Topics: Place Value: The value of a digit depends on its place, or position, in the number. (Through Billions) -Comparing two numbers based on their place value -Ordering numbers based on their place value Knowing how to use as well as the difference between: Standard Form: 128,000 Expanded Form: 100, , ,000 AND (1 x 100,000) + (2 x 10,000) + (8 x 1,000) Word Form: one hundred twenty-eight thousand Patterns/Sequences: Sequence: list of numbers in a specific order Terms: numbers in the sequence ARITHMETIC SEQUENCE: If you can find the next term in the sequence by adding or subtracting the SAME number to the previous term. 4, 12, 20, 28, 36, _____ (+8) GEOMETRIC SEQUENCE: If you can find the next term in the sequence by multiplying or dividing the SAME number to the previous term. 3, 12, 48, 192, _____ (x4) Multiplication: Multi-Digit Multiplication

Powers of Ten Determine the number of places to move the decimal point by counting the number of zeroes in the power of ten. Ex.) 19.7 x 10 1 = x 10 2 = x 10 3 = Ex.) 19.7 x 1000 = (10 3 ) If multiplying by a power of ten LESS than one, count the number of places after the decimal point. Then move the decimal point that many places to the LEFT. Ex.) 23.9 x 0.1 = x.01 =.239 Properties Commutative Property of Addition and Multiplication: (to commute) 2/3 + 1/8 = 1/8 + 2/3 2/3 x 1/8 = 1/8 x 2/3 Associative Property of Addition and Multiplication: (look for parenthesis) 1/5 + (2/5 + 3/4) = (1/5 + 2/5) + ¾1/5 x (2/5 x 3/4) = (1/5 x 2/5) x ¾ Identity Property of Addition and Multiplication: (number keeps its identity) 1/2 + 0 = 1/2 1/2 x 1 = 1/2 Multiplicative Inverse Property: (any number multiplied by its inverse equals ONE) 2/7 x 7/2 = 1 6 x 1/6 = 1 Distributive Property: (look for multiplication and addition) 1/5 x (2/5 + 3/4) = 1/5 x 2/5 + 1/5 x 3/4

Order of Operations – PLEASE EXCUSE MY DEAR AUNT SALLY P.E.M.D.A.S. Do ALL the operations within the PARENTHESES first. Do ALL operations that have EXPONENTS MULTIPLY and DIVIDE in order from Left to Right (Same Step) ADD and SUBTRACT in order from Left to Right (Same Step) An expression is like a phrase and names a number. An equation is a number sentence that describe a relationship between two expressions. (equal sign) H x 6 is an example of an algebraic expression. An algebraic expression uses operation symbols (+,-,x,÷) to combine variables and numbers. A letter that stands for a number is called a variable Exponents/Powers: can be used to show repeated multiplication of a number. Write each power as a product of the same number. 7 4 = 7 x 7 x 7 x 7 Write each product using exponents. 5 x 5 x 5 = 5 3 Evaluate each expression. 3 4 = 81