Content Covered

Semester A

Unit 1: Geometry Foundations

Review basic vocabulary and notation. Use angle and side relationships to solve problems in the context of parallel lines, triangles, and polygons.

Section 1: Introduction to Geometry

1. Naming Lines / Line Segments / Rays
2. Naming Angles
3. Naming Planes
4. Parallel / Perpendicular / Skew Lines
5. Drawing Angles
6. Estimating Angle Measures
7. Estimating Angle Bisectors

Section 2: Segment & Angle Relationships

1. Segment Addition / Subtraction (Numbers)
2. Segment Addition / Subtraction (Algebra)
3. Breaking a Line Segment into Ratios
4. Angle Addition / Subtraction
5. Identifying Angles with Terminology
6. Vertical/Adjacent/Complementary Angles L1
7. Vertical/Adjacent/Complementary Angles L2
8. Vertical/Adjacent/Complementary Angles (Algebraic)

Section 3: Parallel Lines, Transversals, & Angles

1. Finding Angles in Transversal Problems (Level 1)
2. Finding Angles in Transversal Problems (Level 2)
3. Transversal Problems with Equations (Level 1)
4. Transversal Problems with Equations (Level 2)

Section 4: Angles in Polygons

1. Solve for Interior Angles – Triangle (Level 1)
2. Solve for Interior Angles – Triangle (Level 2)
3. Exterior Angles (Triangle)
4. Identify Polygons
5. Interior Angles of Polygons (Level 1)
6. Interior Angles of Polygons (Level 2)

Section 5: Triangle Properties

1. Draw Triangles of a Given Type
2. Identify Triangles of a Given Type
3. The Triangle Inequality
4. Properties of Isosceles Triangles (Diagram)

Unit 2: Constructions

Explore geometric constructions using an interactive compass and straightedge. Copy/bisect segments and angles, construct parallel lines, and more.

Section 1: Basic Constructions

1. Copying a Segment
2. Perpendicular Bisector
3. Perpendicular Line Through Point Off a Line
4. Perpendicular Line Through Point On a Line
5. Copying an Angle
6. Angle Bisector
7. Parallel Line Through a Point

Section 2: Advanced Constructions

1. Constructing an Equilateral Triangle
2. Constructing a Line of Reflection
3. Constructing a Median of a Triangle
4. Constructing an Altitude of a Triangle

Unit 3: Transformations

Explore transformations – translations, reflections, rotations, dilations – on both individual points and figures.

Section 1: Transformations on Coordinate Points

1. Translating a Point
2. Variations on Translating a Point
3. Reflecting a Point over an Axis (Graphically)
4. Reflecting a Point over an Axis
5. Rotating a Point
6. Dilating a Point
7. Composing Transformations
8. Transforming a Point on a Figure

Section 2: Rigid Transformations on Figures

1. Translate a Figure (Graphically)
2. Reflect a Figure over a Line (Level 1)
3. Reflect a Figure over a Line (Level 2)
4. Identify Single Rotation or Reflection
5. Identify Transformations
6. Rotational Symmetry
7. Lines of Symmetry

Section 3: Scaled Figures & Dilations

1. Create Scaled Drawings on a Grid
2. Find the Scale Factor
3. Dilations of Segments & Angles
4. Dilations on the Coordinate Plane
5. Dilated Figures / Direct Scale
6. Scale Factor & Area
7. Scaled Figures Perimeter & Area (L1)
8. Scaled Figures Perimeter & Area (L2)
9. Composition of Transformations: Mapping Shapes

Unit 4: Similarity & Right Triangle Trigonometry

Explore side and angle relationships in similar and right triangles. Introduction to trigonometric ratios: sine, cosine, and tangent.

