# Middle School Mathematics

##### Topic: Use Positive Rational Numbers
• Use algorithms to fluently add, subtract, and multiply decimals.
• Apply fluency in dividing whole numbers to divide with decimals.
• Define terms related to simplifying fractions, describe why fractions are simplified, and
simplify fractions, include use of divisibility rules.
• Interpret and write expressions using whole-number exponents
• Find the greatest common factor and the least common multiple of two whole numbers.
• Add and subtract fractions with like denominators
• Create equivalent fractions that have common denominator to add and subtract fractions with
unlike denominators
• Use an algorithm to multiply fractions and mixed numbers.
• Apply the inverse relationship of multiplication and division to write division expressions as
equivalent multiplication expressions to divide fractions, including dividing a whole number
by a fraction, a fraction by a whole number, and a fraction by a fraction.
• Apply understanding of dividing fractions to divide with mixed numbers by renaming the
mixed numbers as fractions.
• Solve multi-step problems with rational numbers (fractions and decimals).
• Determine the mean, median, mode, and range of a data set.
##### Topic: Integers and Rational Numbers
• Understanding how integers are used to describe quantities. Identify opposites of integers,
as well as compare and order integers.
• Graph rational numbers on the number line. Compare and order rational numbers.
• Apply knowledge that opposites are equidistant from 0 on the number line to develop an
understanding of absolute value. Interpret absolute value in real-world situations.
• Identify and graph points with rational coordinates in all four quadrants on the coordinate
plane.
##### Topic: Numeric and Algebraic Expressions
• Evaluate expressions using the order of operations. Insert grouping symbols in a numerical
expression to affect the value of the expression.
• Write an algebraic expression from a word or phrase, as well as to model real-world
situations. Use precise mathematical language when identifying parts of an expression.
• Evaluate algebraic expressions, including those with whole numbers, decimals, and
fractions.
• Formalize understanding of the commutative, associate, and distributive properties. Apply
the properties to identify and write equivalent algebraic expressions.
• Use properties of operations to simplify algebraic expressions by combining like terms.
##### Topic: Represent and Solve Equations and Inequalities
• Develop an understanding of how to ensure that one side of the equation balances with the other side. Use properties of equality to keep both sides of an equation equal.
• Understand that a solution of an equation is a value for the variable that makes the equation
true. Substitute given values for a variable to see which value, if any, makes the equation
true.
• Use inverse relationships and properties of equality to solve single-step addition and
subtraction equations. Write one-variable addition and subtraction equations.
• Use inverse relationships and properties of equality to solve single-step multiplication and
division equations. Write one-variable multiplication and division equations.
• Write and solve equations with rational numbers, including fractions, decimals, and mixed
numbers.
• Understand the symbols required to write an inequality. Write inequalities to describe
mathematical or real-world situations.
• Describe solutions to inequalities. Represent solutions to an inequality on a number line.
• Analyze real-world situations and identify the independent and dependent variables.
##### Topic: Understand Ratio and Rate
• Develop a conceptual understanding of ratios as a comparison of two quantities and learn to
express ratios in three ways.
• Develop an understanding that an equivalent ratio with greater or lesser terms represents
the same ratio relationship. Learn a procedural method of generating equivalent ratios by
multiplying or dividing the original terms of a ratio by the same non-zero number.
• Understand how to compare ratios using a common term and apply this understanding to
solving real-world and mathematical problems.
• Generate a table of equivalent ratios and represent the ratio relationship by graphing the
corresponding pairs on the coordinate plane.
• Develop an understanding of rates and unit rates and learn how to find them. Solve real-
world problems involving rates and unit rates, including unit price.
• Use ratio reasoning to compare unit rates.
• Use ratio reasoning and conversion factors to convert customary units of measure.
• Use ratio reasoning and conversion factors to convert metric units of measure.
• Use ratio reasoning and conversion factors to convert between customary and metric units
of measure.
##### Topic: Understand and Use Percent
• Develop an understanding that a percent is a special type of ratio comparing a part to a whole in which the whole is 100.
• Further conceptual understanding of percents by learning procedures for finding equivalent
fractions, decimals, and percents.
• Use the decimal form of a percent to find the percent of a number. Write an equation to solve
percent problems.
• Solve an equation to find the whole given a part and the percent. Apply this skill to solve
percent problems.
##### Topic: Solve Area Problems
• Explore and classify quadrilaterals. Find the missing angle measure of a quadrilateral.
• Use formulas to find the areas of parallelograms and rhombuses. Find the base or height of
a parallelogram or rhombus when the area and the height or base are known.
• Find the area of triangle, including right triangles. Find the corresponding base or height of a
triangle.
• Use a formula to find the area of equilateral triangles.
• Use formulas to find the areas of trapezoids and kites.
• Explore and classify polygons. Determine the sum of the measures of the interior and
Exterior angles of a polygon.
• Find the areas of polygons by composing and decomposing shapes, including polygons on
the coordinate plane.

