Ratios
Understand a ratio as a comparison of two quantities and represent these comparisons. 
Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate.
Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinated plane
Solve unit rate problems.
Solve percent problems.
Convert measurement units within and between two systems of measurement.

Number Sense
Solve problems involving division of fractions by fractions.
Demonstrate fluency with division of multi-digit whole numbers.
Demonstrate fluency with addition, subtraction, multiplication and division of decimals.
Find the greatest common factor (GCF) and the least common multiple (LCM).
Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers.

Rational Numbers
Use positive and negative numbers to represent quantities.
Locate rational numbers on a horizontal or vertical number line.
Write, interpret and explain problems of ordering of rational numbers.
Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line.
Understand that the absolute value of a rational number is its distance from 0 on the number line.

Expressions and Equations
Describe the difference between an expression and an equation.
Identify parts of an expression using mathematical terminology.
Evaluate expressions at specific values of the variables.
Evaluate non-negative rational number expressions
Write and evaluate algebraic expressions
Understand the meaning of the variable in the context of the situation.
Identify and generate equivalent algebraic expressions using mathematical properties
Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true.
Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true
Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation.
Solve one-step linear equations in one variable involving non-negative rational numbers
Recognize that inequalities may have infinitely many solutions.
Graph the solution set of an inequality.
Identify and describe relationships between two variables that change in relationship to one another.
Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other.

Area
Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. 
Find the volume of right rectangular prism

Coordinate Plane
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane
Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one 
Find distances between points with the same first coordinate or the same second coordinate. 
Construct polygons in the Cartesian coordinate plane. 

Shapes
Represent three-dimensional figures using nets made up of rectangles and triangles
Use nets to find the surface area of three-dimensional figures whose sides are made up of rectangles and triangles

Data
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it 
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number.
Use dot plots, histograms and box plots to display and interpret numerical data.
Create and interpret circle graphs.
Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data
Expectation Unwrapped –the intent of this section is to describe the elements of the expectation, but are NOT additional standards or expectations.Given a data set the student will recognize the appropriate measure of center based on the shape of the data. Given a data set the student will recognize the appropriate measure of center based on the context of the data.Given a data set the student will recognize the appropriate measure of variability based on the shape of the data.Given a data set the student will recognize the appropriate measure of variability based on the context of the data.DOK Ceiling3 Item FormatSelected Response Constructed ResponseTechnology EnhancedSample StemsState Assessment Content Limits/Boundaries Classroom Work Should Include ExtensionLimited to positive rational numbers and benchmark fractions.Limit data set to no more than five values when calculating MAD.Calculator DesignationYES – a calculator will be available for items

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A letter grade can be provided upon request. This letter grade will be based on IXL Smart Scores.
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Students should have already completed instruction of 6th grade math concepts. This class is meant to be a summer review over standard 6th grade topics and not a substitute for a full year of instruction.