Teach To One Roadmaps - Math Skills

# 7th Grade

## 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.

## 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.