
Multiplication as Equal Groups FP1
Vocabulary
 Equal Groups
 Groups that have the same number of objects. Concept used in multiplication and division situations.
5x6 = 30. There are 5 equal groups of 6 items.
 Equation
 A statement that two expressions are equal. 125=7 3=1 = 4
Student Activities
 Student Activity Book

 Pages 16
 Activity Work Book

 Pages 1
 Homework & remembering Pages

 Math Pages 12
Additional Resources
 Multiplication Game  Math Goodies
 Multiplication Model & Activities
 Video Modeled Lesson
Arrays and Area FP2
Vocabulary
 Array
 An arrangement of objects, pictures, or numbers in equal columns and equal rows.
 Row
 A part of a table or array that contains items arranged horizontally.
 Column
 In a data table, a vertical group of cells. In an array, a group of items arranged vertically.
 Area
 The amount of surface covered or enclosed by a figure measured in square units.
 Length
 The measure of a line segment, or one side or edge of a figure.
 Width
 One dimension of a 2 or 3 dimensional figure.
Student Activities
 Student Activity Book

 Pages 710
 Homework & remembering Pages

 Math Pages 34
Additional Resources
 Multiplication Game  Math Gizmo's
Explore the Multiplication Table FP3
Vocabulary
 Commutative Property
 The property that states that changing the order in which numbers are added or multiplied does not change the sum. For all numbers a + b = b + a
 Row
 A part of a table or array that contains items arranged horizontally.
 Column
 In a data table, a vertical group of cells. In an array, a group of items arranged vertically.
 Inverse Operations
 Opposite or reverse operations that undo each other. Addition and Subtraction are inverse operations. Multiplication and division are inverse operations.
 Factor
 One or two or more numbers multiplied to find a product.
 Product
 The answer to a multiplication. In the problem 3 x 4 = 12, 12 is the product.
Student Activities
 Student Activity Book

 Pages 1112
 Homework & remembering Pages

 Math Pages 56
Additional Resources
 2 digit by 1 digit multiplication Interactive game
 Batters Up Baseball Interactive game Challenging
 Fun Brain Baseball Interactive game
 Flash Card Drills Beat the computer orally
Discover Multiplication Patterns FP4
Student Activities
 Student Activity Book

 Pages 1316
 Homework & remembering Pages

 Math Pages 910
Additional Resources
 2 digit by 1 digit multiplication Interactive game
 Batters Up Baseball Interactive game Challenging
 Fun Brain Baseball Interactive game
 Flash Card Drills Beat the computer orally
Multiplication Strategies FP5
Student Activities
 Student Activity Book

 Pages 1718
 Homework & remembering Pages

 Math Pages 910
Additional Resources
 Rhyming Strategy
Multiplication and Division Practice FP6
Student Activities
 Student Activity Book

 Pages 2122
 Student Workbook

 Pages 518
 Homework & remembering Pages

 Math Pages 1112
Additional Resources
 2 digit by 1 digit multiplication Interactive game
 Batters Up Baseball Interactive game Challenging
 Fun Brain Baseball Interactive game
 Flash Card Drills Beat the computer orally
Making Combinations 11
Vocabulary
 Combination
 A combination situation is one in which pairs or sets are counted. Tables can be used to show combinations.
Types of Sandwiches 
bread 
cheese 
tuna 
peanut butter 
white 
w + c 
w + t 
w + pb 
wheat 
wh + c 
wh + t 
wh + pb 
 Factor
 One of two or more numbers multiplied to find a product.
 Product
 The result of a multiplication. 9 X 7 = 63, 63= product
Student Activities
 Student Activity Book

