Amplify Science (California) Grade 6
Science
Start Learning →6th Grade
AI tutoring for 6th graders. Ratios, proportions, early algebra, and more — aligned to Big Ideas Math, Eureka Math, and other popular textbooks.
Big Ideas Math, Advanced 1
Math
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Big Ideas Math, Course 1
Math
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California myWorld Interactive, Grade 6
History
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Earth Science (Grade 6)
Science
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Elements of Language, 3rd Course
Grammar
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enVision, Mathematics, Grade 6
Math
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History Alive! The Ancient World
History
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Illustrative Mathematics, Grade 6
Math
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IMPACT California Social Studies, Grade 6
History
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myWorld Interactive, World History, Early Ages
History
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Pengi Math (Grade 6)
Math
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Pengi Social Studies (Grade 6)
History
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Reveal Math, Course 1
Math
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Saxon Math, Course 1
Math
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Vocabulary from Classical Roots (Book D)
Vocabulary
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Vocabulary from Classical Roots (Book E)
Vocabulary
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Vocabulary from Latin and Greek Roots, Level IX
Vocabulary
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Yoshiwara Elementary Algebra
Math
Start Learning →6th Grade Skills (1436)
Amplify Science (California) Grade 6
28 chapters, 119 skills
▶
Amplify Science (California) Grade 6
28 chapters, 119 skills
Chapter 1: Microorganisms on and in the Human Body
Chapter 2: Arguing for the Benefits of Fecal Transplants
- Structuring the Final Argument
- Diversity Creates Stability
- Antibiotics Reduce Total Bacteria
- Harmful Bacteria Exploit the Imbalance
- The Gut Sustains a Bacterial Community
- Microorganisms Form a Massive Community
- Competitive Exclusion in the Microbiome
- Fewer Bacteria Free Up Resources
- The Body Hosts a Microbiome
Chapter 1: Molecules Needed by the Cells
Chapter 2: Body Systems
Chapter 3: Cellular Respiration
Chapter 4: Metabolism and Athletic Performance
Chapter 1: Health Bars for Disaster Relief
Chapter 1: Exploring Variation in Spider Silk
Chapter 2: Examining Spider Genes
Chapter 3: Investigating Spider Inheritance
Chapter 4: Explaining Variation in Running Ability
Chapter 1: Understanding Temperature
Chapter 2: Temperature and Energy
Chapter 3: Changes in Temperature
Chapter 4: Water Pasteurization
Chapter 1: Air Temperature
Chapter 2: Ocean Currents
Chapter 3: Ocean Currents and Prevailing Winds
Chapter 4: Science Seminar
Chapter 1: Understanding Rain Clouds
Chapter 2: Investigating Temperature
Chapter 3: Exploring Wind and Pressure
Chapter 4: Mystery of the Carson Wilderness Education Center
Chapter 1: Climate and the Atmosphere
Chapter 2: Energy Entering and Leaving Earth’s System
Chapter 3: Human Activity and Climate
Chapter 4: Volcanic Eruptions and Climate
Chapter 1: Rooftops for Sustainable Cities
- Variable Isolation Determines Causality
- Engineers Ensure Test Validity
- Colors Absorb and Reflect Sunlight
- Engineers Modify Roofs to Reduce Heat
- Engineers Conduct Controlled Experiments
- Different Materials Give Roofs Unique Properties
- Albedo Acts as a Performance Metric
- Albedo Measures Surface Reflection
- Engineers Test Designs with Simulations
- Analysts Compare Roofs Using Set Criteria
Big Ideas Math, Advanced 1
15 chapters, 193 skills
▶
Big Ideas Math, Advanced 1
15 chapters, 193 skills
Chapter 1: Numerical Expressions and Factors
- Reading Powers Aloud
- Finding Pairs with a Given GCF
- Application: Find the Greatest Perfect Square Factor
- GCF in Equal Grouping Problems
- Finding LCM by Listing Multiples
- Evaluating Algebraic Expressions with Exponents
- Left-to-Right Operations
- Factor Trees and Prime Factorization
- Distributive Property for Whole Number Multiplication
- PEMDAS Step-by-Step Evaluation
- Finding All Factor Pairs Systematically
- Real-World Applications of LCM
- Application: Area of a Square
- LCM of Three or More Numbers
- Perfect Squares
- Operation Key Words and Phrases
- Order of Operations with Exponents
- How Parentheses Change Expression Values
- Multi-digit Addition with Place Value Alignment
- Simplifying Ratios Using GCF
Chapter 2: Fractions and Decimals
- Visual Models for Fraction Multiplication
- Converting Whole Numbers to Fractions for Division
- Representing Decimal Multiplication with Grids and Blocks
- Simplifying Fraction Products
- Common Errors in Mixed Number Division
- Standard Algorithm for Multiplying Fractions
- Visual Models and Place Value Charts for Decimals
- Real-World Problems with Fraction Division
- Decimal Place Value Foundation
- Multiplying Decimals by Whole Numbers
- Adding Zeros to Continue Decimal Division
- Applying the Rule for Decimal Point Placement
- Mental Math Shortcuts for Powers of 10
- Multiplying Mixed Numbers and Improper Fractions
- Modeling Decimal Division with Base Ten Blocks
- Dividing Decimals by Whole Numbers
- Complete Procedure for Dividing Mixed Numbers
- Real-World Fraction Multiplication Applications
- Regrouping in Decimal Subtraction
- Visual Models for Fraction Division
Chapter 3: Algebraic Expressions and Properties
- Writing Expressions from Real-World Situations
- Applying Addition and Multiplication Properties to Algebraic Expressions
- Simplifying Expressions Using Properties
- Order in Subtraction and Division Expressions
- Distributive Property with Fractions
- Properties of Addition and Multiplication
- Distributive Property with Variables
- The Anatomy of an Algebraic Expression
- Operation Key Words and Phrases
- Translating Words into Expressions
Chapter 4: Areas of Polygons
- Triangle Area Using Coordinate Grids
- Application: Perimeter of Polygons on the Coordinate Plane
- Finding Trapezoid Area on Coordinate Grids
- Area of Parallelograms on Coordinate Grids
- Identifying Height vs Side Length in Parallelograms
- Area of Composite Figures with Parallelograms
- Real-World Triangle Area Applications