##### Topic: Polynomials and Factoring
• Factor a polynomial by finding the greatest common factor of the terms of a polynomial.
• Factor a trinomial in the form x^2+bx+c or ax^2+bx+c.
• Factoring special case trinomials: perfect square trinomials; difference of squares
• Solve equations by factoring (zero product property)
• Factor the sum and difference of cubes
##### Topic: Exploring Rational Expressions and Equations
• Simplify rational expressions by factoring the numerator and denominator. State the
restrictions (excluded values) on the variable.
• Add and subtract rational expressions with like and unlike denominators.
• Multiplying and divide rational expressions.
• Divide polynomials using long division and synthetic division.
• Simplify mixed expressions and complex fractions.
• Solve rational equations by using the common denominator method with numerical
denominators and with variables in the denominator.
• Identify key features of the graph of a quadratic function using graphs, tables, and
equations. Describe the effects of the leading coefficient a on the quadratic parent function.
• Identify key features of the graph of a quadratic function in vertex form. Graph quadratic
functions in vertex form.
• Graph quadratic functions in standard form. Determine key characteristics of a quadratic
function written in standard form.
• Compare and determine which model — linear, exponential, or quadratic – best fits a set of
data.
• Solve quadratic equations using tables and graphs.
• Solve quadratic equations using the following methods: factoring; using square roots;
completing the square; and using the quadratic formula.
• Simplifying radical expressions and use properties of exponents to rewrite radical
expressions, including operations with radical expressions.
• Describe a non-linear system of equations. Solve a linear-quadratic system of equations by
graphing, elimination, or substitution.
• Add, subtract, multiply, and divide complex numbers.
##### Topic: Exploring Radical Expressions and Equations
• Solve equations that contain radicals or radical expressions. Identify extraneous solutions.
• Use the Pythagorean Theorem to find side lengths of right triangles and to find the areas of
right triangles. Apply the Pythagorean Theorem to find the perimeter and area of right
triangles on a grid.
• Use the distance formula to find the distance between two points in the coordinate plane.
Explain how the distance formula is derived from the Pythagorean Theorem.
• Identify trigonometric relationships (sine, cosine, and tangent) using right triangles,
expressing the relationships as fractions or decimals.
• Use trigonometry to find the area of regular polygons and triangles.
• Determine the side lengths of special right triangles: 45°-45°-90° triangles;
30°-60°-90° triangles. Solve problems using the properties of special right triangles.
##### Topic: Exponents and Exponential Functions
• Extend the properties of integer exponents to rational exponents to rewrite radical
expressions using rational exponents. Solve equations with rational exponents using the
properties of exponents.
• Write and graph exponential functions.
• Construct exponential growth and decay functions given a description of a relationship.
• Write arithmetic sequences both recursively and with an explicit formula, and translate
between the two forms.
• Write geometric sequences both recursively and with an explicit formula, and translate
between the two forms.
• Translate the graph of an exponential function vertically and horizontally, identifying the
effect different values of h and k have on the graph of the function.
##### Topic: Statistics
• Represent data using dot plots, box plots and histograms, and use them to make inferences
• Use measures of center to interpret and compare data sets displayed in dot plots, box plots
and histograms. Explain and account for the effect of outliers on measures of center and
variability.
• Use standard deviation to quantify and analyze the spread of data.
• Calculate measures of frequency to analyze and interpret categorical data using two-way
frequency tables.

