
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 nonperfect 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 additionsubtraction and multiplicationdivision
 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 (multistep)
 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 nonroutine 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 semiconcrete 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