Chapter 5: Ratios and Rates
- Converting Between Percents and Fractions
- Units in Measurement Conversion
- Real-World Applications of Ratio Tables
- Mental Math Strategies for Basic Percentages
- Understanding Percent
- Linear Pattern of Equivalent Ratios
- Cross-System Conversion Factors
- Understanding Ratios in Context
- Comparing Ratios by Analyzing Line Steepness
- Adding Columns in Ratio Tables
- Solving Real-World Rate Problems with Fractions
- Using Double Number Lines for Rate Problems
- Using Ratio Tables for Equivalent Rates
- Using Ratio Tables for Systematic Comparison
- Solving Ratio Problems with Bar Diagrams
- Defining Rates
- Identifying Proportionality in Tables
- Representing Equivalent Ratios in Tables
Chapter 6: Integers and the Coordinate Plane
- Placing Decimals and Mixed Numbers on the Number Line
- Graphing Integers on a Number Line
- Ordering Integers on Number Lines
- Comparing Absolute Values
- The Integer Number Line
- Comparing Fractions and Decimals Using the Number Line
- Absolute Value in Real-World Distance Problems
- Writing Integers with Positive and Negative Signs
- Comparing Integers on a Vertical Number Line
- Graphing Method for Ordering Multiple Integers
- Points on Axes
- Plotting Points in the Coordinate Plane
- Defining the Set of Integers
- Quadrants and Coordinate Signs
- Comparing Integers on a Horizontal Number Line
Chapter 7: Equations and Inequalities
- Identifying Key Words for Operations and Equations
- Multiplication and Division Properties of Equality
- Inverse Operations and Properties of Equality
- Writing Equations in Two Variables
- Solving One-Step Addition and Subtraction Equations
- Distinguishing Between Expressions and Equations
- Solving Equations Using Multiplication or Division
- Using Area Formulas in Equations
- Multiplication and Division Properties for Inequalities (Positive Numbers)
- Standard Forms for Multiplication and Division Inequalities
- Verifying Solutions to Two-Variable Equations
- Common Two-Variable Formulas
- Converting Between Equivalent Inequality Forms
- Graphing All Solutions of Linear Equations
- Verifying Solutions to Inequalities
- Understanding Equations and Solutions
- Solving Inequalities Using Addition and Subtraction
Chapter 8: Surface Area and Volume
- Surface Area Formulas for Prisms
- Volume Formulas for Rectangular Prisms and Cubes
- Nets of Pyramids
- Identifying Components of a Prism
- 2D Views of 3D Figures
- Finding Surface Area Using Nets
- Finding a Missing Dimension
- Counting Faces, Edges, and Vertices
- Drawing Three-Dimensional Figures
- Surface Area Formulas for Square and Triangular Pyramids
- Step-by-Step Surface Area Calculation Using Nets
- Volume Applications with Weight and Capacity
Chapter 9: Statistical Measures
- Interpreting IQR and Range as Measures of Variation
- Identifying Outliers
- Interpreting MAD Values in Context
- Creating and Reading Dot Plots
- Measures of Center and the Population vs. Sample
- Properties of Median and Mode
- Analyzing the Effect of Outliers on the Mean
- Identifying Outliers Using the 1.5×IQR Rule
- Recognizing Statistical Questions
- Choosing Appropriate Measures of Center
- When to Use the Mean
- MAD with Mean and Median Comparisons
- Describing Data Distribution Patterns
Chapter 10: Data Displays
- Comparing Box Plots: Center, Spread, and Shape
- Relationship Between Distribution Shape and Measures of Center
- Drawing Conclusions from Histograms
- Identifying Uniform Distributions
- Analyzing Variability Using a Box Plot
- Stem-and-Leaf Plots
- Identifying Distribution Shapes
- Reading and Interpreting Basic Histogram Features
- Five-Number Summary
- Back-to-Back Stem-and-Leaf Plots
- Creating Stem-and-Leaf Plots
Chapter 11: Integers
Chapter 12: Rational Numbers
Chapter 13: Expressions and Equations
- Solving One-Step Multiplication and Division Equations
- Working Backwards Strategy for Two-Step Problems
- Terms in Algebraic Expressions
- Writing One-Step Addition and Subtraction Equations from Word Problems
- Basic Operations for Two-Step Equations
- Distributing to Expand Linear Expressions
- Solving One-Step Addition and Subtraction Equations
- Concept: Subtracting by Adding the Opposite
- Multiplication and Division Properties of Equality
- Simplifying Expressions: Distribute and Combine
- Vertical and Horizontal Methods for Linear Expressions
Chapter 14: Ratios and Proportions
- Solving Proportions Using Cross Products
- Mental Math Strategies for Solving Proportions
- Graphing Proportional Relationships
- Constructing and Using Ratio Tables
- Using Unit Rates in Proportional Relationships
- Direct Variation Behavior
- Writing Proportions
- Multiplication Property of Equality for Proportions
- Understanding the Constant Rate of Change in Linear Functions
- Cross Products Property
- Graphing Rates as Lines
- Finding Rates from Graphs
- Basic Unit Conversions Using Proportions
Chapter 15: Percents
- Using Number Lines to Compare Fractions, Decimals, and Percents
- Comparing Fractions, Decimals, and Percents by Converting to Common Form
- Evaluating the Simple Interest Formula I = Prt
- Solving for Unknown Variables in Simple Interest Problems
- Real-World Applications of the Percent Equation
- Converting Between Percents and Decimals
- Bar Models for Percents
- Identifying Part, Whole, and Percent in Word Problems
- Defining a percent
- Finding Original Prices Using Equations
- Real-World Percent-Decimal Applications
- Translating Simple Interest Word Problems
- Interpreting Percent Change in Data Tables and Graphs
Big Ideas Math, Course 1
9 chapters, 25 skills
▶
Big Ideas Math, Course 1
9 chapters, 25 skills
Chapter 1: Numerical Expressions and Factors
Chapter 2: Fractions and Decimals
Chapter 4: Areas of Polygons
Chapter 5: Ratios and Rates
Chapter 6: Integers and the Coordinate Plane
Chapter 7: Equations and Inequalities
Chapter 8: Surface Area and Volume
Chapter 9: Statistical Measures
Chapter 10: Data Displays
enVision, Mathematics, Grade 6
8 chapters, 57 skills
▶
enVision, Mathematics, Grade 6
8 chapters, 57 skills
Chapter 1: Use Positive Rational Numbers
- Dividing a Fraction by a Whole Number
- Procedure: Dividing a Whole Number by a Non-Unit Fraction
- Divide Fractions Using Reciprocals
- Divide a Whole Number by a Mixed Number
- A 4-Step Method for Solving Word Problems
- Finding Quotients and Remainders
- Algorithm for Multiplying Unit Fractions
- Find Reciprocals
- Procedure: Multiply Fractions