 Pages 2326
 Homework & remembering Pages

 Math Pages 1314
Additional Resources
 Cyber Chase Combinations Game
 Combination Lock Game
 Math Wire Logic Games
 Combinations Practice
Understanding Comparisons 12
Vocabulary
 Comparison
 – A situation in which two amounts are compared by addition or by multiplication. An additive comparison situation compares by asking or
telling how much more (how much less) one amount is than another. A multiplicative comparison situation compares by asking or telling
how many times as many one amount is as another. The multiplicative comparison may also be made using fraction language. For example,
you can say, “Sally has one fourth as much as Tom has, “instead of saying “Tom has 4 times as much as Sally has.”
Student Activities
 Student Activity Book

 Pages 2332
 Homework & remembering Pages

 Math Pages 1516
Additional Resources
 Multiplication Game  Math Goodies
Practice With Multiplication Problems 13
Vocabulary
 Variable

 An attribute or quantity that changes or varies.
 A symbol that can stand for a variable.
 Area
 The amount of surface covered by a figure measured in square units..
 Array
 An arrangement of objects, symbols, or numbers in equal rows and equal columns.
 Comparison
 – A situation in which two amounts are compared by addition or by multiplication. An additive comparison situation compares by asking or
telling how much more (how much less) one amount is than another. A multiplicative comparison situation compares by asking or telling
how many times as many one amount is as another. The multiplicative comparison may also be made using fraction language. For example,
you can say, “Sally has one fourth as much as Tom has, “instead of saying “Tom has 4 times as much as Sally has.”
 Equal Groups
 Groups that have the same number of objects.
 Combination
 A combination situation is one in which pairs or sets are counted. Tables can be used to show combinations.
Types of Sandwiches 
bread 
cheese 
tuna 
peanut butter 
white 
w + c 
w + t 
w + pb 
wheat 
wh + c 
wh + t 
wh + pb 
Student Activities
 Student Activity Book

 Pages 3334
 Homework & remembering Pages

 Math Pages 1718
Additional Resources
 Multiplication Game
 Baseball Multiplication Game
 Fun Brain Math Games
 School House Flash Cards
 Modeled Lesson
Writing Word Problems 14
Vocabulary
 Factor
 One of two or more numbers multiplied to find a product.
 Product
 The result of a multiplication. 9 X 7 = 63, 63= product
Student Activities
 Student Activity Book

 Pages 3536
 Homework & remembering Pages

 Math Pages 1920
Additional Resources
 Multiplication Game
Functions 15
Vocabulary
 Function
 A consistent relationship between two sets of numbers. Each number in one of the sets is paired with exactly one number in the other set. A function can be shown in a chart, or as a set of ordered pairs. Example: The relationship between the number of yards and the number of feet.
Variable.
Student Activities
 Student Activity Book

 Pages 3738
 Homework & remembering Pages

 Math Pages 2122
Additional Resources
 Cyberchase
Equations with Parentheses 16
Vocabulary
 Equation
 A statement that two expressions are equal. An equation always has an equals sign. Example: 32 + 35 = 67
 Parentheses
 Symbols used to group numbers together. 7 + (3 X 4) = 19
Student Activities
 Student Activity Book

 Pages 3940
 Homework & remembering Pages

 Math Pages 2324
Additional Resources
 Math Mastery Video Model
Combinations and Comparison 17
Vocabulary
 Combination
 A combination situation is one in which pairs or sets are counted. Tables can be used to show combinations.
Types of Sandwiches 
bread 
cheese 
tuna 
peanut butter 
white 
w + c 
w + t 
w + pb 
wheat 
wh + c 
wh + t 
wh + pb 
 Comparison –
 A situation in which two amounts are compared by addition or by multiplication. An additive comparison situation compares by asking or telling how much more (how much less) one amount is than another. A multiplicative comparison situation compares by asking or telling how many times as many one amount is as another. The multiplicative comparison may also be made using fraction language. For example, you can say, “Sally has one fourth as much as Tom has, “instead of saying “Tom has 4 times as much as Sally has.”
 Misleading
 A comparing sentence containing language that may trick you into doing the wrong operation. Example: John’s age is 3 more than Jessica’s. If John is 12, how old is Jessica?
Student Activities
 Student Activity Book

