Math Lesson Notes

Multiplication as Equal Groups FP-1

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. 12-5=7 3=1 = 4

Student Activities

Student Activity Book
  1. Pages 1-6
Activity Work Book
  1. Pages 1-
Homework & remembering Pages
  1. Math Pages 1-2

Additional Resources

Multiplication Game - Math Goodies
Multiplication Model & Activities
Video Modeled Lesson

Arrays and Area FP-2

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
  1. Pages 7-10
Homework & remembering Pages
  1. Math Pages 3-4

Additional Resources

Multiplication Game - Math Gizmo's

Explore the Multiplication Table FP-3

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
  1. Pages 11-12
Homework & remembering Pages
  1. Math Pages 5-6

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 FP-4

Student Activities

Student Activity Book
  1. Pages 13-16
Homework & remembering Pages
  1. Math Pages 9-10

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 FP-5

Student Activities

Student Activity Book
  1. Pages 17-18
Homework & remembering Pages
  1. Math Pages 9-10

Additional Resources

Rhyming Strategy

Multiplication and Division Practice FP-6

Student Activities

Student Activity Book
  1. Pages 21-22
Student Workbook
  1. Pages 5-18
Homework & remembering Pages
  1. Math Pages 11-12

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 1-1

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
  1. Pages 23-26
Homework & remembering Pages
  1. Math Pages 13-14

Additional Resources

Cyber Chase Combinations Game
Combination Lock Game
Math Wire Logic Games
Combinations Practice

Understanding Comparisons 1-2

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
  1. Pages 23-32
Homework & remembering Pages
  1. Math Pages 15-16

Additional Resources

Multiplication Game - Math Goodies

Practice With Multiplication Problems 1-3

Vocabulary

Variable
  1. An attribute or quantity that changes or varies.
  2. 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
  1. Pages 33-34
Homework & remembering Pages
  1. Math Pages 17-18

Additional Resources

Multiplication Game
Baseball Multiplication Game
Fun Brain Math Games
School House Flash Cards
Modeled Lesson

Writing Word Problems 1-4

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
  1. Pages 35-36
Homework & remembering Pages
  1. Math Pages 19-20

Additional Resources

Multiplication Game

Functions 1-5

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
  1. Pages 37-38
Homework & remembering Pages
  1. Math Pages 21-22

Additional Resources

Cyberchase

Equations with Parentheses 1-6

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
  1. Pages 39-40
Homework & remembering Pages
  1. Math Pages 23-24

Additional Resources

Math Mastery- Video Model

Combinations and Comparison 1-7

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
  1. Pages 41-42
Homework & remembering Pages
  1. Math Pages 25-26

Additional Resources

Combinations Practice
Complex Combinations Practice

Practice with Factors 1-8

Vocabulary

Factor
One of two or more numbers multiplied to find a product.

Student Activities

Student Activity Book
  1. Pages 43-44
Homework & remembering Pages
  1. Math Pages 27-28

Additional Resources

The Factor Game

Multistep Problems 1-9

Student Activities

Student Activity Book
  1. Pages 45-46
Homework & remembering Pages
  1. Math Pages 29-30

Additional Resources

The Factor Game

Properties of Multiplication 1-10

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, 6n-5, 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
  1. Pages 47-49
Homework & remembering Pages
  1. Math Pages 31-32

Additional Resources

Property Practice

Use Mathematical Processes 1-11

Student Activities

Student Activity Book
  1. Pages 51-52
Homework & remembering Pages
  1. Math Pages 33-34

Unit Review 1-12

Student Activities

Student Activity Book
  1. Pages 53 -54

Square Units and Area 2-1

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
  1. Pages 55-58
Homework & remembering Pages
  1. Math Pages 35 - 36

Additional Resources

www.Answers.com
Square Units
Area of a Triangle
Area of a Parallelogram

Perimeter and Area of Triangles 2-2

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
  1. Pages 59-62
Homework & remembering Pages
  1. Math Pages 37-38

Additional Resources

Perimeter
Area
Perimeter & Area

Areas of Right Triangles and Parallelograms 2-3

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
  1. Pages 65-67
Homework & remembering Pages
  1. Math Pages 39-40

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 two-dimensional 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 five-sided polygon.
Polygon
A two-dimensional 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
  1. A quadrilateral with four right angles.
  2. A quadrilateral with two pairs of congruent, parallel sides and four right angles.
Rhombus
  1. A quadrilateral with four equal sides.
  2. 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
  1. Lines that are in the same direction
  2. Always the same distance apart. Parallel Symbol - ||
Perpendicular
  1. Lines that meet at right angles (90°).
  2. Forming right angles (90°). Perpendicular Symbol - |_

Additional Resources

Student Definition
Yahoo Math Answers
Practice Activity

Consolidate Perimeter and Area 2-5

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 six-sided 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
  1. Pages 73-76
Homework & remembering Pages
  1. Math Pages 43-44

Additional Resources

Math League
Fun Brain
Math Playground
Area & Perimeter Instruction

Customary Units of Length 2-6

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
  1. Pages 77-80
Homework & remembering Pages
  1. Math Pages 45-46

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
  1. Pages 37-38
Homework & remembering Pages
  1. Math Pages 21-22

Additional Resources

Measurement Chart
Measurement Conversion Game

Decimals as Equal Divisions 3-1

Student Activities

Student Activity Book
  1. Pages 83-84
Homework & remembering Pages
  1. Math Pages 47-48

Additional Resources

Decimals Lesson
Math League- Decimals

Equate and Compare 3-2

Student Activities

Student Activity Book
  1. Pages 85-86
Homework & remembering Pages
  1. Math Pages 49 -50

Thousands and Thousandths 3-3

Student Activities

Student Activity Book
  1. Pages 87 - 90
Homework & remembering Pages
  1. Math Pages 51-52

Additional Resources

Math League - Decimals

Adding and Subtracting Decimals 3-4

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
  1. Pages 91-92
Homework & remembering Pages
  1. Math Pages 53-54

Additional Resources

Adding Decimals Activity
Subtracting Decimals Activity

Billions to Billionths 3-5

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 thirty-nine.
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
  1. Pages 96-97
Homework & remembering Pages
  1. Math Pages 55-56

Additional Resources

I know That- Place Value
AAA Math - Place Value
Place Value

Use Place Value 3-6

Student Activities

Student Activity Book
  1. Pages 99-100
Homework & remembering Pages
  1. Math Pages 57-58

Additional Resources

Place Value Practice
I Know That- Place Value

Add Whole Numbers and Decimals 3-7

Student Activities

Student Activity Book
  1. Pages 101-102
Homework & remembering Pages
  1. Math Pages 59-60

Additional Resources

Quia - Decimal Quiz
Math Frog - Additon & Subtraction of Decimals

Addition to Millions 3-8

Student Activities

Student Activity Book
  1. Pages 103-104
Homework & remembering Pages
  1. Math Pages 61-62

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 1-5

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
  1. Pages 37-38
Homework & remembering Pages
  1. Math Pages 21-22

Additional Resources

Cyberchase