• ## Numbers and Operations

Number Sense

• 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