- Divide a Mixed Number by a Whole Number
- Add and Subtract Decimals
- Procedure: Multiply Mixed Numbers by Converting to Improper Fractions
- Divide a Mixed Number by a Mixed Number
- Find Decimal Quotients for Whole Number Division
- Multiply Decimals
Chapter 2: Integers and Rational Numbers
Chapter 3: Numeric and Algebraic Expressions
- Evaluate variable expressions with fractions
- Simplifying Expressions with Rational Coefficients
- Multiplying by Powers of 10
- Exponents with Decimal and Fractional Bases
- The Zero Exponent Rule
- Evaluating Expressions with Decimals
- Identifying Terms and Coefficients
- Applying Order of Operations with Fractions and Decimals
Chapter 4: Represent and Solve Equations and Inequalities
- Inverse Operations: Multiplication and Division
- Solving Equations with Fractions
- Subtraction and Addition Properties of Equality
- Identifying Independent and Dependent Variables
- Solving One-Step Addition & Subtraction Equations with Decimals
- Division Property of Equality
- The Multiplication Property of Equality
- Representing Relationships: Tables and Equations
- Identifying Multiple Independent Variables
- Solving One-Step Multiplication & Division Equations with Decimals
- Inverse Operations: Addition and Subtraction
- Verify a solution of an equation
- Writing 'Not Equal To' Inequalities
- Solving One-Step Addition & Subtraction Equations with Fractions
- Writing Inequalities from Verbal Phrases
Chapter 5: Understand and Use Ratio and Rate
- Using Ratios to Compare Totals
- Convert Between Customary and Metric Weight/Mass
- Convert Customary Capacities Using Equivalent Ratios
- Metric Conversions Using Equivalent Ratios
- Convert Customary Weights Using Equivalent Ratios
- Convert Between Customary and Metric Capacity
- Convert Between Customary and Metric Lengths
- Convert Customary Lengths Using Equivalent Ratios
Chapter 6: Understand and Use Percent
Chapter 7: Solve Area, Surface Area, and Volume Problems
Chapter 8: Display, Describe, and Summarize Data
History Alive! The Ancient World
6 chapters, 182 skills
▶
History Alive! The Ancient World
6 chapters, 182 skills
Chapter 1: Earliy Humans and the Rise of Civilization
- Surpluses Create Complex Societies
- Hunter-Gatherers Cooperated for Survival
- Scientists Interpret Prehistoric Clues
- Early Humans Adapted to Climate Change
- Hammurabi Unites an Empire with Laws
- Assyrians Conquer with Military Might
- Scientists Uncover Human Origins
- Hominins Evolve Greater Abilities
- Sumerians Build Walled Cities
- Sumerians Engineered a Food Supply
- Sumerian Kings Governed with Divine Authority
- Historians Question Historical Evidence
- People Slowly Adopt Farming
- Sumerians Develop Irrigation Systems
- Historians Debate the Past
- Sumerians Develop a Social Structure
- Historians Explain Change Over Time
- Villages Unite to Control Water
- Nebuchadnezzar Rebuilds Babylon
- Social Scientists Investigate the Past
- Humans Migrate Across the Globe
- Sumerians Record Their World in Cuneiform
- Sargon Creates the World's First Empire
- Historians Define Civilization
- People Learn to Farm Food
- Archaeologists Uncover Sumerian Life
- Farmers Face New Challenges
- Farming Develops Across the Globe
- Agriculture Sparks Community Growth
Chapter 2: Ancient Egypt and the Middle East
- Pharaohs Shape Three Great Kingdoms
- Phoenicians Spread Ideas Through Trade
- Jews Endure Foreign Rule
- Scribes Climbed the Social Pyramid
- Historians Study Ancient Sources
- Babylonians Destroy the Temple and Exile the Jews
- Romans Destroy the Second Temple
- Pharaohs Create Lasting Legacies
- Environment Guides Early Settlement
- Kush and Egypt Trade and Battle
- Judaism Establishes Core Beliefs
- Ancient Peoples Develop Written Language
- Resources Shape a Kingdom's Rise and Fall
- Canaan's Geography Shapes Lifestyles
- Empires Conquer a Weaker Egypt
- Phoenicians Connect Cultures Through Trade
- Pharaohs Ruled as Living Gods
- Kushites Forge a Distinct Identity
- Rabbis Reshape Jewish Life
- Social Class Defines Egyptian Life
- Kings Unite Israel and Build the Temple
- Kush Forges a New Power in Meroë
- Egyptians Organize a Pyramid Society
- God Makes a Covenant with Abraham
- Pharaohs Use Trade to Build Alliances
- Moses Leads the Exodus and Receives the Law
- Kush Rises and Retreats from Egypt
- Scientists Uncover King Tut's Secrets
- The Nile River Creates Fertile Land
Chapter 3: Ancient India
- Beliefs Shape the Soul's Journey
- Farmers Build a Civilization in the Indus Valley
- Ashoka Connects the Empire
- Ancient India Trades with the World
- Ashoka Carves His Rules in Stone
- Nomads Bring New Traditions to India
- A Prince Seeks Enlightenment
- Mountains Create Barriers and Gateways
- Indian Religions Share the Value of Non-Violence
- Hinduism's Roots Form in Ancient India
- Buddhists Shared Teachings Through Words and Art
- Gupta Rulers Balance Power
- Cultures Blend to Shape Ancient India
- Geography Shapes Early Indian Settlements
- Gupta Scholars Advance Arts and Sciences
- Historians Re-examine a Civilization's End
- Ashoka Rejects War for Buddhist Values
- Buddhism Spreads Across Asia
- Hinduism's Beliefs Evolve and Spread
- Gupta Stability Fosters a Golden Age
- A Monk's Diary Reveals a Golden Age
- Dharma Guides Righteous Living
- Indus Valley People Plan Advanced Cities
- Chandragupta Maurya Unites India
- Pollution Threatens the Ganges River
- Rivers Create Fertile Plains
- Artifacts Reveal Mohenjodaro's Secrets
- Vedic Ideas Shape Indian Society
- The Buddha Teaches the Middle Way
- The Bhagavad Gita Teaches Dharma
Chapter 4: Ancient China
- The Silk Road Spreads New Ideas
- The Han Test Officials for Government Jobs
- Traders Navigated Dangerous Sea Routes
- Legalists Propose Strict Rule
- Shang Kings Consulted Ancestors
- The Qin Emperor Unites the Warring States
- Han Inventors Create New Tools
- Han Rulers Create a Golden Age
- The Shang King Organized Society
- Qin Builds the Great Wall
- Emperors Use Exams to Find Officials
- Geography Isolates Early China
- Geography Shapes Lifestyles in China
- The Emperor Pursues an Afterlife
- Traders Pass Goods Along Routes
- Archaeologists Discover the Shang Dynasty
- The Ming Dynasty Chooses Isolation
- Rulers Gain and Lose Heaven's Favor
- The Zhou Overthrow the Shang
- An Explorer's Journey Opens Trade Routes
- Traders Form Caravans for Safety
- Geography Divides Ancient China
- The Emperor Standardizes China
- Han Innovators Explore Science and Medicine
- Daoists Seek Harmony with Nature
