Read, write and order numbers through trillions in standard, expanded and exponential forms
Define, compare, order and use integers and rational numbers on number line
Write a decimal as a fraction in simplest form and write fractions or mixed numbers as decimal numbers
Rename improper fractions as mixed numbers and rename mixed numbers as improper fractions
Write fractions and mixed numbers in standard and word form
Find equivalent fractions using multiplication and division
Find the GCF and LCM (LCD) of two numbers
Define, compare and use rational and irrational numbers
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
Determine square root of a perfect square, make appropriate estimations of a non-perfect square up to 99
Apply divisibility rules
Define and apply scientific notation to place value (negative exponents)
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 (with multiple representation)
Convert fractions, decimals and percents
Find percent of a given number
Apply ratio, direct proportion and percents in real life situations (consumer applications)
Introduce the percent of increase and decrease
Use estimation in all operations and problem solving
Introduce integer operations on a number line
Define absolute value as distance from zero
Geometry/Measurement and Data
Geometry
Plot ordered pairs in all four quadrants
Identify and compare two and three dimensional figures using spatial visualization and visual perception
Construct angles, segments and triangles using straight edge and compass
Apply ratio and proportion to congruent and similar figures
Find area and perimeter of a polygon
Find area and circumference of a circle (the sum of the length of 2 radii is equivalent to the Length of the diameter)
Find area and perimeter of irregular shapes
Apply and use Pythagorean Theorem to find missing sides of a right triangle
Measure and compute volume and surface area of rectangular prisms and cylinders (triangular prisms, cones and pyramids)
Utilize 4 quadrant coordinate geometry
Define and identify quadrants, origin and axes
Use scale factor in ratio and proportion
Operations and Algebra
Patterns
Investigate, describe and create compound patterns (e.g., arithmetic and geometric, Fibonacci, Pascal’s Triangle)
Use number patterns to add, subtract, multiply and divide mentally
Algebra
Translate phrases into algebraic expressions
Simplify expressions using order of operations including like terms
Solve one and two step equations (multi-step)
Describe arithmetic operations as functions, including combining operations and inverse operations
Substitute a number value for a variable
Use input/output table to graph linear equations using ordered pairs
Solve one and two step inequalities and graph solutions on a number line
Statistics and Probability
Data Analysis
Collect, organize and interpret data to solve non-routine problems involving world situations
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
Performs simple 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
Understand that the probability of an event must be between zero and one, inclusive (can be written as fraction, decimal or percent)
Find permutations factorials and combinations
Utilize Venn Diagrams using multiple classification (e.g., classifying quadrilaterals)
Introduce logical reasoning problems
Research how the explorers found America without using a GPS or a map, include Mathematical concepts