Section 1: Proportions in Similar Figures & Triangles

1. Identify Corresponding Parts of Similar Figures
2. Simple Proportions
3. Similar Figures / Proportion (Level 1)
4. Similar Figures / Proportion (Level 2)
5. Similar Figures / Direct Scale
6. Special Triangle Lines – Centroid
7. Circumcenter / Incenter / Orthocenter / Centroid

Section 2: Similar Triangles

1. Proving Triangles Similar
2. Triangle Midsegment (Numeric)
3. Equivalent Proportions, Similar Triangles
4. Solve for Side or Perimeter, Similar Triangles
5. Word Problems, Similar Triangles

Section 3: Right Triangles

1. Simplifying Radicals
2. Pythagorean Theorem (Rounding)
3. Pythagorean Theorem (Radical Answers)
4. Pythagorean Theorem Word Problems
5. Converse of the Pythagorean Theorem
6. Special Right Triangles (Rounding)

Section 4: Triangle Trigonometry

1. Identifying Opposite / Adjacent / Hypotenuse
2. Identifying Trig Ratios (Diagram), Level 1
3. Identifying Trig Ratios (Diagram), Level 2
4. Identifying Trig Ratios (Diagram), Level 3
5. Using Trig to Find a Side
6. Using Trig to Find Angles
7. Trig Word Problems
8. Sine/Cosine of Complementary Angles

Semester B

Unit 5: Congruence & Proof

Formalize what it means for figures to be congruent. Use flowchart and two-column proofs to prove triangles are congruent, then extend to quadrilaterals.

Section 1: Congruence, Mapping, & Corresponding Parts

1. Mapping Without Coordinate Plane
2. Congruence versus Similarity
3. Congruence via Rigid Motions
4. Congruence and Corresponding Parts
5. Identify Corresponding Parts of Congruent Figures
6. Corresponding Parts of Congruent Figures are Congruent

Section 2: Triangle Congruence Proofs

1. Triangle Congruence Criteria
2. Congruence / Mapping without Coordinate Plane
3. Triangle Congruence, Basic Flowchart Proof
4. Triangle Congruence, Flowchart Proof (Level 1)
5. CPCTC, Basic Flowchart Proof
6. Triangle Proofs (Reorder Steps)

Section 3: Quadrilateral Properties & Proofs

1. Identify Quadrilaterals (Basic)
2. Identify Quadrilaterals
3. Parallelogram Properties – Diagonals
4. Parallelogram / Rhombus Properties, Sides & Angles
5. Parallelogram / Rhombus Properties, Sides & Angles (Algebraic)
6. Quadrilateral Properties, Diagonals
7. Quadrilateral Properties, Diagonals (Algebraic)
8. Area of Quadrilaterals

Unit 6: Geometry on the Coordinate Plane

Mix geometry and algebra on the coordinate plane. Find the midpoint and distance between two points, equations of parallel and perpendicular lines, area and perimeter, and equations of circles.

Section 1: Midpoint & Distance Formulas

1. Midpoint Graphically
2. The Midpoint Formula
3. Coordinate Distance, Pythagorean (Rounding)
4. Coordinate Distance

Section 2: Equations of Parallel & Perpendicular Lines

1. Graph Parallel Lines
2. Graph Parallel & Perpendicular Lines
3. Slopes of Parallel/Perpendicular Lines
4. Parallel Equations
5. Parallel & Perpendicular Equations
6. Parallel/Perpendicular Through Point

Section 3: Coordinate Geometry

1. Perimeter Given Coordinates
2. Area of a Triangle on a Coordinate Grid (Level 1)
3. Area of a Triangle on a Coordinate Grid (Level 2)
4. Coordinate that Makes Rectangle/Parallelogram
5. Area of Quadrilateral from Coordinates

Section 4: Circle Equations

1. Graphing Circles
2. Circle Equations
3. Circle Equations with Distance Formula
4. Find Circle Center and Radius from Equation (Conic Form)
5. Write Equation of Circle from Key Features
6. Write Equation of Circle from Key Features

Unit 7: Circles

Find circumference and area of circles and parts of circles (arc length and sector area). Apply circle properties involving segments and angles formed by chords, secants, and tangents.