 Pages 4142
 Homework & remembering Pages

 Math Pages 2526
Additional Resources
 Combinations Practice
 Complex Combinations Practice
Practice with Factors 18
Vocabulary
 Factor
 One of two or more numbers multiplied to find a product.
Student Activities
 Student Activity Book

 Pages 4344
 Homework & remembering Pages

 Math Pages 2728
Additional Resources
 The Factor Game
Multistep Problems 19
Student Activities
 Student Activity Book

 Pages 4546
 Homework & remembering Pages

 Math Pages 2930
Additional Resources
 The Factor Game
Properties of Multiplication 110
Vocabulary
 Commutative Property
 The property that states that changing the order in which numbers are added or multiplied does not change the sum. For all numbers a + b = b + a
 Associative Property
 Changing the grouping of factors does not change the product.
3 X (5 X 7) = (3 X 5) X 7
 Distributive Property
 You can multiply a sum by a number, or multiply each addend by the number and add the products; the result is the same. 3 X (2 + 4) = (3 X 2) + (3 X 4)
 Expression
 A combination of one or more numbers, variables, or numbers
and variables with one or more operations. Examples: 4, 6n, 6n5, 7 + 4, 2(3
+ 4)
 Example
 A specific instance that demonstrates a general statement.
 Counterexample
 An example that proves that a general statement is false.
Student Activities
 Student Activity Book

 Pages 4749
 Homework & remembering Pages

 Math Pages 3132
Additional Resources
 Property Practice
Use Mathematical Processes 111
Student Activities
 Student Activity Book

 Pages 5152
 Homework & remembering Pages

 Math Pages 3334
Unit Review 112
Student Activities
 Student Activity Book

 Pages 53 54
Square Units and Area 21
Vocabulary
 Meter
 The basic unit of length in the metric system.
 Centimeter
 A unit of measure in the metric system that equals one hundredth of a meter.
1 cm = 0.01 m
 Decimeter
 A unit of measure in the metric system that equals one tenth of a meter. 1 dm = 0.1 m
 Millimeter
 A unit of measure in the metric system that equals one thousandth of a meter.
1 mm = 0.001 m
Student Activities
 Student Activity Book

 Pages 5558
 Homework & remembering Pages

 Math Pages 35  36
Additional Resources
 www.Answers.com
 Square Units
 Area of a Triangle
 Area of a Parallelogram
Perimeter and Area of Triangles 22
Vocabulary
 Perimeter
 The distance around a figure.
 Area
 The amount of surface covered by a figure measured in square units.
 Square centimeter
 A unit of area equal to the area of a square with one – cm sides.
 Square unit
 A unit of area equal to the area of a square with one – unit sides.
 Base
 For a triangle or parallelogram, a base is any side. For a trapezoid, a base is either of the parallel sides. For a prism, a base is one of the congruent parallel faces. For a pyramid, the base is the face that does not touch the vertex of the pyramid.
 Height
 The perpendicular distance from a base of a figure to the highest point.
Student Activities
 Student Activity Book

 Pages 5962
 Homework & remembering Pages

 Math Pages 3738
Additional Resources
 Perimeter
 Area
 Perimeter & Area
Areas of Right Triangles and Parallelograms 23
Vocabulary
 Acute angle
 An angle whose measure is less than 90°.
 Right angle
 An angle that measures 90°
 Obtuse angle
 An angle greater than a right angle and less than a straight angle.
 Triangle
 A polygon with three sides.
 Rectangle
 A parallelogram with four right angles.
 Height
 The perpendicular distance from a base of a figure to the highest point.
 Perimeter
 The distance around a figure.
 Parallelogram
 A quadrilateral with both pairs of opposite sides parallel.
 Base
 For a triangle or parallelogram, a base is any side. For a trapezoid, a base is either of the parallel sides. For a prism, a base is one of the congruent parallel faces. For a pyramid, the base is the face that does not touch the vertex of the pyramid.
 Perpendicular
 Lines, line segments, or rays are perpendicular if they form right angles
Student Activities
 Student Activity Book