- The Shang Develop Writing and Master Bronze
- Confucius Defines an Orderly Society
Chapter 5: Ancient Greece
- City-States Educated Boys for Different Goals
- Greeks Use Logic to Explain the World
- Greeks End the Persian Invasion
- Greeks Shape Words and Power
- Disease Changes History
- Greeks Turn to Tyrants for Change
- Greeks Outsmart the Persian Army
- Hellenistic Culture Sparks Innovation
- Greeks Trade Goods Across the Seas
- Hellenistic Trade Links Continents
- Oligarchy Divides Greek Society
- Greeks Adapt Farming to the Land
- Thinkers Map the Earth and Classify Life
- Persian Kings Build a Vast Empire
- Athens Develops Direct Democracy
- Mountains Divide Greek Communities
- Athenians Honor Gods with Athletic Games
- Geography Shapes City-States
- Cultures Mix and Clash in Alexander's Empire
- Greeks Shape Modern Arts and Sports
- Greek Stories Shape Modern Language
- Aristocrats End Monarchy
- Athenians Design Ideal Buildings and Art
- City-States Build Different Economies
- Alexander Blends Cultures to Rule an Empire
- Athenians Explore Ideas Through Drama and Philosophy
- Geography Creates Independent City-States
- Greek Rivals Unite Against Persia
- Pericles Leads Athens into a Golden Age
- Greeks Established Colonies for Resources
- Religion Guided Athenian Culture
- City-States Choose Different Rulers
- City-States Define Social Roles
- The Ionian Revolt Angers Persia
Chapter 6: Ancient Rome
- Roman Law Favors the Wealthy
- Plebeians Gain Power in the Republic
- Roman Stories Shape Modern Culture
- Geography Connects Romans to Neighbors
- Expansion Divides Roman Society
- Paul Spreads Christianity to Non-Jews
- The Christian Church Splits into Branches
- Christianity Rises in the Roman Empire
- Christians Mark Time with Worship and Holidays
- Trade Unites the Roman World
- Disciples Proclaim the Resurrection
- Roman Ideas Influence Western Justice
- Generals End the Roman Republic
- Romans Adapt Greek Buildings and Writing
- Romans Create a Patrician-Led Republic
- Christians Practice Sacred Rituals
- Rome Expands the Idea of a Citizen
- Roman Rule Sparks Hope for a Messiah
- Romans Value Civic Duty
- Rome Expands Across the Mediterranean
- Citizenship Provided Unequal Rights
- Romans Blend Beliefs and Worship Emperors
- Rome Clashes with Eastern Empires
- Etruscans Shape Roman Building and Entertainment
- Social Conflict: Patricians vs. Plebeians
- Roman Builders Shape the World
- Jesus Teaches a Message of Love and Is Executed
- Christians Form Core Beliefs
- The Western Empire Collapses
- The Paterfamilias Rules the Roman Household
- Latin Evolves into Modern Languages
- Inequality Divides Roman Society
- Romans Adopt Greek Art and Gods
Illustrative Mathematics, Grade 6
8 chapters, 44 skills
▶
Illustrative Mathematics, Grade 6
8 chapters, 44 skills
Unit 1 Area and Surface Area
- Visualizing the Area: Triangles and Parallelograms
- Identifying Polygons and Their Components
- Calculating the Area of Polygons
- Finding Area by Rearrangement
- Visual Methods for Finding Parallelogram Area
- Area Invariance with Constant Base and Height
- Comparing Surface Area and Volume
- Properties of Parallelograms
- Assembling a Polyhedron from a Net
- Volume and Surface Area of a Cube
Unit 2 Introducing Ratios
Unit 3 Rates and Percentages
Unit 4 Dividing Fractions
- Translating Comparison Questions: A ÷ B vs. B ÷ A
- Modeling Quotative Division: Whole Number ÷ Unit Fraction
- Real-World Application: Solving Multi-Step Problems
- Applying Partitive Division: Fraction ÷ Whole Number
- Finding Missing Dimensions in 2D and 3D
- Procedure: Dividing Mixed Numbers
- Comparing Quantities: "Times as Large"
- Quotients Relative to 1
- Modeling Partitive Division: Finding the Group Size
- Modeling Division as Repeated Subtraction
- Two Meanings of Division: Quotative and Partitive
- Writing Equations for Division Scenarios
- Concept: Visualizing the Reciprocal Algorithm
- Modeling Quotative Division: Finding the Number of Groups
Unit 5 Arithmetic in Base Ten
Unit 6 Expressions and Equations
Unit 7 Rational Numbers
Unit 8 Data Sets and Distributions
IMPACT California Social Studies, Grade 6
11 chapters, 95 skills
▶
IMPACT California Social Studies, Grade 6
11 chapters, 95 skills
Chapter 1: Early Humans and the Agricultural Revolution
Chapter 2: Mesopotamia
Chapter 3: Ancient Egypt and Kush
- Egyptians Build Tombs and Advance Knowledge
- Hunter-Gatherers Settle the Nile Valley
- Egyptians Master the Nile with Technology
- Geography Protects Egypt
- Invaders End Egypt's Golden Age
- Narmer Unites Upper and Lower Egypt
- Egyptians Prepared for an Afterlife
- Kerma Rises on Trade and Agriculture
- Invaders End Egypt's Empire
- Pharaohs Restore Egyptian Power
- Unique Rulers Change Egypt
- Families Anchor Egyptian Society
- Kush Turns Defeat into Strength
- Meroë Becomes an Iron and Trade Center
Chapter 4: The Israelites
- Scribes Compile the Torah
- Jewish Leaders Organize Sacred Texts
- The Tribes Unite Under a King
- Jews Develop Synagogues in Exile
- Israelites Settle in Canaan
- Biblical Stories Teach Jewish Values
- Alexander's Conquest Spreads Greek Culture
- The Torah Shapes Daily Life
- Jews Resist Greek Rule
- Judaism Establishes Core Beliefs
- The Kingdom Falls
- The Israelite Kingdom Splits
- Jews Divide Under Roman Rule
Chapter 5: The Ancient Greeks
- Greeks Build City-States and Become Citizens
- Athenian Society Defines Strict Roles
- Greeks Endure a Dark Age
- Athenians Govern Themselves Directly
- Persia's Empire Crumbles
- Minoans and Mycenaeans Shape Early Greece
- Persian Kings Ruled by Divine Power
- Persia Governs a Vast Empire
- Athens Builds an Empire
- Rivalry Sparks the Peloponnesian War
Chapter 6: Greek Civilization
- Greek Thinkers Explained the Natural World
- Greeks Investigate the Past
- Philip II Unites a Divided Greece
- Philosophers Seek Happiness
- Homer's Epics Taught Greek Values
- Greek Thinkers Design Governments
- Artists Depict Realistic People and Emotions
- Alexander Leads His Army to Victory
- Generals Divide Alexander's Empire
- Hellenistic Scientists Explain the World
- Greeks Honored Human-Like Gods
- Greeks Debate the Meaning of Truth
- Greeks Teach Morals with Fables
- Alexander Builds a Vast Empire
Chapter 7: Ancient India
Chapter 8: Early China
- The Family Builds Chinese Society
- Buddhism Travels the Silk Road
- Han Inventors Develop New Tools
- Shang Kings Rule Society
- Aristocrats Challenge the King
- Geography Shapes Early China
