NAME __________________________ DATE _______________
PLACE VALUE, MULTIPLICATION & EXPRESSIONS
 Whole number, multi-digit ( + , − , × , ÷ )
 Patterns
 Place Value
 Standard, Word, Expanded Form of numbers
 Properties
Properties of Addition:
Commutative Property of Addition
If the order of addends changes, the sum stays the same
12 + 7 = 7 + 12
Associative Property of
Addition
If the grouping of addends changes, the sum stays the same
5 + (8+14) = (5+8) + 14
Identity Property of
Addition
The sum of any number and 0 is that number.
13 + 0 = 13

Multiplicative Inverse Property
Another name for reciprocal.
When you multiply a number by its
"Multiplicative Inverse" you get 1.
Properties of Multiplication:
Commutative Property of Multiplication
Example: 8 × (1/8) = 1
If the order of factors changes, the product stays the same
4 x 9 = 9 x 4
Associative Property of
Multiplication
If the grouping of factors changes, the product stays the same
11 x (3 x 6) = (11 x 3) x 6
Identity Property of
Multiplication
The product of any number and 1 is that number
4 x 1 = 4
Distributive Property
Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products
5 x (7 + 9) = (5 x 7) + (5 x 9)
 Sequences: Arithmetic & Geometric Sequences
 Powers of 10 and Exponents o Base: the number that is used as the repeated factor o Exponent: number that tells how many times the base is used as a factor
 Multiplication Patterns
 Multiply by multi-digit numbers

 Relate Multiplication to Division o You can use the relationship between multiplication and division to solve a division problem. Using the same numbers, multiplication and division are opposite, or
inverse operations.
 Numerical Expressions (Evaluate) o A numerical expression is a mathematical phrase that has numbers and operation signs but does not have an equal sign o To evaluate, or find the value of, a numerical expression with more than one operation, you must follow rules called the order of operations. The order of operations tells you in what order you should evaluate an expression. o To evaluate an expression with parentheses, follow the order of operations. Perform the operations in parentheses first. Multiply from left to right. Then add and subtract from left to right.
 Order of Operations (P.E.M.D.A.S.)
 Grouping Symbols o When evaluating an expression with different grouping symbols (parentheses, brackets, and braces), perform the operation in the innermost set of grouping symbols first, evaluating the expression from the inside out.
 Expressions & Equations
DIVIDE WHOLE NUMBERS
 Divide by 1- Digit divisors
 Division with 2- Digit divisors
 Estimate with 2-Digit Divisors
 Divide by 2-Digit Divisors
 Interpret the Remainder (make fractions)
ADD AND SUBTRACT DECIMALS

 Place Value of Decimals (millions  millionths)
 Compare and Order Decimals
 Round Decimals
 Estimate Decimal Sums and Differences
 Add Decimals
 Subtract Decimals
 Patterns with Decimals (Geometric & Arithmetic Patterns) o A sequence is an ordered list of numbers. A term is each number is a sequence. You can find the pattern in a sequence by comparing one term with the next term.
 Add and Subtract Money (Deposit & Withdrawal)
MULTIPLY DECIMALS
 Multiplication Patterns with Decimals
 Multiplication with Decimals and Whole Numbers
 Multiply using expanded form
 Multiply money
 Multiply decimals
DIVIDE DECIMALS
 Division patterns with decimals
 Divide decimals by whole numbers
 Decimal division
 Terminating & repeating decimals using bar notation
 Decimal Operations ( + , − , × , ÷ decimals)
 Divisibility Rules
 Prime & composite numbers
 Prime factorization
 GCF
 LCM/LCD

ADD AND SUBTRACT FRACTIONS WITH UNLIKE
DENOMINATORS
 Addition with unlike denominators
 Subtraction with unlike denominators
 Common denominators and equivalent fractions o You can use a common denominator or common multiple of 2 or more denominators to write fractions that name the same part of a whole.
 Add and subtract fractions
 Add and subtract mixed numbers
 Subtraction with renaming (borrowing)
 Patterns with fractions
MULTIPLY FRACTIONS
 Multiply fractions and mixed numbers
 Comparing fractions
 Compare mixed number factors and products
 Order fractions
DIVIDE FRACTIONS
 Divide fractions and mixed numbers (keep – change – flip)
 Perimeter
 Area (Triangle, Rectangle, Circle, Trapezoid, Parallelogram)
 Area of Irregular shapes
ALGEBRA: PATTERNS AND GRAPHING
 Line Plots
 Ordered pairs

o The horizontal number line on the coordinate plane is the
x-axis. The vertical number line on the coordinate plane is the y-axis. o Each point on the coordinate plane can be described by an ordered pair of numbers. The x-coordinate is the first number in the ordered pair. It is the horizontal location, or the distance the point is from 0 in the direction of the x-axis. The y- coordinate is the second number in the ordered pair. It is the vertical location, or the distance the point is from 0 in the direction of the y- axis. o The x-axis and y-axis intersect at the point (0,0), called the point of origin.
 Graph data
 Line graphs o A line graph is a graph that uses line segments to show how data changes over time. The series of numbers placed at fixed distances that label the graph are the graph’s scale. The intervals, or difference between the values of the scale, should be equal.
 Numerical patterns
 Find a rule for patterns
 Graph and analyze relationships
CONVERT UNITS OF MEASURE
 Customary System o Length o Capacity o Weight
 Metric System o Length o Capacity o Weight

 Elapsed time
GEOMETRY AND VOLUME
 Polygons o A polygon is a closed plane figured formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has.
 Names of polygons
 Regular polygons
 Types of triangles
 Types of Quadrilaterals
 Three- Dimensional Figures o Prisms o Pyramids o Cone o Cylinder o Sphere
 Faces, Bases, Edges, Vertices of 3-D figures
 Find volume of rectangular prisms o Volume is the measure of the amount of space a solid figure occupies and is measured in cubic units. Each unit cube has a volume of 1 cubic unit.