Teach To One Roadmaps - Math Skills
7th 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 7
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 subtract 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 solve real world and mathematical problems involving the four operations with rational numbers, especially negative numbers.
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 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 solve algebraic equations using the I will translate verbal sentences into algebraic inequalities.
- I will solve one and two-step inequalities and graph the solution set of an inequality on a number line.
Proportional Reasoning
- I will compute unit rates associated with ratios of fractions.
- 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.
Applying Percents
- I will solve problems involving percent increase/decrease.
- I will solve multistep percent problems.
- I will calculate percent of change and percent of error.
- I will solve real world and mathematical problems about simple interest.
Representing Numbers
- I will represent fractions as terminating or repeating decimals.
- I will represent rational numbers in multiple ways.
Data Analysis
- I will explore and explain the validity of sampling methods.
- I will use measures of center and variability to compare data sets.
- I will use data from random samples to draw inferences about a population and gauge variation in estimates or predictions using multiple samples.
Probability
- I will recognize independent and dependent events and calculate the probabilities of compound events.
- I will list the possible outcomes for compound events.
- I will identify the outcomes of an event and determine the probability of an outcome represented by a ratio, fraction, decimal, or percent.
- I will interpret data to establish experimental probabilities and use probabilities to predict the outcome of an experiment.
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.
- I will use a variety of strategies to find the area of two-dimensional geometric shapes composed of polygons and circles.
- I will solve problems involving volume and surface area of three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Scale Figures
- I will solve real world and mathematical problems using similar triangles or other similar shapes.
- I will solve real world and mathematical problems using maps and scale drawings.
- I will reproduce scale drawings at a different scale.
Angle Relationships
- I will use angle relationships of intersecting lines to solve mathematical and real world problems.
- I will explore how planes intersect with three-dimensional shapes.
- I will construct triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Volume and Surface Area
- I will solve problems involving volume and surface area of three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Grade 6
Dividing Fractions
- I will divide with fractions using visual models.
- I will divide with fractions using an algorithm.
Number Lines and the Coordinate Plane
- 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.
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.
Simple Equations and Inequalities
- I will understand solving an equation as finding the values for the variable that make the equation true.
- 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.
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.
Percents
- I will represent percents as decimals to hundredths, fractions out of 100, and on a 100 grid.
- 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.
Representing Data
- I will make and use dot or line plots to represent and analyze data.
- I will calculate the mean of a data set and use it to describe the data set.
- I will determine the median and mode of a data set and use these measures of center to describe the data set.
- I will make and use box plots to represent and analyze data.
- I will record data in frequency tables and make and use histograms to represent and analyze data.
- I will describe data sets and their overall shape.
Area of Polygons
- I will develop and use an area formula in order to determine the area of any parallelogram.
- I will develop and use an area formula in order to determine the area of any triangle.
- I will use decomposition to find the area of trapezoids and other polygons.
Volume and Surface Area
- I will identify two-dimensional shapes that make up the faces and bases of three-dimensional objects and use nets to represent the objects.
- I will represent figures using nets made up of rectangles and triangles and use the nets to find the surface area of these figures.
Grade 5
Number Lines and the Coordinate Plane
- I will use a pair of perpendicular lines, called axes, to define a coordinate system and locate points using coordinates.
Adding & Subtracting Fractions
- I will simplify fractions to lowest terms.
- I will add and subtract fractions with unlike denominators.
- I will add and subtract mixed numbers with unlike denominators.
- I will solve problems by adding and subtracting fractions and mixed numbers with unlike denominators.
Decimal Operations
- I will add and subtract decimals using a variety of strategies.
- 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.
Dividing 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 divide whole numbers by unit fractions in real world and mathematical problems.
- I will divide unit fractions by whole numbers in real world and mathematical problems.
- I will solve word problems involving division between unit fractions and whole numbers.
Multiplying Fractions
- I will multiply whole numbers by fractions.
- I will find the area of a rectangle with fractional side lengths.
- I will develop and use an algorithm for multiplying fractions.
- I will multiply mixed numbers.
- I will interpret multiplication as scaling.
Understanding Decimals
- 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.
- I will explain patterns about multiplying or dividing decimal numbers by powers of ten.
Numerical Expressions
- I will use the order of operations, including parentheses, to evaluate numerical expressions involving whole numbers.
Polygons
- I will classify and draw triangles by their angles and sides.
- I will classify and draw quadrilaterals by their angles and sides.
Volume of Rectangular Prisms
- I will understand volume and measure it using unit cubes.
- I will develop and use a formula for finding the volume of rectangular prisms.
- I will solve real world and mathematical problems involving additive volume and right rectangular prisms.
Multiplying & Dividing Large Numbers
- I will fluently multiply multi-digit whole numbers using the standard algorithm.
- I will divide large whole numbers by whole numbers with two or more digits and explain remainders within context.
- I will fluently divide multi-digit whole numbers using the standard algorithm.
Grade 4
Polygons
- I will recognize area as additive and find the area of polygons composed of rectangles.
Angle Relationships
- 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 solve addition and subtraction problems to find unknown angles.
Decomposing Fractions
- I will understand a fraction as a multiple of a unit fraction.
- I will recognize and generate equivalent products of fractions and whole numbers.
- I will decompose a fraction or mixed number into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.
- I will decompose a fraction or mixed number into a sum of fractions with the same denominator in I will add and subtract mixed numbers with like denominators.
Fraction Equivalence
- I will create equivalent fractions and explain fraction equivalence.
- I will add and subtract fractions with like denominators using models.
- I will add and subtract fractions with like denominators.
Multiplying & Dividing
- I will identify and use the distributive property of multiplication over addition, relating it to area models.
- I will make sense of multiplicative comparisons.
Multiplying & Dividing Large Numbers
- I will multiply 2-digit by 2-digit numbers using area models to represent partial products.
- I will divide large whole numbers by one-digit whole numbers and explain remainders within context.
- I will identify all the factors of a given whole number and identify prime and composite numbers.
Understanding Decimals
- I will use fraction equivalence to add fractions with denominators of 10 and 100.
- I will compare decimals using models.
- I will understand decimals are part of a whole and express decimals as fractions to tenths or hundredths.
- I will compare and order fractions using the math symbols <, >, and =.
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 Values in Equations
- I will determine an unknown whole number in a multiplication or division equation.
Multiplying & Dividing
- 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.
Understanding Fractions
- I will recognize and generate equivalent fractions using visual models.
- I will recognize and generate fractions and whole numbers that are equivalent.
- I will compare fractions with the same numerator or denominator.
Basic Algebraic Thinking
- I will solve two-step word problems using all four operations.
Grade 2
Missing Values in Equations
- I will determine an unknown whole number in an addition or subtraction equation.
