Jump to another unit
Math · Course contents
Unit 1 · Counting and Numbers
Unit 2 · Adding and Subtracting
Unit 3 · Place Value to 1,000
Unit 4 · Measuring, Time and Money
Unit 5 · Shapes and Equal Shares
Counting and how many
Adding and subtracting within 20
Tens and ones, then hundreds
Adding and subtracting within 1,000
Length, time and money
Shapes and equal shares
Math · Course contents
Unit 6 · Multiplication and Division
Unit 7 · Place Value and Multi-Digit Arithmetic
Unit 8 · Fractions
Unit 9 · Decimals
Unit 10 · Measurement and Data
Unit 11 · Geometry and the Coordinate Plane
Multiplication and division: what they mean
Multi-digit multiplication
Fractions: add, subtract, multiply
Decimals
Measurement: area, perimeter, volume
Geometry and the coordinate plane
Math · Course contents
Unit 12 · Ratios, Rates and Proportions
Unit 13 · The Number System
Unit 14 · Expressions, Equations and Inequalities
Unit 15 · Functions and Linear Equations
Unit 16 · Geometry
Unit 17 · Statistics and Probability
The 7th-grade year, month by month
Number Concepts & Data
The Fall Skills
September · Integers
October · Multiply, Divide & Properties
November · Expressions
December · Equations
6th Grade Review — Quiz
Rounding & Order of Operations
Decimals
GCF, LCM & Fraction Names
Fraction Operations
The Coordinate Plane
6th Grade Review — In Class & HW
Rounding & Order of Operations
Decimals
GCF, LCM & Fraction Names
Fraction Operations
The Coordinate Plane
Ratios, rates and unit rates
Proportional relationships and percent
Math 6–8 · Inequalities
Area, surface area and volume
Angles, triangles and scale drawings
Probability and sampling
Exponents, roots and scientific notation
Linear equations and systems
Functions and slope
Transformations, congruence and similarity
The Pythagorean theorem
Math · Course contents
Unit 18 · Algebra I: Linear Equations, Functions and Systems
Unit 19 · Algebra I: Exponents, Polynomials and Quadratics
Unit 20 · Geometry: Reasoning, Congruence and Triangles
Unit 21 · Geometry: Similarity, Trigonometry and Circles
Unit 22 · Statistics in Algebra I
Algebra I: linear equations and inequalities
Algebra I: functions and linear models
Algebra I: systems
Algebra I: exponents, polynomials, factoring
Algebra I: quadratics
Geometry: proof, congruence and triangles
Geometry: similarity and right-triangle trigonometry
Geometry: circles, area and volume
Math · Course contents
Unit 23 · Algebra II: Polynomial, Rational and Radical Functions
Unit 24 · Algebra II: Exponential, Logarithmic and Trigonometric Functions
Unit 25 · Sequences, Series and Modeling
Unit 26 · Statistics: From a Sample to a Claim
Unit 27 · Financial Math and Capstone
Algebra II: polynomial and rational functions
Algebra II: exponential and logarithmic functions
Trigonometric functions
Sequences and series
Statistics: from a sample to a claim
Financial math
Capstone: model it
All of Math — every band
All of Science — every band
All of Social Studies — every band
All of Economics — every band
All of English — every band
All of Spanish — every band
All of Family & Consumer Sciences — every band
All of World Religions — every band
Science · Course contents
Unit 1 · Pushes, Pulls and Stuff
Unit 2 · Light, Sound and Waves
Unit 3 · Living Things and Where They Live
Unit 4 · Earth, Sky and Weather
Pushes and Pulls
Sun, Moon and Sky
What Living Things Need
Weather and Seasons
Light and Sound
Materials and How They Change
Science · Course contents
Unit 5 · Forces, Motion and Energy
Unit 6 · Matter and Waves
Unit 7 · Life: Cycles, Traits and Survival
Unit 8 · Ecosystems and the Flow of Energy
