressions and equations.
- I will represent fractions as terminating or repeating decimals.
- I will represent rational numbers in multiple ways.
Circles
- I will explore the relationship between the circumference and diameter of a circle in order to determine the circumference of a circle.
- I will develop and use the formula for the area of a circle.
Grade 6
Positive & Negative Numbers on Number Line
- I will use integers and other rational numbers to represent numerical situations and place them on a number line.
- I will write, interpret, and explain statements of order for rational numbers on the number line and in real world contexts.
- I will find and interpret the absolute value of positive and negative rational numbers in mathematical and real world situations.
- I will identify and plot points in all four quadrants of a coordinate plane.
Algebraic Expressions
- I will use variables to represent numbers and write expressions to represent a real world or mathematical problem.
- I will substitute values into algebraic expressions and evaluate the expressions.
- I will use substitution to evaluate algebraic expressions or formulas using the order of operations, including parentheses and exponents.
Numerical Expressions
- 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.
- I will evaluate numerical expressions using the order of operations, including parentheses and exponents.
Solving Simple Equations
- I will understand solving an equation as finding the values for the variable that make the equation true.
- I will solve one-step algebraic equations.
- I will solve problems by writing, solving, and interpreting one-step equations.
Standard Algorithm Operations
- I will fluently multiply multi-digit decimals using the standard algorithm.
- I will fluently divide multi-digit decimals using the standard algorithm.
Ratio Thinking
- I will know how ratios work and express ratios in different forms using ratio language.
- 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 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.
- I will represent percents as decimals to hundredths, fractions out of 100, and on a 100 grid.
- I will determine percents from ratios.
Area of Triangles and Quadrilaterals
- I will develop and use an area formula in order to determine the area of any triangle.
- I will develop and use an area formula in order to determine the area of any parallelogram.
Grade 5
Decimal Place Value
- I will understand the value of a single digit in a multi-digit number and explain the relationship between the digits.
- I will read and write decimal numbers using base ten numerals, number names, and expanded form.
- I will compare and order decimals using the math symbols <, >, and =.
- I will use rounding rules to round numbers to the ones place and decimal place values.
Understanding the Coordinate Plane
- 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.
- 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
- 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 use the order of operations, including parentheses, to evaluate numerical expressions involving whole numbers.
Powers of 10
- I will explain patterns in the number of zeros in the products when multiplying whole numbers by 10; 100; and 1,000.
- I will explain patterns about multiplying or dividing decimal numbers by powers of ten.
Decimal Operations
- 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.
- I will multiply a decimal by a decimal using a variety of strategies.
- I will divide a decimal by a decimal using multiple strategies.
Fraction Operations
- I will simplify fractions to lowest terms.
- I will multiply whole numbers by fractions.
- I will interpret multiplication as scaling.
Volume
- I will understand volume and measure it using unit cubes.
- I will develop and use a formula for finding the volume of rectangular prisms.
Understanding 2-D Objects
- I will classify and draw quadrilaterals by their angles and sides.
Grade 4
Decimal Place Value
- I will compare decimals using models.
Multiplying & Dividing
- I will calculate and list multiples of whole numbers.
- I will make sense of multiplicative comparisons.
- 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.
Understanding 2-D Objects
- I will identify and classify lines, line segments, rays, and angles.
- I will understand angles measured in degrees as a fraction of a circle.
- I will draw and measure angles and classify angles as acute, obtuse, right, and straight.
- I will identify and draw intersecting, perpendicular, and parallel lines.
- I will solve addition and subtraction problems to find unknown angles.
Understanding Fractions
- I will create equivalent fractions and explain fraction equivalence.
- I will understand decimals are part of a whole and express decimals as fractions to tenths or hundredths.
- I will understand a fraction as a multiple of a unit fraction.
- I will recognize and generate equivalent products of fractions and whole numbers.
Whole Numbers
- I will read and write whole numbers up to millions using base-ten numerals, number names, and expanded form.
- I will round whole numbers to the nearest ten, hundred, or thousand.
- I will compare whole numbers up to millions.
Basic Algebraic Thinking
- I will solve word problems involving operations with whole numbers.
- 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.
Grade 3
Missing Equation Values
- I will determine an unknown whole number in a multiplication or division equation.
Multiplying & Dividing
- I will multiply one-digit whole numbers by multiples of 10.
Understanding Area
- I will understand the concept of area and find area of figures by counting square units.
- I will develop and use a formula for finding the area of rectangles.
Basic Algebraic Thinking
- I will solve two-step word problems using all four operations.
Grade 2
Missing Equation Values
- I will determine an unknown whole number in an addition or subtraction equation.