 Pages 6567
 Homework & remembering Pages

 Math Pages 3940
Additional Resources
 Area of a Triangle Lesson
 Area of a Triangle
 Area of a Triangle Interactive Quiz
 Area of a Triangle Activity
Angle Measures  AL1
Vocabulary
 Acute Angle
 An angle that measures less than 90°.
 Angle
 The amount of turning or the amount of opening between two rays that have the same endpoint.
 Complementary Angle
 Two angles are complementary angles if the sum of their measures is 90°.
 Degree (°)
 A degree is a unit of measure for angles. There are 360 degrees in a circle.
 End point
 The point at either end of a line segment or the point at the end of a ray.
 Obtuse Angle
 An angle that measures more than 90°.
 Protractor
 A tool for measuring angles.
 Ray
 A part of a line with one endpoint that extends indefinitely in one direction.
 Reflex Angle
 An angles that measures greater than 180°.
 Right Angle
 An angle that measures 90°.
 Sides
 The sides of an angle are two rays with the same endpoint.
 Straight Angle
 An angle that measures 180°.
 Supplementary Angle
 Two angles are supplementary angles if the sum of their measures is 180°.
 Vertex
 A common point of two rays or line segments that form an angle.
Additional Resources
 Investigating Protractors
 Cyberchase Game Angle Measurement
 Fun Brain Game Angle Measurement
Angle in the Real World  AL2
Vocabulary
 Acute Angle
 An angle that measures less than 90°.
 Angle
 The amount of turning or the amount of opening between two rays that have the same endpoint.
 Complementary Angle
 Two angles are complementary angles if the sum of their measures is 90°.
 Degree (°)
 A degree is a unit of measure for angles. There are 360 degrees in a circle.
 End point
 The point at either end of a line segment or the point at the end of a ray.
 Obtuse Angle
 An angle that measures more than 90°.
 Protractor
 A tool for measuring angles.
 Ray
 A part of a line with one endpoint that extends indefinitely in one direction.
 Reflex Angle
 An angles that measures greater than 180°.
 Right Angle
 An angle that measures 90°.
 Sides
 The sides of an angle are two rays with the same endpoint.
 Straight Angle
 An angle that measures 180°.
 Supplementary Angle
 Two angles are supplementary angles if the sum of their measures is 180°.
 Vertex
 A common point of two rays or line segments that form an angle.
Additional Resources
 Investigating Protractors
 Cyberchase Game Angle Measurement
 Fun Brain Game Angle Measurement
Angles in Polygons  AL3
Vocabulary
 Parallel Lines
 Lines that do not intersect. 2. Lines that are always the same distance apart.
 Polygon
 A twodimensional connected figure made of line segments in which each endpoint of every side meets with
an endpoint of exactly one other side.
 Quadrilateral
 A polygon with four sides.
 Regular Polygon
 A polygon with all sides equal. 2. A polygon with all sides the same length an all angles the same measure.
 Trapezoid
 A quadrilateral with exactly one pair of parallel sides.
Additional Resources
 Angles in Polygons
 Angles in Polygons Quiz
 Angles in Polygons Activity
 Angles In Polygons Information
Making Shapes  AL4
Vocabulary
 Concave
 A polygon is concave if at least one of its interior angles is greater than 180°. If two points on the perimeter
of a polygon are joined by a line segment, and the line segment is outside the polygon, then the polygon is concave.
 Convex
 A polygon with all interior angles measuring less than 180°. If any two points on the perimeter of a polygon are
joined by a line segment, and the line segment is inside the polygon, then the polygon is convex. All regular polygons
are convex.
 Mammal
 A vertebrate that usually has hair and nurses its young.
 Obtuse Triangle
 A triangle that has an obtuse angle. 2. An obtuse triangle contains one angle greater than 90°.
 Parallelogram
 A quadrilateral with two pairs of congruent, parallel sides.
 Pentagon
 A fivesided polygon.
 Polygon
 A twodimensional connected figure made of line segments in which each endpoint of every side meets with an
endpoint of exactly one other side.
 Quadrilateral
 A polygon with four sides.
 Rectangle