Unit 9 · Earth, Weather and Space
Forces and Motion
Life Cycles and Traits
Weather and Climate
Energy
Earth’s Changing Surface
Matter: Properties and Changes
Ecosystems and Food Webs
Earth in Space
Science · Course contents
Unit 10 · Matter and Its Interactions
Unit 11 · Forces, Motion and Energy
Unit 12 · Waves and Information
Unit 13 · Cells, Bodies and Reproduction
Unit 14 · Ecosystems and Heredity
Unit 15 · Earth and Space Systems
Science 1 · Living Things in the Biosphere
Science 2 · The Cell System
Science 3 · Human Body Systems
Science 4 · Reproduction and Growth
Science 5 · Ecosystems
Science 6 · Populations and Communities
Science 7 · Genes and Heredity
Matter and Its Interactions
Forces, Energy and Waves
Earth’s Systems
Space Systems
Science · Course contents
Unit 16 · Biology: Cells and Energy
Unit 17 · Biology: Genetics and Inheritance
Unit 18 · Biology: Ecosystems and Human Impact
Unit 19 · Physical Science: Matter and Reactions
Unit 20 · Physical Science: Forces, Energy and Waves
Unit 21 · Earth and Space
Biology: Cells and Energy
Biology: Ecosystems and Human Impact
Physical Science: Matter and Reactions
Physical Science: Forces, Energy, Waves
Earth and Space
Science · Course contents
Unit 22 · Chemistry: Atoms, Bonding and Reactions
Unit 23 · Chemistry: Stoichiometry, Solutions and Energy
Unit 24 · Physics: Motion and Forces
Unit 25 · Physics: Energy, Waves and Electricity
Unit 26 · Environmental Science
Unit 27 · Capstone: Argue From Evidence
Chemistry: Atoms, Bonding, Reactions
Chemistry: Stoichiometry and Solutions
Physics: Motion and Forces
Physics: Energy, Waves, Electricity
Environmental Science
Capstone: Argue From Evidence
Social Studies · Course contents
Unit 1 · Me, My Family, My School
Unit 2 · Our Community
Unit 3 · Maps and Places
Unit 4 · Then and Now, and Our Country
Me, My Family, My Class
Rules and Fair Choices
Maps: Where Things Are
Then and Now
Needs, Wants and Work
Symbols and Stories of Our Country
Social Studies · Course contents
Unit 5 · Illinois: Land and People
Unit 6 · The First Peoples of North America
Unit 7 · Colonies to a New Nation
Unit 8 · Government: Local, State, National
Unit 9 · Money, Markets and Regions
Government: Local, State, National
Communities and Illinois
The First Peoples
Explorers, Colonies, a New Nation
Money, Markets and Choices
Maps and Regions of the United States
Social Studies · Course contents
Unit 10 · The First Civilizations
Unit 11 · Classical Worlds
Unit 12 · Faiths, Empires and Exchange
Unit 13 · Geography of the World
Unit 14 · Citizens of Illinois
U.S. History · Course contents
Unit 1 · Early Encounters
Unit 2 · English Settlement
Unit 3 · A New Nation
Unit 4 · The Early Republic
Unit 5 · Pushing National Boundaries
Unit 6 · Civil War and Reconstruction
Unit 7 · America on the Move
Unit 8 · Twentieth-Century Crises
Unit 9 · Postwar America
Unit 10 · America in a Changing World
A More Perfect Union
The Founding · 1776–1791
Civics · The Three Branches
Growth & Economy
The Road to War & Freedom
The World Before 1500
The World’s Regions
Reconstruction to the Present
Social Studies · Course contents
Unit 15 · World History: Empires and Exchange
Unit 16 · Revolutions and the Modern World
Unit 17 · The Twentieth-Century World
Unit 18 · Human Geography
Unit 19 · Civics: Rights, Power and Participation
Empires and Exchange
Revolutions and the Modern World
Human Geography
Civics: Rights, Power and Participation
Social Studies · Course contents
Unit 20 · U.S. History: Industry to the Progressive Era
Unit 21 · U.S. History: World Wars and the Cold War
Unit 22 · U.S. History: Civil Rights to Today
