Course Details:

The sign-up fee covers the CTC curriculum cost, which includes access to all math levels K-12 for one year. All other resources are provided.

6th grade Math: Putting the Pieces Together

$40.00 / week and a $40.00 sign-up fee

This course follows CTC’s renowned mastery-oriented approach, helping sixth graders build genuine mathematical understanding through clear explanations, visual models, and conceptual depth. Our live classes complement the CTC curriculum with spiral review, fluency practice, encouragement, and biblical connections that help students see God’s perfect order and design in mathematics.

Section Options / Enroll:

Clear

Description

A Dream Outcome: Putting all the Pieces Together

Picture this: Your sixth grader faces their first algebraic expression and, instead of panic, their eyes light up with recognition. “This is just like the patterns we learned!” they exclaim, confidently connecting their elementary math foundation to these new abstract concepts. They see how fractions, decimals, and percentages are different pieces of the same mathematical puzzle, how geometric formulas build on area concepts they’ve mastered, and how statistics help them understand the world around them. When asked how they adapted so well to middle school math, they smile and say, “I just put the pieces together!” This is the dream outcome for students entering middle school mathematics—the ability to bridge elementary understanding with abstract mathematical thinking.

Course Description

Our 6th Grade Math course helps students put together all the mathematical pieces they’ve learned through the proven CTC math curriculum enhanced by our expert live instruction. Students master the beginnings of algebra, deepen their understanding of rational numbers, and develop sophisticated problem-solving abilities in a nurturing, Christ-centered environment.

This course follows CTC’s renowned mastery-oriented approach, helping sixth graders build genuine mathematical understanding through clear explanations, visual models, and conceptual depth. Our live classes complement the CTC curriculum with spiral review, fluency practice, encouragement, and biblical connections during the live classes that help students see God’s perfect order and design in mathematics.

How It Works

Asynchronous Learning (Daily): Students work through CTC math lessons in Canvas 4-5 days per week, progressing through clear explanations, visual models, and comprehensive exercises at their own pace.

Live Classes: Our expert teachers lead sessions focusing on:

  • Re-teaching concepts based on student questions and progress monitoring
  • Spiral review of previously learned skills
  • Advanced problem-solving strategies with bar modeling
  • Mental math techniques and number sense development
  • Biblical connections and prayer time
  • Encouragement and confidence building

Assessment & Communication:

  • Complete grading of all assignments and assessments
  • Regular progress monitoring and parent updates
  • Monthly progress reports with specific recommendations

Social, Emotional & Spiritual Growth

Building Mathematical Confidence: We understand that sixth grade is the crucial bridge between elementary arithmetic and abstract mathematical thinking. Our piece-by-piece approach emphasizes how all previous mathematical learning connects to create a solid foundation for algebra and beyond. Students learn that with God’s help and systematic thinking, they can DO HARD THINGS and successfully navigate the transition to middle school mathematics.

Faith Integration: Students discover that God is a God of connection through the beautiful relationships between different mathematical concepts, the logical structure of algebraic thinking, and the patterns revealed through statistical analysis. We begin each class with prayer, thanking God for minds capable of understanding these mathematical connections. As students explore how elementary concepts connect to abstract thinking, they learn that “God is not a God of disorder but of peace” (1 Corinthians 14:33) and see how mathematical unity reflects His perfect design throughout creation.

Developing Bridge-Building Thinking: At this pivotal age, we intentionally build sophisticated mathematical reasoning through CTC’s renowned mastery-oriented approach. Students learn that mathematics is not a collection of isolated procedures but a unified system where elementary concepts provide the foundation for abstract mathematical thinking.

In our 6th Grade Math: Putting the Pieces Together course, we help each student successfully bridge the gap between elementary mathematics and abstract algebraic thinking, creating the deep understanding and sophisticated reasoning they need for success in advanced mathematics, while helping them see the beauty of God’s unified design in the connected nature of mathematical truth.

Content Covered: Scope & Sequence

Beginning Algebra (Putting Abstract Pieces Together!)

  • Understanding algebraic expressions and variables
  • Solving one-variable equations and inequalities
  • Working with integers and coordinate planes
  • Connecting arithmetic patterns to algebraic thinking
  • Building foundation for advanced mathematical reasoning

Rational Numbers Mastery (Connecting the Number Pieces!)

  • Deep study of fractions: operations, comparisons, and applications
  • Comprehensive decimal operations and place value understanding
  • Introduction to percentages and real-world applications
  • Converting seamlessly between fractions, decimals, and percentages
  • Understanding rational numbers as a unified system

Ratios and Proportional Relationships (Scaling the Pieces!)

  • Understanding ratios as comparisons between quantities
  • Working with rates and unit rates in real-world contexts
  • Solving proportional relationship problems
  • Connecting ratios to percentages and fractions
  • Building foundation for linear relationships

Geometric Connections (Spatial Pieces Coming Together!)

