Lumi Academy — Level 6 Curriculum Workbook

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LUMI ACADEMY

Level 6

Master Scholars

Grades 7–8 · Ages 12–14

🤖 ACE says:
"Logic, creativity, and courage — that's what scholars are made of. Let's solve this world together."

Learner Information

Student Name:
Grade:
School Year:
Parent / Teacher:

lumi-learning.web.app · YourSpace LLC · Aligned to CCSS · TEKS · NGSS

🌟 Lumi Academy — Level 6: Master ScholarsTable of Contents

📋 Table of Contents

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Grades 7–8 are the edge — algebra, exponents, advanced writing, body chemistry, earth systems, and world history. You're becoming a real scholar now.

🔢 Section 1 — Mathematics

Unit 1: Exponents & Scientific Notation	Pages 4–9
Unit 2: Linear Equations & Graphing	Pages 10–15
Unit 3: Systems of Equations	Pages 16–20
Unit 4: Functions	Pages 21–25
Unit 5: Radicals & Pythagorean Theorem	Pages 26–30
Math Review	Pages 31–33

📖 Section 2 — ELA

Unit 6: Textual Analysis & Author's Argument	Pages 34–39
Unit 7: Rhetoric & Persuasive Techniques	Pages 40–45
Unit 8: Research Essay & MLA Citation	Pages 46–51
Unit 9: Advanced Grammar & Syntax	Pages 52–56
ELA Review	Pages 57–58

🔬 Section 3 — Science

Unit 10: Chemistry & Atomic Structure	Pages 59–64
Unit 11: Earth Systems & Climate	Pages 65–69
Unit 12: Genetics & Evolution	Pages 70–74
Science Review	Pages 75–76

🌍 Section 4 — Social Studies

Unit 13: World History — Renaissance to Modern Era	Pages 77–81
Unit 14: Global Cultures & Civics	Pages 82–85
Completion Certificate	Page 86

🌟 Lumi Academy — Level 6Unit 1 · Exponents & Scientific Notation

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Unit 1 — Exponents & Scientific Notation

Laws of Exponents · Zero & Negative Exponents · Scientific Notation · Very Large/Small Numbers

📚 Laws of Exponents

Product Rule

x^a · x^b = x^(a+b)
Example: 2³ · 2⁴ = 2⁷ = 128

Quotient Rule

x^a ÷ x^b = x^(a-b)
Example: 5⁶ ÷ 5² = 5⁴ = 625

Power Rule

(x^a)^b = x^(ab)
Example: (3²)³ = 3⁶ = 729

Zero Exponent

x⁰ = 1 (x ≠ 0)
Example: 7⁰ = 1, 100⁰ = 1

Negative Exponent

x^(-a) = 1/x^a
Example: 2⁻³ = 1/8 = 0.125

Scientific Notation

a × 10^n where 1 ≤ a < 10
Example: 4,500 = 4.5 × 10³

Part 1 — Simplify Using Exponent Laws

3² · 3⁴ =

5⁶ ÷ 5³ =

(2³)² =

10⁰ =

2⁻⁴ =

6⁻² =

Part 2 — Scientific Notation

Write in scientific notation:
45,000 =

Write in scientific notation:
0.000082 =

Expand from scientific notation:
3.5 × 10⁴ =

Expand from scientific notation:
7.2 × 10⁻³ =

The distance to the sun is about 93,000,000 miles. Write in scientific notation:

A virus is about 0.0000001 meters. Write in scientific notation:

🌟 Lumi Academy — Level 6Unit 2 · Linear Equations & Graphing

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Unit 2 — Linear Equations & Graphing

Slope · y = mx + b · Graphing Lines · Slope-Intercept Form

📚 Key Concepts

slope (m)Rise over run — how steep a line is: m = (y₂−y₁)/(x₂−x₁)

y-intercept (b)Where the line crosses the y-axis — when x = 0

slope-intercept formy = mx + b — the most useful form for graphing

positive slopeLine goes up from left to right

negative slopeLine goes down from left to right

zero slopeHorizontal line; undefined slope is vertical

Part 1 — Find the Slope

Points: (2, 4) and (6, 12)
m = (12-4)/(6-2) = __/__
m =

Points: (1, 7) and (4, 1)
m = (1-7)/(4-1) = __/__
m =

Points: (−3, 2) and (3, 8)
m = (8-2)/(3-(-3)) = __/__
m =

Part 2 — Write Equations in Slope-Intercept Form

m = 3, b = −2
y =

m = −½, b = 4
y =

Line passes through (0, 5) with slope 2
y =

Line passes through (2, 1) and (4, 5)
First find slope: m =
Then: y =

Part 3 — Graph the Line

y = 2x + 1
y-intercept: (0, ___)
slope: rise/run = ___/___
Second point: (1, ___)

y = −x + 3
y-intercept: (0, ___)
slope: rise/run = ___/___
Second point: (1, ___)

🌟 Lumi Academy — Level 6Unit 3 · Systems of Equations

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Unit 3 — Systems of Equations

