Content Covered

Semester A

Unit 1: One-Variable Equations & Inequalities

Master solving one-variable linear equations and inequalities that may involve positive and negative numbers, fractions and decimals, and the distributive property.

Section 1: Solving Equations

1. Two Step Equations
2. Three Step Linear Equations
3. Linear Equations w/ Distribution (Lev 1)
4. Linear Equations w/ Distribution (Lev 2)
5. Simple Proportions
6. Solving Linear Proportions

Section 2: Solving Equations (Fractions & Decimals)

1. Two Step Equations with Decimals
2. Two Step Equations with Fractional Coefficients (L1)
3. Two Step Equations with Fractional Coefficients (L2)
4. Value that Makes Equation True (Multiple Choice – L2)

Section 3: Solving Inequalities

1. Linear Inequality and Number Line (L1)
2. Linear Inequality and Number Line (L2)
3. Linear Inequalities (Level 1)
4. Linear Inequalities (Level 2)

Section 4: Modeling with Equations & Inequalities

1. Solve Equations in Context (Unwinding)
2. Write and Solve Equations in Context
3. Age Word Problems
4. Solve Inequalities in Context (Unwinding)
5. Literal Equations (Level 1)
6. Literal Equations (Level 2)
7. Transforming Formulas

Unit 2: Linear Equations, Inequalities, & Systems

Two-variable linear equations, inequalities, and their graphs. Explore how different forms of linear equations reveal different information. Includes scatter plots, regression, and systems of equations and inequalities.

Section 1: Linear Equations

1. Graphing Lines from Equations
2. Table to Linear Equation (Level 1)
3. Writing Equations of Lines
4. Standard to Slope Intercept Form
5. Lines from Point & Slope
6. Horizontal & Vertical Lines
7. Lines from Two Points (Graphically)
8. Lines from Two Points
9. x/y-Intercept (Ax + By = C)
10. Graphing Ax + By = C from Intercepts

Section 2: Modeling with Linear Equations

1. Write Expression from Context (mx+b)
2. Interpreting Slope & Intercepts
3. Interpreting Points on a Linear Graph
4. Make Table and Equation Given Linear Situation
5. Write Equation for Linear Situation
6. Write Equation for Linear Situation (Level 2)
7. Interpreting Graph Stories

Section 3: Scatter Plots & Regression

1. Create Scatter Plot from Data Table
2. Association/Correlation (Scatter Plot)
3. Interpret Line of Best Fit: Slope & y-int
4. Interpret Line of Best Fit: Points
5. Draw Line of Best Fit
6. Linear Regressions
7. Calculate Residual from Context (Linear)
8. Linear Regression / Residuals / Best Model

Section 4: Systems of Equations

1. Solve Linear System Graphically (Graphs Given)
2. Solve Linear System Graphically
3. Substitution (Level 1)
4. Substitution (Level 2)
5. Elimination (Level 1)
6. Elimination (Level 2)
7. Determine Number of Solutions in System
8. Identifying Quad / Linear System Solutions

Section 5: Modeling with Systems of Equations

1. Write Expression from Context (Ax+By)
2. Write System of Equations from Context
3. Solve System of Equations from Context
4. Comparing Two Linear Functions (Context)
5. Comparing Two Linear Functions (Context – Graphically)

Section 6: Inequalities: Graphs & Systems

1. Graphing Linear Inequalities (mx+b)
2. Graphing Linear Inequalities (Ax+By)
3. Identify Point in Region of Inequalities
4. Linear Inequality Systems Graphically
5. Write Single Inequality from Context
6. System of Inequalities Word Problems

Unit 3: Exponential Functions

Develop a strong understanding of exponent rules. Analyze multiple representations of exponential functions – tables, graphs, and equations. Includes exponential growth and exponential decay.

Section 1: Exponent Rules

1. Exponents: Expand/Condense (Level 1)
2. Exponents: Expand/Condense (Level 2)
3. Exponent Rules (Variable Only)
4. Exponent Rules (Variable & Coefficients)
5. Multiplying Powers
6. Raising Powers to Powers
7. Dividing Powers

Section 2: Percent Increase & Decrease

1. Percent More or Less (Formula) L1
2. Percent More or Less (Formula) L2
3. Percent Change Word Problems (L1)
4. Percent Increase / Decrease Expressions

Section 3: Equations of Exponential Functions

1. Evaluating Exponential Functions
2. Find Growth/Decay Percentage (Level 1)
3. Match Exponential Equation & Context (Growth)
4. Match Exponential Equation & Context (Decay)
5. Rewrite Exponential Function with Exponent Rules
6. Table to Exponential Function
7. Exponential from Two Points (Level 1)
8. Linear vs. Exponential Contexts (MC)
9. Linear vs. Exponential Functions and Models

Section 4: Graphs of Exponential Functions

1. Plot Points & Graph Exponential Function
2. Translate Exponential Functions
3. Write Translated Exponential Function
4. Stretch / Compress Exponential Functions

Semester B

Unit 4: Sequences

Learn about a special type of function called a sequence. Write equations and find missing terms for arithmetic and geometric sequences.

Section 1: Intro to Sequences

1. Common Difference
2. Common Ratio
3. Nth Term of an Arithmetic Sequence
4. Nth Term of a Geometric Sequence
5. Distinguish Arithmetic vs. Geometric Sequences
6. Find Common Diff / Ratio with Missing Terms

Section 2: Formulas for Sequences

1. Formula for Arithmetic Sequence
2. Formula for Geometric Sequence (Level 1)
3. Formula for Geometric Sequence (Level 2)
4. Select Explicit Formula for Sequence
5. Sequences vs. Functions (from Graph)
6. Find Explicit Sequence or Function from Graph

Unit 5: Polynomial & Quadratic Expressions

Introduction to polynomial and quadratic expressions. Practice adding, subtracting, multiplying, and factoring these expressions.

