Read, write and order numbers through 1,000,000,000,000 in standard and exponential forms
Use exponents to represent powers of ten
Recognize and use whole number exponents
Compare, order and round whole numbers, decimals and fractions
Use and order proper and improper fractions and mixed numbers
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 rational and irrational numbers. Distinguish between terminating and repeating decimals
Define and apply ratios, unit rates and percents
Write numbers in expanded notation up to 1,000,000
Divisibility rules 2, 3, 4, 5, 6, 8, 9 and 10
Express composite numbers as products of prime numbers (e.g. factor tree)
Order fractions on a number line
Introduce absolute value
Numerical Operations
Use cummutative and associative properties of addition, distributive, identity (additive and multiplicative), multiplicative inverse (reciprocal) zero product properties
Use Order of Operations to simplify expressions (*error analysis to spot mistakes in computation)
Use inverse relationships of addition-subtraction and multiplication-division
Add and subtract fractions with like and unlike denominators
Multiply and divide fractions, decimals and mixed numbers
Understand when to use each operation in word problems
Convert fractions, decimals and percents (also apply to geometry)
Find percent of a given number
Find simple interest, sales tax and tips
Write various number sentences using any of the four operations
Determine when estimation is appropriate and understand the usefulness of an estimate as distinct from an exact answer
Use estimation in all operations and problem solving
Geometry and Measurement
Geometry
Identify and compare two and three dimensional figures using spatial visualization and visual perception
Use proper symbols to identify lines, rays, segments and angles
Construct angles and two dimensional figures using straight edge, protractor and compass
Identify corresponding parts of congruent and similar figures
Identify and draw commonly used polygons and regular polygons
Identify and define parts of a circle
Define pi verbally and in written form
Classify all quadrilaterals
Classify solid figures (3-dimensional)
Identify shape and quantity of faces, edges and vertices of 3-dimensional figures
Find area and perimeter of polygons
Find area and circumference of a circle
Measurement and Data
Measure and compute volume using centimeter and inch cubic units (blocks). Measure and compute (whole square unit areas) surface area of objects and regions enclosed by geometric figures which can be decomposed into rectangles
Compare temperatures on a thermometer in Celsius and Fahrenheit degrees
Measure and compute area, length, width of a rectangle, square or (*triangle) using ruler or yardstick, 1 inch squares or 1 centimeter squares
Find the missing value given area and length of a rectangle or area and width of a rectangle
Financial Literacy
Identify the difference between credit and debit, deposit and withdrawal (*profit and loss)
Operations and Algebra
Patterns
Use number patterns to add, subtract, multiply and divide mentally
Recognize patterns in sums, differences and products of even and odd numbers
Describe , analyze and complete patterns involving fractions
Algebra
Find missing addends, subtrahends, factors, divisors (without use of a calculator)
Represent unknown quantities with a symbol; learn the importance of x and y as algebraic symbols
Describe arithmetic operations as functions, including combining operations and inverse operations
Explore substituting a number value for a variable
Statistics and Probability
Data Analysis
Take a survey using real life situations, tally and graph the results using frequency distribution tables; discuss outcomes and draw conclusions from the data and ask statistical questions
Compute measures of central tendency (mean, median, mode and range)
Create and interpret pictographs, horizontal and vertical bar graphs (single and double), line graphs, tree diagrams, stem and leafpots, and tables (use available technology to create data displays)
Create and interpret box plots including inter-quartile range
Probability
Perform simple probability experiments of simulations, record results and make predictions
Express probability in fraction form using concrete and semi-concrete activities
Utilize Venn Diagrams using multiple classifications (e.g. classifying quadrilaterals)