 A quadrilateral with four right angles.
 A quadrilateral with two pairs of congruent, parallel sides and four right angles.
 Rhombus

 A quadrilateral with four equal sides.
 An equilateral parallelogram. Its diagonals are perpendicular.
 Square
 A quadrilateral with four congruent (equal) sides and four right angles.
 Vertebrate
 An animal with a hard internal skeleton including a backbone and a brain enclosed in a skull.
Additional Resources
 Polygon Models
 Polygon Data
 Polygon Images
 Polygon Playground
 Polygon Game Helps with identifying Polygons & their Properties
 Polygon ID Game
Diagonals and Sides AL5
Vocabulary
 Adjacent
 Next to.
 Congruent
 Having exactly the same size and shape.
 Diagonal
 A line segment that connects nonadjacent corners (vertices) of a polygon.
Additional Resources
 Interactive Exploration of Diagonals & Sides
 Advanced Explanation
 Diagonals & Sides Model
Parallel, Perpendicular  Diagonals and Sides AL6
Vocabulary
 Adjacent
 Next to.
 Congruent
 Having exactly the same size and shape.
 Diagonal
 A line segment that connects nonadjacent corners (vertices) of a polygon.
 Parallel

 Lines that are in the same direction
 Always the same distance apart. Parallel Symbol  
 Perpendicular

 Lines that meet at right angles (90°).
 Forming right angles (90°). Perpendicular Symbol  _
Additional Resources
 Student Definition
 Yahoo Math Answers
 Practice Activity
Consolidate Perimeter and Area 25
Vocabulary
 Triangle
 A polygon with three sides.
 Dimensions
 The height, length, or width.
 Parallelogram
 A quadrilateral with both pairs of opposite sides parallel.
 Complex figures
 A figure made by combining simple geometric figures like rectangles and triangles.
 Hexagon
 A sixsided polygon.
 Pentagon
 A polygon with five sides.
 Right triangle
 A triangle with one right angle.
 Acute triangle
 A triangle with three acute angles.
 Obtuse triangle
 A triangle with one obtuse angle.
 Equilateral triangle
 A triangle where all sides are equal.
 Isosceles triangle
 A triangle with at least two congruent sides.
 Scalene triangle
 A triangle with no equal sides is a scalene triangle.
Student Activities
 Student Activity Book

 Pages 7376
 Homework & remembering Pages

 Math Pages 4344
Additional Resources
 Math League
 Fun Brain
 Math Playground
 Area & Perimeter Instruction
Customary Units of Length 26
Vocabulary
 Inch
 A U.S. customary unit of length. There are 12 inches in 1 foot.
 Square inch
 A unit of area equal to the area of a square with one inch sides.
 Foot
 A U.S. customary unit of length equal to 12 inches and 1/3 yard.
 Square foot
 A unit of area equal to the area of a square with one foot sides.
 Yard
 A U.S. customary unit of length equal to 3 feet or 36 inches
 Square yard
 A unit of area equal to the area of a square with one yard sides.
Student Activities
 Student Activity Book