Two Linear Equations · Substitution · Elimination · Graphing Solutions

📚 Solving Systems

Substitution Method: Solve one equation for a variable, substitute into the other

Elimination Method: Add or subtract equations to eliminate a variable

Graphing Method: Graph both lines; intersection point is the solution

Solution: The point (x, y) that satisfies both equations

Part 1 — Solve Using Substitution

System:
y = 2x + 1
y = −x + 4

Step 1: Substitute the first equation into the second:
2x + 1 = −x + 4

Step 2: Solve for x:

Step 3: Find y:

Solution: (, )

Part 2 — Solve Using Elimination

System:
3x + y = 7
x − y = 1

Step 1: Add the equations to eliminate y:
3x + y + x − y = 7 + 1
4x = 8

Step 2: Solve for x: x =

Step 3: Find y (substitute back): y =

Solution: (, )

Part 3 — Word Problem

A movie theater sells tickets at $8 for adults and $5 for kids. One day they sold 100 tickets and made $650. How many of each type were sold?

Let a = adult tickets, k = kid tickets
Equation 1: a + k =
Equation 2: 8a + 5k =

Solve using substitution or elimination:
Adult tickets:
Kid tickets:

🌟 Lumi Academy — Level 6Unit 4 · Functions

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Unit 4 — Functions

Function Notation · Domain & Range · Evaluating Functions · Linear & Quadratic Functions

📚 Function Concepts

functionA relationship where each input has exactly one output

f(x) notation"f of x" — the output value when input is x

domainAll possible input values (x values)

rangeAll possible output values (y values)

linear functionf(x) = mx + b — graphs as a straight line

quadratic functionf(x) = ax² + bx + c — graphs as a parabola

Part 1 — Evaluate Functions

f(x) = 3x − 2
f(4) = 3(4) − 2 =

f(x) = x² + 1
f(5) = (5)² + 1 =

f(x) = 2x² − 3x
f(−2) = 2(−2)² − 3(−2) =

Part 2 — Domain & Range

f(x) = 2x + 3
Is this a function? Yes / No
Domain (all x values):
Range (all y values):

f(x) = x²
Is this a function? Yes / No
Domain:
Range:
(Hint: squares are always ≥ 0)

Part 3 — Quadratic Functions

f(x) = x² − 4x + 3
Find the zeros (where f(x) = 0):
0 = x² − 4x + 3
0 = (x − 1)(x − 3)
Zeros: x = or x =

Vertex (line of symmetry): x = −b/(2a) = −(−4)/(2·1) =

🌟 Lumi Academy — Level 6Unit 5 · Radicals & Pythagorean Theorem

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Unit 5 — Radicals & Pythagorean Theorem

Square Roots · Cube Roots · Simplifying Radicals · a² + b² = c²

📚 Pythagorean Theorem

a² + b² = c²

In a right triangle:
a and b are the two legs (perpendicular sides)
c is the hypotenuse (longest side, opposite the right angle)

Part 1 — Simplify Square Roots

√16 =

√100 =

√2 ≈

√50 = √2

Part 2 — Use the Pythagorean Theorem

Right triangle with legs 3 and 4:
3² + 4² = c²
9 + 16 = c²
25 = c²
c =

Right triangle with legs 5 and 12:
5² + 12² = c²
25 + 144 = c²
c² =
c =

Right triangle with one leg 6 and hypotenuse 10:
6² + b² = 10²
36 + b² = 100
b² =
b =

A ladder leans against a wall. The ladder is 13 feet long and the base is 5 feet from the wall. How high does it reach?
5² + h² = 13²
25 + h² = 169
h = feet

🌟 Lumi Academy — Level 6Unit 6 · Textual Analysis

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Unit 6 — Textual Analysis & Author's Argument

Central Claim · Supporting Evidence · Counterarguments · Credibility

📚 Analyzing Arguments

claim (thesis)The main point the author is trying to prove

evidenceFacts, statistics, examples, or quotes that support the claim

logical appeal (logos)Using reason and evidence

emotional appeal (pathos)Using feelings to persuade

ethical appeal (ethos)Using credibility and trustworthiness

counterargumentAn opposing viewpoint that the author addresses

refutationProving a counterargument wrong

logical fallacyA flawed argument (hasty generalization, false cause, etc.)

📖 Analyze This Argument:

Climate Change and Youth

"Young people today face a climate crisis unlike any previous generation. Rising sea levels threaten coastal cities. Record temperatures worsen droughts. Scientists agree with 97% certainty that human activity drives climate change. Yet many politicians still deny these facts. Young people must vote and demand action — not for themselves, but for their children. The time to act was yesterday; the time to start is now."

Analysis Questions

Q1 — What is the author's central claim?

Q2 — List three pieces of evidence the author provides:

Q3 — Identify one appeal (logos, pathos, or ethos) used in this passage:

Q4 — What counterargument does the author mention? ("Many politicians...")

Q5 — How does the author refute this counterargument?

