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## 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