Section 1: Intro to Polynomials

1. Polynomial Vocabulary
2. Classifying Polynomials
3. Rewrite Polynomials in Standard Form
4. Adding Polynomials
5. Subtracting Polynomials

Section 2: Multiplying Polynomials

1. Distributive Property (Area Model)
2. Distributive Property
3. Intro to Box Method
4. Multiply Binomials
5. Squaring Binomials
6. Arithmetic on Polynomial Expressions
7. Simplify by Distributing
8. Multiplying Binomials with Fractional Coefficients
9. Multiply Polynomials

Section 3: Factoring Polynomials

1. Greatest Common Factor (Level 1)
2. Greatest Common Factor (Level 2)
3. The X Game (Level 1)
4. The X Game (Level 2)
5. The X Game (Level 3)
6. Factor Trinomials (a=1)
7. Difference of Perfect Squares
8. Factor Trinomials (a>1) Level 1
9. Factor Trinomials (a>1) Level 2
10. Factor Trinomials (a>1) Level 3
11. Multi-step Factoring

Unit 6: Quadratic Equations

Solve quadratic equations using a variety of strategies. Includes factoring, square roots, completing the square, and the quadratic formula.

Section 1: Solving Equations by Factoring

1. Quadratic Equation to Standard Form
2. Solve Quadratic by Factoring (Level 1)
3. Solve Quadratic by Factoring (Level 2)
4. Factor Cubics (Equation)
5. Quadratic Word Problems
6. Consecutive Integer Problems – Quadratic

Section 2: Rational & Irrational Numbers

1. Simplifying Radicals
2. Solving with Square Roots (Level 1)
3. Solving with Square Roots (Level 2)
4. Multiply / Divide Radical Expressions
5. Adding / Subtracting Radical Expressions
6. Rationalize Monomial Denominators
7. Determine if Number is Rational / Irrational

Section 3: Completing the Square

1. Solving Quadratics with Square Roots (Level 1)
2. Solving Quadratics with Square Roots (Level 2)
3. Solving Quadratics with Square Roots (Level 3)
4. Find Complete the Square Constant
5. Complete the Square (Part 1 of Method)
6. Complete the Square (Rational Only)
7. Complete the Square (Irrational Only)
8. Complete the Square with a>1

Section 4: The Quadratic Formula

1. Finding Coefficients of Polynomials
2. Quadratic Formula (Level 1)
3. Quadratic Formula (Level 2)
4. Quadratic Formula (Level 3)
5. Quadratic Formula (Approximate Solutions)

Unit 7: Quadratic Functions

Analyze multiple representations of quadratic functions – tables, graphs, and equations – including roots, vertex, and axis of symmetry.

Section 1: Graphs of Quadratic Functions

1. Parabola Features (Level 1)
2. Parabola Features
3. Graphing Parabolas (Level 1)
4. Graphing Parabolas (Level 2)
5. Graphing Parabolas (Level 3)
6. Graphing Parabolas (Level 4)
7. Parabola a-Value

Section 2: Analyzing Quadratic Functions

1. Quadratic Extreme Value from Equation
2. Axis of Symmetry and Vertex (with Formula)
3. Quadratic Extreme Value from Equation (Level 2)
4. Determine Intercepts from Factored Form
5. Parabolas: Standard Form Coefficients
6. Parabolas: Intercept Form Coefficients
7. Parabolas: Vertex Form Coefficients
8. Factored to Standard Form
9. Vertex to Standard Form
10. Standard to Vertex Form
11. Standard to Vertex Form (a>1)
12. Select Form to Find Quadratic Feature

Section 3: Quadratic Functions w/ Technology

1. Axis of Symmetry
2. Maximum/Minimum Values
3. Roots / Zeros / x-intercepts
4. Roots & Vertex

Section 4: Modeling with Quadratic Functions

1. Interpret Graphs of Quadratics (Level 1)
2. Interpret Graphs of Quadratics (Level 2)
3. Interpret Graphs of Quadratics (Graphing Tech)
4. Appropriate Domain for Quadratic Model (Graphing Tech)
5. Quadratic Word Problems (Profit/Gravity)

Unit 8: Statistics

Analyze data displayed in dot plots, histograms, box plots, and two-way tables.

Section 1: Summary Statistics & Data Displays

1. Create Histograms
2. Interpret Histograms / Bar Charts
3. Interpret Dot Plot
4. Interpret Box Plot
5. Create Box Plot
6. Center and Spread Visually
7. Interpret Mixed Representations

Section 2: Two-Way Tables

1. Fill in Values, Two-Way Tables (L1)
2. Fill in Values, Two-Way Tables (L2)
3. Interpret Two-Way Tables
4. Percents Two-Way Tables

Class Introduction Video

✨ 🍋 ✨ 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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WORKSHOP TIME: We use “workshop time” so students will work while the teacher answers questions, gets them started, and holds them accountable. In a writing class, the teacher “visits” learners on their Google Documents and watches and helps them write. The immediacy of the feedback/revision cycle with the instructor allows writers to improve rapidly. Additionally, once we started using this method in writing classes, we saw nearly a 100% completion rate in student essays!

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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.

Outschool Coupon Code:
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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