Expressions And Equations 
6.EE: Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions. 
6.EE.1  Write and evaluate numerical expressions involving wholenumber exponents. 
8.EE: Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations. 
8.EE.7  Solve linear equations in one variable. 
Work With Radicals And Integer Exponents. 
8.EE.1  Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. 

8.EE.2  Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. 

8.EE.3  Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. 

8.EE.4  Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 
Functions 
8.F: Define, Evaluate, And Compare Functions. 
8.F.1  Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1 
Geometry 
7.G: Solve RealLife And Mathematical Problems Involving Angle Measure, Area, Surface Area, And Volume. 
7.G.6  Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 
Ratios And Proportional Relationships 
6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems. 
6.RP.1  Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” 

6.RP.2  Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1 

6.RP.3  Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 
7.RP: Analyze Proportional Relationships And Use Them To Solve RealWorld And Mathematical Problems. 
7.RP.2  Recognize and represent proportional relationships between quantities. 
The Number System 
6.NS: Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers. 
6.NS.5  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation. 

6.NS.7.c  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a realworld situation. For example, for an account balance of –30 dollars, write –30 = 30 to describe the size of the debt in dollars. 
Compute Fluently With MultiDigit Numbers And Find Common Factors And Multiples. 
6.NS.4  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). 
8.NS: Know That There Are Numbers That Are Not Rational, And Approximate Them By Rational Numbers. 
8.NS.1  Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 