 Pages 7780
 Homework & remembering Pages

 Math Pages 4546
Additional Resources
 Harcourt Measurement Activity
 AAA Math Measurement
Estimate the measure of an object in one system given the measure of that object in another system
AL7
Vocabulary
 Gallon
 A U.S. customary unit for measuring capacity. One gallon is equal
to 4 quarts.
 Liter
 The basic unit of capacity in the metric system.
 Quart
 A U.S. customary unit for measuring capacity. One quart equals 32
ounces.
 Mile
 A U.S. customary unit of length that equals 5280 feet.
 Yard
 A U.S. customary unit of length equal to 3 feet or 36 inches
 Inch
 A U.S. customary unit of length. There are 12 inches in 1 foot.
 Meter
 The basic unit of length in the metric system. A meter is a little
longer than a yard.
 Kilometer
 A metric unit of length equal to 1,000 meters.
 Centimeter
 A metric unit of length equal to 0.01 (1/100) of a meter.
Student Activities
 Student Activity Book

 Pages 3738
 Homework & remembering Pages

 Math Pages 2122
Additional Resources
 Measurement Chart
 Measurement Conversion Game
Decimals as Equal Divisions 31
Student Activities
 Student Activity Book

 Pages 8384
 Homework & remembering Pages

 Math Pages 4748
Additional Resources
 Decimals Lesson
 Math League Decimals
Equate and Compare 32
Student Activities
 Student Activity Book

 Pages 8586
 Homework & remembering Pages

 Math Pages 49 50
Thousands and Thousandths 33
Student Activities
 Student Activity Book

 Pages 87  90
 Homework & remembering Pages

 Math Pages 5152
Additional Resources
 Math League  Decimals
Adding and Subtracting Decimals 34
Vocabulary
 Meter (m)
 The basic unit of length in the metric system.
 Decimeter (dm)
 A unit of measure in the metric system that equals one tenth of a meter.
 Centimeter (cm)
 A unit of measure in the metric system that equals one hundredth of a meter.
 Millimeter (mm)
 A unit of length in the metric system that equals one thousandth of a meter. 1mm=0.001 m
Student Activities
 Student Activity Book

 Pages 9192
 Homework & remembering Pages

 Math Pages 5354
Additional Resources
 Adding Decimals Activity
 Subtracting Decimals Activity
Billions to Billionths 35
Vocabulary
 Standard form
 The form of a number written using digits.
 Short word form
 A way of writing a number that uses digits and words. Example: Short word form of 12,835. 12 thousand, 832
 Word form
 the form of a number written using words instead of digits. Example: Six hundred thirtynine.
 Expanded form
 A way of writing a number that shows the value of each of its digits.
835 = 800 + 30 + 5
Student Activities
 Student Activity Book

 Pages 9697
 Homework & remembering Pages

 Math Pages 5556
Additional Resources
 I know That Place
Value
 AAA Math  Place Value
 Place Value
Use Place Value 36
Student Activities
 Student Activity Book

 Pages 99100
 Homework & remembering Pages

 Math Pages 5758
Additional Resources
 Place Value Practice
 I Know That Place Value
Add Whole Numbers and Decimals 37
Student Activities
 Student Activity Book

 Pages 101102
 Homework & remembering Pages

 Math Pages 5960
Additional Resources
 Quia  Decimal Quiz
 Math Frog  Additon & Subtraction of Decimals
Addition to Millions 38
Student Activities
 Student Activity Book

 Pages 103104
 Homework & remembering Pages

 Math Pages 6162
Add'um Up  Fractions/Judging the Reasonableness
of a Solution  AL
Vocabulary
 Numerator
 The number written above the line in a fraction. The numerator tell the number of parts being considered. For example,
the 2 is the numerator in the fraction 2/5. In this case, we are interested in two of the five parts.
 Denominator
 The number below the line in the fraction. The denominator indicates the number of equal parts in which the unit whole
is divided.
Additional Resources
 Fractions parts of a Whole
 Naming Fractions
Functions 15
Vocabulary
 Function
 A consistent relationship between two sets of numbers. Each number in one of the sets is paired with exactly one number in the other set. A function can be shown in a chart, or as a set of ordered pairs. Example: The relationship between the number of yards and the number of feet.
Variable.
Student Activities
 Student Activity Book

 Pages 3738
 Homework & remembering Pages

 Math Pages 2122
Additional Resources
 Cyberchase