  • Calculating area of triangles, parallelograms, and complex polygons
  • Understanding volume and surface area of rectangular prisms
  • Working with fractional edge lengths in volume calculations
  • Using nets to visualize three-dimensional relationships
  • Connecting geometry to algebraic expressions

Statistics and Data Analysis (Information Pieces!)

  • Understanding statistical distributions and variability
  • Calculating measures of center (mean, median, mode)
  • Analyzing measures of spread and variability
  • Creating and interpreting dot plots, histograms, and box plots
  • Making sense of data in real-world contexts

Advanced Problem-Solving (All Pieces Working Together!)

  • Multi-step word problems involving multiple concepts
  • Using bar models for complex problem-solving
  • Connecting different mathematical areas within single problems
  • Developing logical reasoning and analytical thinking
  • Applying mathematics to real-world scenarios

Class Introduction Video

Coming soon…

Taught From a Christian Perspective

Our mission is to equip learners’ minds and shepherd their hearts. We want them to have saving faith in our Lord Jesus Christ and then develop a biblical worldview. This means they view their world, themselves, and God in a way that aligns with what the Bible teaches. This brings great peace and understanding to the believer because we serve a good, sovereign God. This course is taught with these goals in mind. In class, we may pray, read scripture, and discuss how to view the content from a Christian perspective.

MATH:

God has created our brains with the ability to study and comprehend amazing, complex things! Math is such a unique subject to study and master. We can see math in God’s creation, and we can appreciate His order through the complex skills we learn.

We have adopted The Master’s Seminary Doctrinal Statement.

Philosophy of Mathematics Learning:

At Lemons-Aid Learning, we believe mathematics education should build both deep understanding and lasting confidence. Our approach combines the best of proven methodologies to create a complete learning experience that serves every type of learner.

Mastery with Spiral Support: We use mastery-based curricula that allow students to deeply understand concepts before moving forward, but we enhance this with intentional spiral review in our live classes. This means students gain true mastery while keeping previous skills fresh and connected—avoiding both the shallow coverage of pure spiral curricula and the “forgetting gap” that can occur with mastery-only approaches.

Conceptual Understanding with Procedural Fluency: Our students learn the “why” behind mathematical concepts through visual models, manipulatives, and clear explanations, then develop speed and accuracy through targeted practice. This dual approach ensures they can both solve problems creatively and execute procedures confidently—essential for success in higher mathematics.

Emotional and Spiritual Growth: We recognize that mathematics often triggers anxiety and frustration. Our classes provide a safe, supportive environment where students learn they can “do hard things” through Christ’s strength. We address math anxiety head-on with encouragement, multiple pathways to understanding, and the biblical truth that God has designed our minds for complex thinking and problem-solving.

Complete Support System: While our carefully chosen curricula provide excellent instruction, our live classes add the human element students need: immediate help with challenging concepts, accountability for consistent practice, test preparation, real-world applications, and the joy of learning alongside peers who share their faith.

Mathematics reveals God’s order, beauty, and design throughout creation. As students master mathematical concepts, they’re not just preparing for the next grade level—they’re developing logical thinking, perseverance, and wonder at the intricate patterns woven throughout God’s world.

✨ 🍋 ✨ Why Lemons-Aid? ✨ 🍋 ✨


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!


RICH CONTENT / CORE KNOWLEDGE: While other schools and systems try to align their content to broad standards that are vague and open to wild interpretations, we focus our content on what students should know and be able to do so they see the world biblically and head into their adult lives filled with knowledge, wisdom, and mastery of skill such as computing and writing. 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.


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.


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.


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!


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.


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!


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

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!


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!


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.


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!


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!

KENDRA MANCUSO: Math
#energetic, #caring, #blessed, #organized, #experienced
Mrs. Mancuso’s favorite book of the Bible is James. This book is filled with wisdom, instructions and encouragement for believers. James exhorts believers to grow in their faith and maturity. Mrs. Mancuso remembers James 1:2-4 when she encounters trials; “Consider it pure joy, my brothers and sisters, whenever you face trials of many kinds, because you know that the testing of your faith produces perseverance. Let perseverance finish its work so that you may be mature and complete, not lacking anything. Mrs. Mancuso earned her bachelor’s degree in mathematics from University of Northwestern – St. Paul. She has over 20 years of experience as a private math tutor. Mrs. Mancuso has taught in a private high school setting and as an adjunct at a university. She has taught math levels ranging from upper elementary to college level. She has taught in both a classroom setting and as a private math tutor. Mrs. Mancuso engages her students in her lessons by asking lots of questions. These questions help students discover new concepts, remember old skills and build a strong foundation in math. Her classroom is interactive and exciting for students. When Mrs. Mancuso isn’t teaching or working, she enjoys spending quality time with her husband and sons. She loves to spend time outside hiking, being on the water, or just hanging out in the fresh air.

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

Visit Lemons-Aid Learning on

Christian Outschool Classes

Request a New Section

Want to see this class offered at another time? Send a request, and we’ll see what we can do!