🌟 Lumi Academy — Level 6Unit 7 · Rhetoric & Persuasive Techniques

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Unit 7 — Rhetoric & Persuasive Techniques

Rhetoric · Tone · Diction · Syntax · Repetition & Parallelism

📚 Rhetorical Devices

Anaphora
Repetition at the start of consecutive clauses: "Yes we can, yes we will."

Assonance
Repetition of vowel sounds: "The light and bright design"

Allusion
Indirect reference to another text or event

Juxtaposition
Placing contrasting ideas side by side for emphasis

Rhetorical Question
A question asked for effect, not to get an answer

Parallelism
Using similar structure in repeated phrases: "First do this, then do that."

Identify the Rhetorical Device

"We shall never surrender, never falter, never fail."
Device:

"Do you really think that's fair?"
Device:

"The old guard dwindles while youth surges forward."
Device:

"Ask not what your country can do for you; ask what you can do for your country."
Device:

"The long and the strong bonds of community"
Device:

"Tilting at windmills" (reference to Don Quixote)
Device:

🌟 Lumi Academy — Level 6Unit 8 · Research Essay & MLA Citation

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Unit 8 — Research Essay & MLA Citation

MLA Format · In-Text Citations · Works Cited · Avoiding Plagiarism

📚 MLA Basics

In-text citation (parenthetical): (Author Page#) at the end of borrowed info

Works Cited entry: Alphabetical list on last page with full source info

Format: Last name, First name. "Title of Work." Title of Container, Date, Pages or URL.

Sample MLA Citations:

Book: Smith, John. The Great Discovery. ABC Publishers, 2020.

Website: Johnson, Sarah. "Climate Science Explained." Science Today, 15 Mar. 2022, www.sciencetoday.com.

Magazine: Lee, Michelle. "The Future of AI." Tech Weekly, vol. 45, no. 3, 2023, pp. 28–35.

Practice: Create MLA Citations

Book by Jane Austen titled "Pride and Prejudice," published by Penguin Classics in 2003.

Website article by Dr. Chen about "The Benefits of Meditation" from MindHealth.org, accessed March 15, 2024.

In-text citation for the Austen book, quoting page 45:

🌟 Lumi Academy — Level 6Unit 10 · Chemistry & Atomic Structure

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Unit 10 — Chemistry: Atomic Structure

Atoms · Protons, Neutrons, Electrons · Periodic Table · Bonding

📚 Atomic Structure

Proton

Positive charge (+)
In nucleus
Mass ≈ 1 amu

Neutron

No charge (neutral)
In nucleus
Mass ≈ 1 amu

Electron

Negative charge (−)
Orbits nucleus
Mass ≈ 0 (negligible)

Part 1 — Atomic Details

Hydrogen atom (atomic number 1):
Protons: ___
Electrons: ___
Neutrons (in most H): ___

Carbon-12 (atomic number 6, mass number 12):
Protons: ___
Electrons: ___
Neutrons: 12 − 6 = ___

Oxygen-16 (atomic number 8, mass number 16):
Protons: ___
Electrons: ___
Neutrons: ___

What determines the atomic number of an element?

Part 2 — Chemical Bonding

Bond Type	Description	Example	Strength
Ionic	Electron transfer; + and − charges attract	NaCl (salt)	Very strong
Covalent	Electron sharing between atoms	H₂O (water)	Strong
Metallic	Electrons shared among metal atoms	Fe (iron)	Strong

Is NaCl (table salt) held together by ionic, covalent, or metallic bonds?

Is H₂O (water) held together by ionic, covalent, or metallic bonds?

🌟 Lumi Academy — Level 6Unit 13 · World History: Renaissance to Modern

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Unit 13 — World History: Renaissance to Modern Era

Renaissance · Age of Exploration · Enlightenment · Industrial & French Revolutions · 20th Century

📚 Key Eras & Events

Era	Time Period	Major Events & Ideas
Renaissance	14th–17th century	Rebirth of Greek/Roman learning; humanism; art and science flourish (Leonardo, Michelangelo)
Age of Exploration	15th–17th century	European explorers sail to Americas, Africa, Asia (Columbus 1492, da Gama, Magellan)
Enlightenment	17th–18th century	Reason and science; natural rights (Locke, Rousseau); separation of powers (Montesquieu)
French Revolution	1789–1799	Overthrow of monarchy; Declaration of Rights; Reign of Terror; Napoleon
Industrial Revolution	1760–1840	Machines, factories, urbanization; changed society and labor
20th Century	1901–2000	Two World Wars; Cold War; technology; civil rights movements

Analysis Questions

Certificate of Completion

🤖⭐🏆

This certifies that

has successfully completed

Lumi Academy Level 6

Master Scholars — Grades 7–8 (Ages 12–14)

✅ Exponents & Scientific Notation

✅ Linear Equations & Graphing

✅ Systems of Equations

✅ Functions

✅ Pythagorean Theorem

✅ Textual Analysis

✅ Rhetoric & Persuasion

✅ MLA Research Writing

✅ Advanced Grammar

✅ Atomic Chemistry

✅ Earth Systems

✅ World History & Global Cultures

Parent Signature

Date Completed

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