Unit 23 · Government and Economics
Unit 24 · Capstone: Inquiry from the Sources
Industry to the Progressive Era
The World Wars and the Cold War
Civil Rights to Today
Government
Economics
Capstone: An Inquiry from the Sources
Economics · Course contents
Unit 1 · Scarcity, Choice and Opportunity Cost
Unit 2 · Supply, Demand and the Market
Unit 3 · Prices, Controls and Market Failure
Unit 4 · Competition, Firms and Market Structure
Scarcity, Choice and Opportunity Cost
Supply, Demand and the Market
Prices, Controls and Market Failure
Competition, Firms and Market Structure
Economics · Course contents
Unit 5 · Measuring the Economy
Unit 6 · The Business Cycle and Fiscal Policy
Unit 7 · Money, Banking and the Federal Reserve
Unit 8 · Trade, Taxes and the World Economy
Measuring the Economy
The Business Cycle and Fiscal Policy
Money, Banking and the Federal Reserve
Trade, Taxes and the World Economy
English · Course contents
Unit 1 · Sounds and Letters
Unit 2 · Words and Sentences
Unit 3 · Stories and True Books
Unit 4 · Writing and Telling
Sounds and Letters
Words You Know by Sight
A Sentence Is a Whole Thought
Who, Where, What Happens
Beginning, Middle, End
True Books and Story Books
English · Course contents
Unit 5 · Word Power
Unit 6 · Reading Stories
Unit 7 · Reading to Learn
Unit 8 · Writing
Unit 9 · Grammar, Speaking and Listening
Word Parts: Prefixes, Suffixes, Roots
Context Clues
Main Idea and Details
Story Elements and Theme
How a Text Is Built
The Paragraph: a Claim and Reasons
English · Course contents
Unit 10 · The Novel
Unit 11 · Nonfiction and Argument
Unit 12 · Words: Stems and Meaning
Unit 13 · Grammar and Style
Unit 14 · Writing Across Forms
The Outsiders (novel study)
Grammar · 16 Modules
English · Course contents
Unit 15 · Literature: Close Reading
Unit 16 · The Language of Persuasion
Unit 17 · Words and Structure
Unit 18 · Grammar for Writers
Unit 19 · Research and Writing
Context Clues and Word Parts
Figurative Language
Tone and Voice
Rhetoric: How a Writer Persuades
Punctuation That Changes the Meaning
Clauses, Parallel Structure and Usage
English · Course contents
Unit 20 · Literary Devices and American Voices
Unit 21 · Diction, Syntax and Style
Unit 22 · Reasoning and Argument
Unit 23 · Advanced Grammar and Usage
Unit 24 · Capstone: Research, Cite, Defend
Literary Devices
Diction and Syntax
Reasoning and Fallacies
Advanced Punctuation
Concision and Style
Capstone — Research, Cite, Defend
Spanish · Course contents
Unit 1 · Sounds of Spanish
Unit 2 · Colors and Numbers
Unit 3 · El and La: Naming Things
Unit 4 · One and Many, Big and Little
Five Vowels That Never Change
Colors and Counting to Twenty
El and La — Naming What Is Here
One and Many, Big and Little
Spanish · Course contents
Unit 5 · A Whole Thought in Spanish
Unit 6 · Soy and Estoy
Unit 7 · Who, Where, When, Why
Unit 8 · First, Then, Last: Telling a Day
A Whole Thought in Spanish
Soy and Estoy — Who I Am, How I Am
Who, Where, When, Why
First, Then, Last — Telling a Day
Spanish · Course contents
Unit 9 · Greetings and Introductions
Unit 10 · Numbers, Time and Dates
Unit 11 · The Classroom: Nouns and Articles
Unit 12 · Ser, Estar and Describing People
Greetings and Introductions
Numbers, Time and Dates
The Classroom — Nouns and Articles
Ser, Estar and Describing People
Spanish · Course contents
Unit 13 · The Present Tense
Unit 14 · Tener, Gustar and Stem Changes
Unit 15 · The Preterite: What Happened
Unit 16 · The Imperfect and Telling a Story
The Present Tense
Tener, Gustar and Stem Changes
The Preterite
The Imperfect and Telling a Story
Spanish · Course contents