- Thinkers Respond to a Chaotic China
- Qin Shihuangdi Unifies China
- Ancient China Organizes Its Society
- Thinkers Propose New Paths to Order
Chapter 9: Rome: Republic to Empire
- Romans Overthrow Monarchy and Establish a Republic
- Generals Use Armies to Seize Power
- Reform Ends in Violence
- Rome Unites a Diverse Empire
- Romans Establish Rule of Law with the Twelve Tables
- Romans Divide Government Power
- Augustus Reforms the Government
- Romans Tell Stories of Their Origins
- Rome Unites the Italian Peninsula
- Leadership Shapes the Empire
- Marius Builds a New Kind of Army
- Romans Championed Civic Duty
Chapter 10: Roman Civilization
Chapter 11: The Rise of Christianity
Pengi Math (Grade 6)
4 chapters, 9 skills
▶
Pengi Math (Grade 6)
4 chapters, 9 skills
Chapter 1: Rational Numbers — Whole Numbers, Fractions, and Decimals
Chapter 3: Ratios, Rates, and Percent
Chapter 4: Expressions, Equations, and Patterns
Chapter 6: Geometry
Pengi Social Studies (Grade 6)
7 chapters, 88 skills
▶
Pengi Social Studies (Grade 6)
7 chapters, 88 skills
Chapter 1: Early Humankind and the Rise of Civilization
- Adaptation to the Ice Ages
- Hunter-Gatherers Organized into Small Groups
- People Slowly Adopt Farming
- Social Scientists Investigate the Past
- Humans Created Technology to Survive
- Uncovering Ancient Life
- Hunter-Gatherers Express Complex Ideas
- Characteristics of Civilization
- Surpluses Create Complex Societies
- The Neolithic Revolution: People Learn to Farm
- Migration from Africa
- Primary and Secondary Sources
Chapter 2: The Early Civilizations of the Near East and Africa
- The Kushite Conquest of Egypt
- The Gift of the Nile
- Hammurabi Unites Mesopotamia
- Villages Unite to Control Water
- Meroë: The Iron Center
- Recording the World in Cuneiform
- Egyptians Organize a Pyramid Society
- The Assyrian War Machine
- Religion and the Afterlife
- Hammurabi's Code Establishes the Rule of Law
- Sumerians Built City-States
- Geographic Challenge: Sumerians Develop Irrigation
- Interdependence and Trade
Chapter 3: The Ancient Israelites (Hebrews)
Chapter 4: Ancient India
- Buddhism vs. Hinduism: The Caste System
- Planned Cities: Harappa and Mohenjodaro
- The Caste System (Varna and Jati)
- The Gupta Golden Age: Science and Math
- The Eightfold Path and Nirvana
- Aryan Migration and the Vedic Tradition
- Sacred Texts: Vedas and Bhagavad Gita
- The Life of Siddhartha Gautama
- Asoka's Conversion and Edicts
- Core Beliefs: Brahman and Reincarnation
- The Mystery of Decline
- A Monk's Diary: A Primary Source
Chapter 5: Ancient China
- Daoism: Harmony with Nature
- The Terracotta Army
- Standardization Strengthens the Empire
- The Civil Service System
- Rivers Shape Early Chinese Civilization
- Thinkers Respond to a Chaotic China
- Confucianism: Relationships and Filial Piety
- The Shang Dynasty: Writing and Bronze
- The Silk Road and Trade
- Unifying China through Legalism
- The Zhou Dynasty and the Mandate of Heaven
- Legalism: Strict Laws and Punishment
- Geography Isolates Early China
- Han Achievements in Technology
- The Great Wall
Chapter 6: Ancient Greece
- Greek Philosophy: Socrates, Plato, and Aristotle
- Women and Non-Citizens
- Education: Thinkers vs. Soldiers
- Art, Architecture, and Drama
- The Persian Wars Unite the Greeks
- Hellenistic Culture: A Blend of Traditions
- The Greek Legacy
- Economy: Trade vs. Conquest
- Two Paths: Democracy vs. Oligarchy
- Alexandria: The Center of Learning
- Alexander Builds an Empire
- Forms of Government: Monarchy to Tyranny
- Geography Molds Independent City-States
- The Polis and Citizenship
- Pericles and Direct Democracy
Chapter 7: Ancient Rome
- Paul and the Spread of Christianity
- The Legalization and Official Adoption of Christianity
- The Life and Teachings of Jesus
- Legacy of Engineering and Architecture
- Legacy of Law and Language
- The Augustan Age and the Pax Romana
- The Collapse of the Republic
- The Conflict of the Orders and Twelve Tables
- From Monarchy to Republic
- The Fall of the Western Empire
- Checks and Balances
Reveal Math, Course 1
10 chapters, 142 skills
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Reveal Math, Course 1
10 chapters, 142 skills
Module 1: Ratios and Rates
- Describing Ratios with "For Every" and "For Each"
- Using Double Number Lines for Rate Problems
- Scaling in Both Directions to a Non-Unit Intermediate Ratio
- Translating and Interpreting Line Steepness in Context
- Convert Using Equivalent Ratios
- Number Size in Measurement Conversion
- Calculating Unit Rates
- Correctly Setting Up Unit Price Calculations
- Finding Unit Rates Using Ratio Tables
- Comparing Rates
- Review: Plotting Points in the First Quadrant
- Selecting Appropriate Ratio Strategies
- Customary Unit Conversion Factors
- Solving Real-World Rate Problems
- Types of Ratios: Part-to-Part and Part-to-Whole
- Solving Rate Problems with Equivalent Rates
- Scaling in Both Directions Using Ratio Tables
- Aligning Units in Equivalent Ratios
Module 2: Fractions, Decimals, and Percents
- Application: Estimating Percents in Real-World Scenarios
- Strategy: Ratio Tables for Percents
- Modeling Percents with 10x10 Grids
- Modeling Percents Less Than 1% with Grids
- Identifying Percents from Bar Diagrams
- Convert Mixed Numbers to Percents
- Representing Percents Greater Than 100%
- Application: Percents Greater Than 100%
- Modeling Percents Greater Than 100% with Grids
- Using Ratio Tables to Find the Whole
- Representing Percents Less Than 1%
Module 3: Compute with Multi-Digit Numbers and Fractions
Module 4: Integers, Rational Numbers, and the Coordinate Plane
Module 5: Numerical and Algebraic Expressions
Module 6: Equations and Inequalities
- Inverse Operation of Division
- Inverse Operations: Undoing Addition
- Modeling with Subtraction Equations
- Writing Division Equations from Word Problems
- Inverse Operation of Multiplication
- Writing Multiplication Equations from Word Problems
- Translating Word Problems to Addition Equations
- Inverse Operations: Addition
Module 7: Relationships Between Two Variables
- Two-Variable Equations and Axes
- Finding the Dependent Variable (Output)
- Writing an Equation from a Word Problem
- Representations of Relationships
- Graphing an Equation
- Correctly Placing Rate of Change and Initial Value
- One-Step Multiplicative Relationships
- Variables on the Coordinate Plane
- Writing an Equation from a Graph
- Continuous and Discrete Data in Graphs
- Using Input-Output Tables
- From Table to Graph (Ordered Pairs)
