# Eighth Grade - Math

• ## Number Operations

Number Sense

• Change numbers between standard form and scientific notation
• Define and apply scientific notation to place value with positive and negative exponents
• Multiply and divide numbers in scientific notation
• Write decimal as a fraction in simplest form and write fractions or mixed numbers as decimal numbers
• Find the GCF and LCM of two or more numbers and monomials
• Define, compare and use rational and irrational numbers (between any two rational numbers there is at least one irrational number)
• Determine and explain rational, whether to overestimate or underestimate in problem solving
• Use base, exponent and exponential form
• Apply rules for exponents by multiplying and dividing with same base (Multiplication Property of Exponents)
• Express a square or cubed number in standard, factored and exponential form
• Know perfect squares up to 15 (*25) and perfect cubes up to 10
• Apply divisibility rules
• Recognize and apply concept of significant digits
• Express composite numbers as products of prime numbers (e.g., factor tree, Fundamental Theorem of Arithmetic)

Numerical Operations

• Define and use commutative and associative properties of addition, distributive, identity (additive and multiplicative), multiplicative inverse (reciprocal) zero product properties using algebraic notation
• Use Order of Operations to simplify expressions
• Use inverse relationships of addition-subtraction and multiplication-division
• Use all operations with rational numbers
• Convert fractions, decimals and percents
• Use estimation in all operations and problem solving
• Apply rational number operations
• Define absolute value as distance from zero (absolute value of variables, e.g. lxl=9)
• Using absolute value in adding and subtracting
• Simple interest (Compound interest)

## Geometry/Measurement and Data

Geometry

• Identify and complete symmetrical figures on a grid using ordered pairs
• Identify and compare two and three dimensional figures using spatial visualization and visual perception
• Find the circumference and area of a circle using pi
• Find the diameter and radius of a circle given the circumference or area
• Find the area and perimeter of a polygon and find missing sides (find area of a triangle using only side lengths, Heron's Formula)
• Find area and perimeter of irregular shapes and common shaded/unshaded regions
• Measure and compute volume and surface area of prisms, cylinders and cones (spheres)
• Utilize 4 quadrant coordinate geometry

## Operations and Algebra

Patterns

• Describe and create compound patterns (e.g., arithmetic and geometric, Fibonacci, Pascal's Triangle)
• Use proper vocabulary when explaining patterns that repeat, grow or compress
• Evaluate infinite sequences (converging and diverging)
• Represent, analyze and predict relations between quantities, especially quantities changing over time

Algebra

• Translate phrases into algebraic expressions and equations
• Simplify expressions using order of operations including like terms
• Solve multi-step equations and inequalities using rational numbers with parenthesis and distributive property
• Substitute a number value for a variable

## Statistics and Probability

Data Analysis

• Collect, organize and interpret data to solve non-routine problems involving world situations (e.g., random sampling)
• Compute measures of central tendency (mean, median, mode and range) with or without a calculator
• Draw inferences and construct convincing arguments based on data analysis

Probability

• Perform compound probability experiments of simulations, record results and make predictions
• Discuss low or high probability and possibility of various events using real life situations
• Express probability in fraction form using concrete and semi-concrete activities
• Find permutations and combinations using factorial notation
• Discrete Math
• Utilize Venn Diagrams using multiple classifications (e.g., classifying quadrilaterals)
• Overlapping and disjoint events