Unit 17 · Pronouns, Reflexives and Commands
Unit 18 · The Subjunctive
Unit 19 · The Spanish-Speaking World and Register
Unit 20 · Capstone: Present and Defend
Pronouns, Reflexives and Commands
The Subjunctive
The Spanish-Speaking World and Register
Capstone — Present and Defend
FACS · Course contents
Unit 1 · Clean Hands
Unit 2 · Hot, Cold and Sharp
Unit 3 · Everyday Food and Sometimes Food
Unit 4 · A Job Done to the End
Clean Hands
Hot, Cold and Sharp
Everyday Food and Sometimes Food
A Job Done to the End
FACS · Course contents
Unit 5 · Measure It Right
Unit 6 · The Needle and the Button
Unit 7 · Money and Choices
Unit 8 · Plan It, Cook It, Clean It Up
Measure It Right
The Needle and the Button
Money and Choices
Plan It, Cook It, Clean It Up
FACS · Course contents
Unit 9 · Kitchen Safety and Sanitation
Unit 10 · Knife Skills
Unit 11 · Measuring and Reading a Recipe
Unit 12 · Hand Sewing
Kitchen Safety and Sanitation
Knife Skills
Measuring and Reading a Recipe
Hand Sewing
FACS · Course contents
Unit 13 · The Sewing Machine
Unit 14 · Fabric, Fibers and Patterns
Unit 15 · Cooking Methods and Heat
Unit 16 · Nutrition and Meal Planning
The Sewing Machine
Fabric, Fibers and Patterns
Cooking Methods and Heat
Nutrition and Meal Planning
FACS · Course contents
Unit 17 · Food Science: What Happens When You Cook
Unit 18 · Child Development and Care
Unit 19 · Independent Living and Money
Unit 20 · Capstone: Plan, Cost, Produce
Food Science
Child Development and Care
Independent Living and Money
Capstone — Plan, Cost, Produce
World Religions · Course contents
Unit 1 · How to Read a Sacred Text
Unit 2 · The Biblical Lens I: The Hebrew Bible
Unit 3 · The Biblical Lens II: The New Testament
Unit 4 · Judaism: Torah, Talmud and a People
Unit 5 · Islam: The Qur'an and the Five Pillars
Unit 6 · Hinduism: Dharma, Karma and the Gita
How to Read a Sacred Text
The Hebrew Bible
The New Testament
Judaism
Islam
Hinduism
World Religions · Course contents
Unit 7 · Buddhism: The Four Noble Truths
Unit 8 · Confucianism and Daoism
Unit 9 · Sikhism, Jainism, and the Traditions of Africa and the Americas
Unit 10 · Religion and the World
Unit 11 · One Question, Many Lenses
Unit 12 · Capstone: The Sources Speak
Buddhism
Confucianism and Daoism
Sikhism, Jainism, Africa and the Americas
Religion and the World
One Question, Many Lenses
Capstone
Pick your module
Start Here
Study Cards
Helpful Hints
Practice Quiz
Lab
Start Here
Start here
One answer, or a whole stretch
An equation has exactly one answer. Here it is: x = 5.
Now make it an inequality
Open circle: 5 does not count, x > 5. Filled circle: 5 counts, x ≥ 5. The line under the symbol is the ink in the circle.
Four things people get wrong
⚠️ People often think…
Subtracting a negative flips the symbol.
What is actually true
Adding and subtracting never flip anything. Only multiplying or dividing by a negative does.
Only × or ÷ by a negative flips it.
⚠️ People often think…
A negative answer means you flip the symbol.
What is actually true
The sign of the ANSWER changes nothing. 2x < −8 is x < −4 — negative answer, same symbol, because you divided by positive 2.
Look at what you divided BY, not what came out.
⚠️ People often think…
“At least 8” means fewer than 8.
What is actually true
At least 8 means 8 or more: x ≥ 8. At most 8 means 8 or fewer: x ≤ 8. They sound backward, and they are not.
At least = the floor. At most = the ceiling.
⚠️ People often think…
5 < x shades to the left, because the arrow points left.
What is actually true
Put x on the left first. 5 < x is the same as x > 5, which shades to the RIGHT.
Rewrite it with x first, then draw.