- Four Representations of Linear Functions
- Testing One-Step Rules to Identify Two-Step Equations
- Structure of Two-Step Equations
- Writing Equations in Two Variables
- Representing Relationships: Tables and Equations
- Independent and dependent variables
Module 8: Area
- Visualizing the Area: Two Magic Tricks
- Real-World Applications: Area of Trapezoids
- Formula for the Area of a Parallelogram
- Base, Height, and the "Slanted Side" Trap
- Finding a Missing Dimension
- Definition of a Parallelogram
- Real-World Coverage Problems with Parallelograms
- Formula for the Area of a Parallelogram
- Common Error: Forgetting the Half
- Formula for the Area of a Triangle
- The Formula for the Area of a Trapezoid
- Area on the Coordinate Plane
- Definition of a Parallelogram
- Finding Horizontal and Vertical Side Lengths
- Calculating Total Area of a Regular Polygon
- Definition of a Regular Polygon
- Identifying Base and Height
- Area of Irregular Polygons: The Box Method
- Real-World Coverage Problems with Parallelograms
- Finding Missing Dimensions of a Trapezoid
- Visualizing Area: Decomposing a Parallelogram
- Visualizing the Area: Triangles and Parallelograms
- Real-World Scale Factors
- Visualizing Area: Decomposing a Parallelogram
- Finding Missing Dimensions of a Triangle
- Graphing Polygons on the Coordinate Plane
- Base, Height, and the "Slanted Side" Trap
- Finding a Missing Dimension of a Parallelogram
- Definition and Parts of a Trapezoid
- Calculating Perimeter
- Real-World Applications and Cost Estimation
- The Decomposition Strategy: Slicing the Shape
Module 9: Volume and Surface Area
- Calculating Partial Surface Area in Real-World Contexts
- Accounting for Congruent Opposite Faces
- Introduction to Volume and Unit Cubes
- Surface Area and Nets of Rectangular Prisms
- Finding a Missing Dimension of a Rectangular Prism (and Avoiding Errors)
- Calculating Total Surface Area of a Triangular Prism
- Volume Formula for Rectangular Prisms
- Prerequisite: Area of the Triangular Bases
- Surface Area of a Triangular Pyramid
- Anatomy and Net of a Triangular Prism
- Surface Area of a Square Pyramid
- Anatomy and Nets of Pyramids
- The Height Trap: Slant Height vs. Pyramid Height
- Volume with Fractional Edge Lengths
- The Lateral Rectangular Faces (Side Lengths Matter)
- Calculating the Surface Area Formula
Module 10: Statistical Measures and Displays
- Constructing a Box Plot
- The Vulnerable Measures: Mean and Range
- Choosing the Best Measure of Center
- Identifying Statistical Questions
- The Five-Number Summary, Range, and IQR
- Comparing Dot Plots and Histograms
- Calculating the Mean (The Average)
- Analyzing Variability Using a Box Plot
- Calculating Mean and MAD from Dot Plots
- The Ultimate Pairing Guide
- The Anatomy of a Distribution (Peaks, Clusters, and Gaps)
- Finding a Missing Data Value Given the Mean
- Dot Plots: Construction and Analysis
- Calculating the Mean Absolute Deviation (MAD)
- Collecting Data: Populations and Samples
- The Shape of the Data (Symmetric vs. Skewed)
- Finding Absolute Deviation (The Distance)
- The Resistant Measures: Median and IQR
- Calculating the Median and the Mode
- Quartiles and the Importance of Ordering Data
- Comparing Distributions (Consistency vs. Average)
- Constructing Histograms (and the Zero-Frequency Trap)
- Grouping Data with Frequency Tables
- Organizing Data: Frequency Tables
- The Ultimate Decision Matrix (Look Before You Calculate!)
- Reading the Secrets of a Box Plot
- Identifying Outliers (The 1.5 x IQR Rule)
Saxon Math, Course 1
8 chapters, 359 skills
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Saxon Math, Course 1
8 chapters, 359 skills
Chapter 1: Number, Operations, and Algebra
- Order of Operations, Part 1
- Finding a Missing Minuend
- Adding Whole Numbers and Money
- Commutative Property of Multiplication
- Fraction Bars are Secret Grouping Symbols
- Perimeter of a regular polygon
- Finding a Missing Subtrahend
- Zero Property of Multiplication
- Finding a Fraction of a Number
- Lines, Segments, and Rays
- Checking Division with Multiplication
- Even and Odd Numbers
- Fact Families and Inverse Operations
- Frequency table
- Finding the Unknown Dividend
- Number line
- Fractions
- Perimeter of a square
- Unknown Numbers in Addition
- Multiplying with Partial Products
- The Associative Property
- Identity Property of Addition
- Survey
- Commutative Property of Addition
- Sequences
- Perimeter
- Unknown Numbers in Addition
- Adding Whole Numbers
- Fact Families
- Unknown Numbers in Addition
- Unknown Numbers in Multiplication
- Left-to-Right for Multiplication and Division
- Metric system
- Finding the Unknown Divisor
- Scales
- Comparing Numbers
- Histogram
- Left-to-Right for Addition and Subtraction
- Investigation 1: Frequency Tables, Histograms, Surveys
- The Power of Parentheses
- Sequences
- U.S. Customary System
- Multiplying Whole Numbers and Money
- Unknown Numbers in Addition
- Fractional Parts
- The Number Line: Ordering and Comparing
- Finding Unknown Factors in Multiplication
- Finding a Missing Addend
Chapter 2: Problem Solving with Number and Operations
- Problems About Separating
- Problems About Comparing
- Line Graphs
- Measuring with a ruler
- Place Value Through Trillions
- Problems About Comparing
- Factors
- Factors
- Problems About Combining • Problems About Separating
- Estimating with Real-World Data
- Comparing Negative Numbers
- Subtracting into the Negatives
- Factors
- Comparing fractions
- Finding an Unknown Factor
- Multistep Problems
- Factors
- Problems About Equal Groups
- Reading Math
- Welcome to the Other Side of Zero
- Improper fractions and mixed numbers
- Factors
- Greatest Common Factor
- Gauss's Quick Addition Trick
- Place Value Through Trillions
- Meet the Opposites
- Improper fractions
- Average
- The Number Line: Negative Numbers
- Mixed numbers on the number line
- Investigation 2: Investigating Fractions with Manipulatives
- Estimating
- Equal groups
- GCF Of Prime Numbers
- Problems About Comparing
- Problems About Comparing
- Average
- Greatest Common Factor (GCF)
- Problems About Combining
- Rounding whole numbers
- The Number Line: Fractions and Mixed Numbers
- Rounding Whole Numbers
- Finding the Halfway Point
Chapter 3: Number, Operations, and Geometry
- Fractions of Dollars and Percents
- Reading Math
- Measuring Angles with a Protractor
- Fractions That Equal Whole Numbers
- Writing Division Answers as Mixed Numbers
- Ratio
- What is an Angle?