#### Regular 7th & Advanced 6th

##### Topic: Integers and Rational Numbers
• Understand how integers, their opposites, and absolute value are related.
• Add, subtract, multiply, and divide integers
• Add, subtract, multiply, and divide rational numbers
##### Topic: Generate Equivalent Expressions
• Write and evaluate algebraic expressions.
• Use properties of operations to generate equivalent expressions
• Simplify expressions with rational coefficients, using the properties of operations to combine
like terms.
• Use the distributive property to expand an expression, which provides an equivalent way to
represent the expression.
• Find common factors of linear expressions using the distributive property. Recognize
factoring is the opposite of expanding expressions.
• Use properties of operations to add and subtract expressions.
##### Topic: Solve Problems Using Equations and Inequalities
• Solve two-step equations using properties of equality, as well as compare algebraic and
arithmetic solutions.
• Solve multi-step equations using the distributive property.
• Analyze word problems to write two-step equations. Understand the relationship between the terms of the equation and values they represent.
• Solve and graph the solution sets for inequalities using the addition, subtraction,
multiplication, and division properties of inequalities.
• Extend prior understanding of inequalities to write and solve two-step inequalities.
• Extend prior knowledge of how to write and solve two-step inequalities and apply this
understanding to solving and graphing solutions sets for multi-step inequalities.
##### Topic: Analyze and Use Proportional Relationships
• Use ratios and rates to describe the relationship between quantities. Find equivalent ratios
and use unit rates to solve multi-step problems.
• Determine whether quantities are a proportional relationship by testing for equivalent ratios.
• Represent proportional relationships with equations in the form y=kx, where k is the
constant of proportionality that relates two proportional quantities.
• Graph proportional relationships on the coordinate plane. Understand the characteristics of
a graph of a proportional relationship.
• Explain whether a problem situation describes a proportional relationship in order to
choose an appropriate solving strategy.
##### Topic: Analyze and Solve Percent Problems
• Apply an understanding of equivalent ratios to solve percent problems.
• Construct a percent proportion. Use a percent proportion to find an unknown part, whole, or
percent.
• Understand the relationship between proportional reasoning and percent in order to solve a
percent equation.
• Use the percent equation to solve percent change and percent error problems.
• Use the percent equation to analyze the relationship between proportional reasoning and
percent, then solve problems related to markups, markdowns, and sales tax.
• Use the simple interest formula that is related to the percent equation to solve problems
involving simple interest.
##### Topic: Solve Problems Involving Geometry
• Make connections between scale factors and proportional relationships, and solve problems
involving scale drawings of geometric figures.
• Identify corresponding parts and find missing measures of similar triangles. Solve problems
involving indirect measurement by using similar triangles.
• Find the measure of angles using angle relationships. Recognize the relationship between
different angles formed by intersecting lines and rays.
• Identify the relationships of angles formed by parallel lines and a transversal.
• Calculate the circumference, radius, and diameter of a circle. Recognize the relationship
between the circumference of a circle, diameter of a circle, and .
• Find the area of a circle. Use the area of a circle to find the radius and diameter. Solve
problems involving the area of a circle.
• Solve problems involving surface area of geometric shapes, including rectangular and
triangular prisms, cylinders, pyramids, and cones.
• Solve problems involving volume of geometric shapes, including rectangular and triangular prisms, cylinders, pyramids, cones, and spheres.

#### Topic: Probability

• Develop an initial understanding of the concept of probability. Evaluate the likelihood of
outcomes in various situations. Calculate the probability that an event will occur.
• Develop an understanding of theoretical probability. Find the theoretical probability for an
event.
• Compare and contrast theoretical and experimental probability. Use experimental probability
to make predictions.
• Determine possible outcomes of compound events. Use different methods to model
compound events in order to determine their probabilities.

#### Regular 8th & Advanced 7th (Algebra 1)

##### Topic: Solving Equations and Inequalities
• Use the properties of operations to find sums and products of rational and irrational numbers
and explain why the result is rational or irrational.
• Create and solve multi-step linear equations in one variable, including problems involving
consecutive, consecutive even, and consecutive odd integers, and solve by writing
equivalent equations using the properties of equality.
• Use properties of equality to solve linear equations with a variable on both sides. Identify
whether linear equations have one solution, infinitely many solutions, or no solution.
• Solve basic matrix operations and equations using addition, subtraction, and multiplication.
• Solve literal equations and formulas by using the same reasoning as used when solving
equations by rearranging the equation or formula to highlight (isolate) a variable of interest.
• Solve and graph the solution sets for multi-step inequalities in one variable. Relate solving
inequalities in one variable to their understanding of solving equations in one variable.
• Solve and graph the solution sets of compound inequalities involving or and and.
• Solve absolute value equations and inequalities.

#### Topic: Linear Equations

• Investigate and analyze function (linear) families and their characteristics both algebraically
and graphically determining where a relation is a function, representing functions using
multiple representations, such as tables, graphs, and equations, and evaluating functions in
function notation.
• Calculate the slope of a line when given an equation of the line, the graph of a line, or two points on the line.
• Write the linear equation of a line in slope-intercept form, point-slope form, and standard
form.
• Graph a linear equation using slope-intercept form, standard form, x- and y-intercepts, or a table of values.
• Recognize parallel or perpendicular lines by analyzing the slope or angle relationships. Write
an equation of a line parallel or perpendicular to a given line.
• Find the midpoint of a line segment given the coordinates of the endpoints. Find the missing
endpoint of a line segment given the coordinates of the midpoint and a given endpoint.

#### Topic: Systems of Linear Equations and Inequalities

• Find the solution to a system of linear equations with, integer coefficients, by using the
following methods: graphing, substitution, and elimination.
• Find and graph the solution set to a linear inequality in two variables with integer coefficients.
• Find and graph the solution set of a system of linear inequalities in two variables with integer
coefficients.

#### Topic: Polynomials and Factoring

• Apply the multiplication properties of exponents to simplify products of exponents.
• Apply the division properties of exponents, and zero and negative exponents to divide powers
with the same base and simplify expressions with zero and negative exponents.
• Write numbers in scientific and standard notation. Multiply and divide numbers in scientific
notation.