Solve it, then draw it
1 Watch one
Solve 3x + 2 ≤ 14.
Subtract 2 from both sides.
3x ≤ 12.
Divide by 3. Positive, so no flip.
x ≤ 4. Filled circle at 4, shade left.
My turn
2 Do one with me
Solve 5x − 3 > 12.
Add 3: 5x >
Divide by 5: x >
The circle at 3 is open or filled?
Check these
💬 One sentence, then you move on
How do you know whether to use an open circle or a filled one?
Your sentence
That's my answer
3 Try one
Solve −2x < 10. Write the whole answer, symbol and all.
Check
I want a hint first
You divided by −2. A negative mirrors the number line, so the symbol turns around.
💬 Last one — then you're done here
Why does dividing by a negative turn the symbol around?
Your sentence
That's my answer
Where this goes
Where this lives
A speed limit, a height requirement for a ride, “at least eight hours of sleep,” a balance that cannot go below zero. All inequalities.
What this feeds
Next unit is area, surface area and volume — where the answer is a measurement, and the units tell you if you picked the right formula.
Write one rule from your own life as an inequality.
Your answer
Study Cards
Foundation
On-Level
Challenge
One card at a time — tap “Show me” to check yourself, then Next. Start at Foundation; when those feel easy, climb.
Helpful Hints
🪜 From words to a graph — the ladder
Name the unknown → find the limit number → pick the symbol (is the limit itself allowed?) → solve like an equation → FLIP only if you multiplied or divided by a negative → graph: circle, then arrow → test a point.
Name it, limit it, solve it, draw it, test it. 🤝 The whole topic in one idea
An inequality is an equation whose answer is a whole stretch of the number line instead of one point. Every solving move is the same — with ONE extra rule: a negative multiplier mirrors the number line, so the symbol turns around.
⚠️ Traps the test loves
Forgetting the flip when dividing by a negative: −2x < 10 is x > −5.
Flipping when you shouldn't: a negative ANSWER does not flip anything. 2x < −8 is x < −4.
Subtracting never flips. Only multiplying or dividing by a negative does.
“At least” is ≥. “At most” is ≤. They sound backward; they are not.
Open or closed? No line under the symbol, no ink in the circle.
5 < x shades to the RIGHT. Rewrite it as x > 5 before you draw.
📐 Words, symbol, circle, arrow — the chart
Words Symbol Circle Arrow (x first)
more than · greater than · above · over x > 8 open right fewer than · less than · below · under x < 8 open left at least · no fewer than · minimum x ≥ 8 closed right at most · no more than · up to · maximum x ≤ 8 closed left
🎯 How the test will ask
A sentence with a limit word — “write the inequality.”
A list of numbers — “which are solutions?” (substitute each one and read the sentence).
A number line — “which inequality is graphed?” (circle, then direction).
A one- or two-step inequality with a negative coefficient — the flip question.
A money or goal story — write px + q ≤ r or px + q ≥ r, solve it, and say what the answer means.
Someone’s wrong work — find the step where the symbol should have flipped.
✅ Before the test, can you…
Turn at least, at most, more than and fewer than into symbols?
Decide whether a number is a solution by substituting it?
Graph an inequality and read a graph back into symbols?
Solve a two-step inequality, flipping only when you should?
Explain with 2 < 5 why a negative multiplier flips the symbol?
Say what your answer means in the story — and round it sensibly?
Pick your level
🟤 Foundation 12 questions. Everyone needs these cold. 🟢 On-Level 10 questions, real test format. 🔵 Challenge 6 explain-and-apply questions with model answers.
✅ I had it
🌓 Partly
🌱 Not yet
Show the model answer
Next
Pick a different level
Start this level over
Look back at anything you missed — the hint that appeared is exactly what to reread tonight.
How sure did you feel?
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🌱 A little
🙂 Okay
😎 Confident
🔥 Very confident
Try another level
Do this level again
Workshop
Work like a mathematician: read the graph, put the steps in order, decide what flips, then find someone’s mistake and prove it. Every activity checks itself, and hints are free.
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Date —
Topic —
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Lab —
Traps met 0
Explained in own words 0
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