- Lines in a Plane
- Angles
- "Equal Groups" Problems with Fractions
- Reciprocals
- Least Common Multiple
- Multiplying whole numbers and fractions
- Multiplying two fractions
- Using Manipulatives to Reduce Fractions
- Types of Angles
- Measures of a Circle
- Concentric circles
- Adding Fractions With Common Denominators
- Improper fraction
- Equivalent fractions
- Diameter and Radius
- Naming an Angle
- Using Manipulatives to Reduce Fractions
- Circumference
- Investigation 3: Measuring and Drawing Angles with a Protractor
- Least Common Multiple (LCM)
- Adding and Subtracting Fractions That Have Common Denominators
- Multiplying Fractions
- Rate
- Divisibility
- Ratio
- Multiples
- Last-Digit Tests
- Reducing fractions
- Sum-of-Digits Tests
- Product, Sum, and Difference
- Thinking Skill: Infer
- Reading the Correct Scale
- Improper Fractions to Mixed Numbers
- Finding a Fraction of a Whole
- Solving Rate Problems
- Subtracting Fractions With Common Denominators
- Adding and Subtracting Mixed Numbers
- Drawing Angles with a Protractor
- Writing Division Answers as Mixed Numbers
Chapter 4: Number, Operations, and Measurement
- Perfect Square
- Decimal Place Value
- Bias
- Using zero as a placeholder
- Thinking Skill: Analyze
- Math Language
- Principal Square Root
- Real-world Decimal Multiplication
- Area of a Rectangle
- Investigation 4: Collecting, Organizing, Displaying, and Interpreting Data
- Circle graphs
- Decimal Place Value
- Annexing Zeros for Alignment
- Adding and Subtracting Decimal Numbers and Whole Numbers
- Percent
- Area
- Connecting Decimals to Money
- Reading and Writing Decimal Numbers
- Expanded Notation
- Thinking Skill
- Statistics
- Elapsed time
- Greatest Common Factor
- Population and Sample
- Adding and Subtracting Decimal Numbers and Whole Numbers
- Counting Decimal Places
- Subtracting From a Whole Number
- Quantitative and Qualitative Data
- Standard Notation
- Decimal Point
- Areas of Rectangles
- Using Zero as a Placeholder
- Subtracting Fractions and Mixed Numbers from Whole Numbers
- Adding and Subtracting Decimal Numbers
- Expanded Notation
- Writing Percents as Fractions, Part 1
- Multiplying Decimal Numbers
- Writing Decimal Numbers as Fractions, Part 1
- Writing Percents as Fractions
- Squaring A Decimal
- Multiplying Decimals
- Finding a Square's Side from its Area
- Adding and Subtracting Decimals
- Writing Decimals as Fractions
- Multiplying Decimals As Fractions
Chapter 5: Number and Operations
- Dividing With Decimals
- Finding a Percent of a Number
- Multiplying Decimals by Powers of 10
- Simplifying Decimal Numbers
- Mentally Multiplying Decimals
- Simplifying Decimal Division
- Equivalent Division Problems
- Expanded notation
- Simplifying Decimal Numbers
- Equivalent Division Problems
- Equivalent fractions
- Decimal Number Line (Tenths)
- Sales tax
- Subtracting Mixed Numbers with Regrouping
- Solving with Reciprocals
- Circle Graph
- Dividing by a Decimal Number
- Attaching Zeros To Finish Dividing
- Pi
- Circumference from Diameter
- Represent
- Reciprocals
- Pictograph
- Dividing a Decimal Number by a Whole Number
- Writing Decimal Numbers in Expanded Notation
- Changing Percents to Decimals or Fractions
- Identity Property of Multiplication
- Visualizing Regrouping with Models
- Comparing Decimal Numbers
- Investigation 5: Displaying Data
- Finding a Percent of a Number
- Renaming Fractions by Multiplying by 1
- Line Plot
- Circumference
- Subtracting Mixed Numbers with Regrouping, Part 1
- Adding Fractions with Different Denominators
- Arranging Decimal Numbers
- Finding Unknowns in Fraction and Decimal Problems
- Decimal number line
- Circumference from Radius
- Mean, Median, Mode, and Range
- Dividing by a Decimal Number
- Using Zeros As Placeholders
- Subtracting from a Whole Number
- Dividing by a fraction
Chapter 6: Geometry and Number Operations
- Chance
- Mentally Dividing Decimal Numbers by 10 and by 100
- Reducing by Grouping Factors Equal to 1
- Adding and Subtracting Fractions
- Faces, Edges, and Vertices
- Attributes of Geometric Solids
- Investigation 6: Attributes of Geometric Solids
- Rounding Decimal Numbers
- Regular Polygon: Definition
- Common Denominators
- Least Common Denominator
- Sample space
- Dividing Fractions
- Range
- Reducing by Grouping Factors Equal to 1
- Common Denominators, Part 2
- Dividing Decimals by 10
- Adding Fractions Adventure
- Surface Area
- Simplifying Fractions
- Three Steps For Fractions
- Decimals Chart
- Net
- Decimal Arithmetic Reminders
- Comparing Unlike Fractions
- Probability
- Complement of an event
- Probability and Chance
- Common Denominators, Part 1
- Lowest terms
- Polygons
- Adding Mixed Numbers
- What Is a Polygon?