Section 1: Circumference & Area

1. Circumference (in terms of pi)
2. Circumference (rounding)
3. Find Radius / Diameter from Circumference
4. Area of a Circle (in terms of pi)
5. Area of a Circle (rounded)
6. Circumference & Area of a Circle

Section 2: Arc Length & Sector Area

1. Fractional Part of a Circle
2. Naming Arcs
3. Arc Length
4. Sector Area
5. Fraction of a Semicircle / Degrees to Radians
6. Radians, Radius and Arc Length

Section 3: Circle Properties

1. Parts of Circles (Level 1)
2. Parts of Circles (Level 1)
3. Central / Inscribed Angles (Level 1)
4. Central / Inscribed Angles (Level 2)
5. Central / Inscribed Angles (Algebraic)
6. Angles Formed by Chords, Tangents, Secants
7. Cyclic Quadrilaterals

Unit 8: Three-Dimensional Figures

Work with surface area and volume of more advanced 3D figures, including oblique prisms and pyramids. Determine how surface area and volume change when a figure is scaled, and apply these concepts to real-world objects.

Section 1: Basic Volume

1. Volume of Prisms
2. Volume of a Cylinder
3. Volume of a Cone
4. Volume of a Pyramid
5. Volume of a Sphere

Section 2: 3D Figures & Advanced Volume

1. Identify Prism / Pyramid from a Net
2. Surface Area from a Net
3. Identify Cross Sections of Solids
4. Scaled Solids Surface Area and Volume
5. Match 2D Figure / Solid of Revolution
6. Volume of Solid of Revolution
7. Cavalieri’s Principle
8. Volume of Oblique Solids

Section 3: Modeling with 3D Figures

1. Conversions with Dimensional Analysis (Level 1)
2. Conversions with Dimensional Analysis (Level 2)
3. Volume Word Problems (Basic)
4. Volume Word Problems
5. Volume, Density, and Unit Conversions

✨ 🍋 ✨ Why Lemons-Aid? ✨ 🍋 ✨

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A BIBLICAL WORLDVIEW: The Bible, infallible and inerrant, is the very written word of God, who has revealed Himself to man. The Bible is like the light we cast on all content areas in order to understand it, whether that be literature, physical science, history, or geometry. Students learn all content through a Biblical lens. Theology is important for understanding all subject areas. We carefully curate courses that capture learners’ imagination while pointing them to God through sound doctrine. THIS is most important!

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EXPLICIT TEACHING: We understand the skills and concepts students need to learn and know how to teach them. Lemons-Aid’s materials are top-notch, organized, and clear for students and parents to understand. We are especially skilled at breaking down a complicated process into understandable parts. Further, explicit instruction is “a structured, systematic, and effective methodology for teaching academic skills. It is called explicit because it is an unambiguous and direct approach to teaching that includes both instructional design and delivery procedures. Explicit instruction is characterized by a series of supports or scaffolds, whereby students are guided through the learning process with clear statements about the purpose and rationale for learning the new skill, clear explanations and demonstrations of the instructional target, and supported practice with feedback until independent mastery has been achieved.”

• Explicit Instruction: Effective and Efficient Teaching by Anita L. Archer and Charles A. Hughes.

Anita Archer trained Mrs. Lemons in workshops, and it changed her teaching. Read a little more about the research behind explicit teaching here and here.

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STUDENT ACCOUNTABILITY = ACHIEVEMENT: Students master skills with us and make gains. We have a high degree of accountability. Since we make promises here and parents are paying good money, we understand you trust us to work! Students have to work too, and let’s be honest: they’re kids and don’t always want to. We push it. We teach them how to stay engaged, we cold-call on kids, we tell them to use the chatbox, and we want them to use emojis! If they are resistant, we contact the student through the teacher tab first. If that doesn’t work, we call in the big guns–Mom and Dad. We want kids to learn. We don’t want them to pass through our classes without gaining skills and doing great learning.

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DO HARD THINGS. Boost your confidence, master new skills, learn new concepts. This takes a commitment to do hard things. Like the standards we have for our teachers, we also expect our learners to do hard things, whether that means they stand firm in their convictions, learn geometry, write an essay, or give an oral presentation. You can do hard things!

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HEALTHY RELATIONSHIPS: To balance our high expectations for their learning and behavior, we build relationships with them. We want them to know we care about and know them. We’ll ask about their play last weekend or the new trick they’re trying to master on the skateboard. We also want students to get to know each other and encourage community engagement.

