• ## Number Operations

Number Sense

• 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 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)