- Adding and Subtracting Fractions: Three Steps
- The Great Fraction Subtraction
- Naming Polygons
- Rounding to the Nearest Tenth
- Estimating by Rounding
- Calculating Probability
- Renaming a Fraction
- Adding Mixed Numbers
- Rounding to the Nearest Cent
- Regrouping Improper Fractions
- Finding a Common Denominator
- Dividing Decimals by 100
Chapter 7: Fractions and Geometric Concepts
- Lengths of Segments
- Canceling Common Factors
- Justify
- Ordered Pair
- Prime Factorization
- Taming Large Fractions
- Supplementary angles
- The Coordinate Plane
- Multiplying Mixed Numbers
- Dividing Fractions with Canceling
- Writing Mixed Numbers as Improper Fractions
- Dividing is Multiplying
- Lengths of Segments
- Subtracting Mixed Numbers with Regrouping
- Parallelogram vs. Trapezoid
- Solving An Arithmetic Problem With Fractions
- Simplify The Product
- Adding Three or More Fractions
- Least Common Denominator
- Using Prime Factorization to Reduce Fractions
- Multiplying Mixed Numbers
- Complementary angles
- Parallelogram
- Adding Mixed Numbers
- Subtracting Mixed Numbers with Regrouping, Part 2
- Dividing Mixed Numbers
- Factor Trees
- Prime Factorization
- Canceling
- Dividing Mixed Numbers
- Multiplying Mixed Numbers
- Investigation 7: The Coordinate Plane
- Reducing Fractions Before Multiplying
- Multiplying with Mixed Numbers
- A Quick Method for Improper Fractions
- Division by Primes
- Perimeter and Area on the Plane
- Classifying Quadrilaterals
- Reducing Fractions With Prime Factors
- Writing Mixed Numbers as Improper Fractions
- Adding Three or More Fractions
Chapter 8: Advanced Topics in Geometry and Number Operations
- Fraction vs. Decimal Showdown
- S.O.S. for Fractions
- No Mixed Numbers at the Multiply Party
- Perpendicular Base and Height
- What is a Percent?
- Metric Liquid Measures
- Probability as a Decimal
- Thinking Skill: Explain
- Perpendicular bisector
- Comparing Fractions by Converting to Decimal Form
- Writing Fractions as Decimal Numbers
- Using a Constant Factor to Solve Ratio Problems
- Writing Fractions as Decimal Numbers
- U.S. Customary Liquid Measures
- Finding Unstated Information
- Exponents
- Area of a Triangle
- Area of a Triangle
- Constant factor
- Supplementary angles
- Calculating Sale Discounts
- Introduction to Exponents and Powers
- Area of a Parallelogram
- Angle bisector
- Multiplying Three Fractions
- Fractions Chart
- Parallelogram
- Comparing U.S. and Metric Capacity
- Writing Fractions as Decimal Numbers
- Probability and Complements
- Bisect and Segment Bisector
- Writing Fractions as Percents
- Writing Decimals as Percents
- Writing Fractions and Decimals as Percents, Part 1
- New Concept
- Parallelograms
- Writing Fractions as Decimal Numbers
- Finding Unstated Information in Fraction Problems
- Capacity
- Investigation 8: Geometric Construction of Bisectors
- Writing Decimal Numbers as Fractions
- Solving ratio problems
- An Equivalent Area Formula
- Finding a Percent from Data
- Prime Factorization with Exponents
- Setting up a ratio box
Yoshiwara Elementary Algebra
9 chapters, 123 skills
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Yoshiwara Elementary Algebra
9 chapters, 123 skills
Chapter 1: Variables
Chapter 2: Linear Equations
- Cartesian Coordinate System
- Like Terms
- Integers and Order Symbols
- Graph as a Picture of Solutions
- Solving inequalities
- Testing Equivalence with Substitution
- Linear Equation
- Inequalities
- Evaluating Algebraic Expressions
- Adding and Subtracting Like Terms
- Quotients of Signed Numbers
- Steps for Solving Linear Equations
Chapter 3: Graphs of Linear Equations
- Slope Criterion for Parallel Lines and its Geometric Proof
- Graph using the slope-intercept method
- Slope
- Interpreting Slope: Direction and Steepness
- Meaning of slope
- Two-point formula for slope
- Finding the slope-intercept form
- Proportional variables
- Ratios
- Perpendicular lines
- Intercepts of a line
- Horizontal and vertical lines
- Slope-intercept form
- Proportions
Chapter 4: Applications of Linear Equations
- Definition of a Solution to a System
- The Distributive Law
- Solving Equations with the Distributive Property
- System of Linear Equations
- Slope vs. Point-Slope Formula
- Types of Linear Systems
- Inconsistent and Dependent Systems
- Point-Slope Formula
- Solving Systems by Graphing
- The Distributive Law
- Applications of Linear Equations
- Products
Chapter 5: Exponents and Roots
- Decimal Form of a Rational Number
- What is a cube root
- Order of operations
- Solving for one variable
- Combining Like Terms
- Definition of a Square Root
- Volume and surface area
- Exponents
- Products of variables
- Powers of Negative Numbers
- Multiplying binomials
- Solving Equations of the Form x^2 = p
- Exponents vs Coefficients
- Pythagorean theorem
- Vocabulary: Radical, Radicand, and Principal Root
- Pythagorean theorem
Chapter 6: Quadratic Equations
- Sign patterns for factoring
- Factoring quadratic trinomials
- Extraction of roots
- Factoring out a common factor
- Number of x-intercepts
- Zero-factor principle
- The zero-factor principle
- The quadratic formula
- x-intercepts of a parabola
- Solving quadratic equations by factoring
- Standard form for quadratic formula
- Finding the vertex of a parabola
Chapter 7: Polynomials
- Products of polynomials
- Products of powers
- Subtracting polynomials
- Quadratic trinomials in two variables
- Special products
- Second law of exponents
- Adding polynomials
- Factoring Special Products
- Degree and descending powers
- Multiplying Monomials
- Squares of Binomials
- Greatest common factors
- First law of exponents
- Polynomials
- What is a polynomial?
- Factoring by guess-and-check
- Special factorizations
- Multiplying by a monomial
- Quotients of powers
Chapter 8: Algebraic Fractions
- Solving Formulas with Fractions
- Finding the Lowest Common Denominator
- Canceling Factors vs. Terms
- To Add or Subtract Algebraic Fractions
- Building Fractions
- To Multiply Algebraic Fractions
- Extraneous Solutions
- Fundamental Principle of Fractions
- To Reduce an Algebraic Fraction
- Adding and Subtracting Like Fractions
- Motion Problems with Fractions
- Products of Fractions
Chapter 9: More About Exponents and Roots
- Power of a Product Property
- Zero as an Exponent
- Product and Quotient Rules for Radicals
- Using the Laws of Exponents
- Negative Exponents
- Equations with cube roots
- Adding and Subtracting Radicals
- Laws of Exponents
- Power of a Quotient
- Negative and Zero Exponents
- Convert to Scientific Notation
- Power of a Power Property
- Simplifying Square Roots
- Rationalizing the Denominator
- Solving Radical Equations
- Extraction of roots