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DEPENDABLE: Multiple teachers are teaching this class, and we have an entire year of lessons planned and scheduled. Since we are a mission-driven organization, we protect our brand and the relationships with our families. We are accountable to our learners. When things come up for teachers, we work to get substitutes and do everything we can before canceling a class. We do not like canceling or changing, and we often teach classes at a loss to give others a chance to join. We have limits, of course, but we are not flippant or irresponsible about canceling! When things come up for students, since we have multiple sections, they can transfer from section to section. All our teachers teach the same content the same week, giving families even more flexibility!

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TEACHER FEEDBACK: The back-and-forth work between a student and teacher significantly benefits a student if done well. We follow best practices in designing class time, assignments, and routines. According to Pennington Publishing, effective writing feedback (or grading) is:

• Specific, not general
• Immediate, not postponed
• Routine with a revision / feedback cycle
• Explanatory
• The right amount
• Targeted to the most critical issues
• Varied (written, audio, and video comments)
• Holding students accountable

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GRAPHIC ORGANIZERS: Students need graphic organizers to help them see the structure and breakdown of a concept or process. For example, we use them to help learners understand how to write a paragraph or essay and to use the writing process. This is how they learn to develop coherent ideas. They don’t figure out how to do this magically; the graphic organizers and the intentional, explicit teaching help them learn the skills!

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STUDENT MASTERY: Each class includes explicit, direct instruction with teacher modeling. Students are guided toward mastery of skills and understandings to grasp the concepts and become independent. Students are held to a high standard of academic work, including often ignored skills like the use of grammar and neatness in math.

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STUDY THE BEAUTIFUL

We are surrounded by the mediocre, which is not good! We see this in expectations at some schools, the poor customer service at a store, and even architecture like in a gray, uninspiring complex of high-occupancy housing.

In contrast, we are surrounded by the beautiful, which is good! We see the beautiful in classic literature, music, and beautiful architecture like pictured here.

The mediocre demoralizes learners while the beautiful inspires.

At Lemons-Aid Learning, we study the beautiful: classic literature, artful sentence construction, art, poetry, maths, God’s hand in all of history, and God’s very creation. His creation glorifies Him, and in our study of all content areas, we learn about who God is.

We do not compromise. This means we don’t choose a graphic novel of Shakespeare’s A Midsummer Night’s Dream. We read the original play. We know how to make the complexity and beauty of classic study approachable and understandable to a modern audience. It’s more difficult, but worth the effort!

For over a century, progressive education reform has been “anti-content,” which means they de-emphasize rich content and focus instructional time on things such as self-esteem and “skills” they hope will benefit a learner in the future. This is why American kids do so poorly in testing compared to nations with content-rich curricula. We want our learners to increase in knowledge and grow in wisdom, which our content-area experts foster while teaching.

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CUSTOMER SERVICE

We serve the Lord and we work hard for families. We work to give quick responses to questions, authentic and careful feedback, and to solve any conflict. As home educators ourselves, familiar with the joys and struggles of teaching our own children, we can relate! We are supporting families, equipping learners, and serving Christ. We are 100% devoted to Him and to you!

To read more about our teaching and learning methods, read our blogs, written by our teachers and staff.

The Lemons-Aid Team

Lemons-Aid teachers have a few things in common.
❤️ They love their students and value each of their unique strengths and personalities that make our classes special. Our classes can be described as fun, personal, academic, challenging, and supportive.
🤩 We work to keep learners engaged, so there is always a degree of student accountability for their attention and focus, whether that be through asking them direct questions or by using the chatbox.
💭 We know all kids can learn, but sometimes things are hard! To support students, we teach them how to develop effective thinking and learning habits that will bring them success in class and in life.
🌟 Building relationships with students so they know we care about them helps us balance the high expectations we have for them regarding their effort, work quality, and behavior. Our students are encouraged, cared for, and they achieve!

Christian Teachers on Outschool

Lemons-Aid Coupon Code:
We want to serve you on Lemons-Aid! For first-time learners on Lemons-Aid, you can use the coupon code Newbie20 to get $20 off your first class.

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If the schedule on this platform doesn’t work for you, we will happily teach you on Outschool, but we can’t talk about Jesus. Use this referral code and get $20 off your first class on Outschool: LEMONSA2020

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