## Math Level 5 (Grade 5-6)

Number System, Expressions and Equations​ :

​● Fluently divide multi-digit numbers using standard algorithm
● Fluently perform addition, subtraction, multiplication, and division of multi-digit decimals using standard algorithm for each operation
● Understand a rational number as a point on the number line, and recognize opposite signs of numbers as indicating locations on opposite sides of zero on the number line
● Understand the concept of absolute value, compare and order absolute value of rational numbers
● Write and evaluate numerical expressions involving whole-number exponents
● Write and evaluate algebraic expressions in which letters stand for numbers, and identify when two expressions are equivalent without substituting values into them
● Solve simple linear equation in one variable, and form simple linear equation to solve problems

Measurement and Data :

​● Understand the concept of unit rate associated with a ratio, and use ratio and rate reasoning to solve real-world mathematical problems
Understand the meaning of percentage, reverse percentage, look for percentage increase and decrease, and solve discount, sales tax, and other mathematical problems
Understand speed and average speed, and solve more challenging word problems related to speed
Read and interpret data from multiple graphs (pie charts, histograms, and line graphs), and use data to solve related problems

Geometry :

●  Recognize supplementary, complementary, vertical, and adjacent angles, and use the properties to look for unknown angles
●  Look for the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes
●  Look for the volume of a right rectangular prism with fractional edge lengths, and solve related word problems

## Math Level 6 (Grade 6-7)

Number System, Expressions and Equations :

● Apply and extend previous understanding of operations with rational numbers, and solve real-word and mathematical problems involving the four operations with rational numbers
Use variables to represent numbers, expressions, and a constraint or condition in a real-world or mathematical problem, to solve one-variable equations and inequalities
Represent and analyze quantitative relationships between dependent and independent variables

Ratios and Proportional Relationships :

● Use ratio language to describe a ratio relationship between two quantities, and use ratio and rate reasoning to solve real-world and mathematical problems
Recognize whether two quantities are in a proportional relationship, and represent proportional relationships by equations
Use proportional relationships to solve multi-step ratio and percent problems

Statistics and Probability :

● Develop understanding of statistical variability, and understand that statistics can be used to gain information about a population by examining a sample of population
Look for quantitative measures of center (mean/median) and variability (interquartile range/mean absolute deviation)
Understand the meaning of probability, and look for probability of simple events

Geometry :

● Understand perpendicular bisector and angle bisector, and use the properties to solve mathematical problems
Draw polygons in the coordinate plane given coordinates for the vertices, and use coordinated to find the length of a side joining points with the same first coordinate or the same second coordinate
Look for the surface area of three-dimensional figures using their nets made up of rectangles and triangles

## Math Level 7 (Grade 7-8)

Number System, Expressions and Equations :

Understand rational and irrational numbers, prime and composite numbers
Know and apply the properties of integer exponents and fractional exponents to generate equivalent numerical expressions
Perform radical expressions simplification and denominators rationalization
Graph proportional relationships, interpreting the unit rate as the slope of the graph
Perform factorization on polynomial expressions
Solve linear equations in one variable and system of two linear equations in two variables, and form linear equation system to solve problems

Functions :

● Understand that a function is a rule that assigns to each input exactly one output, and graph the function given a set of ordered pairs
Understand even/odd functions, some special functions and their properties
Describe qualitatively the functional relationship between two quantities by analyzing a graph

Statistics and Probability :

Analyze a population by examining a sample of population, and look for mean, median, and mode given a set of numerical data
Understand and apply basic probability formula, general addition/multiplication rule of probability to calculate the probability of independent and dependent events

Geometry :

Explore the relationship of angles formed by parallel lines and sum principles to look for unknown angles
Understand similar triangles and figures and look for length/area in similar and complicated figures
Understand transformation (rotation, reflection, and translation) and apply the properties to solve problems related to coordinate system and geometric objects
Calculate the volume of cylinder, cone, pyramid, and sphere and solve related real-world and mathematical problems

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