Course Details:
- 1 live class per week
- 16 weeks
- Live Class Length: 45 minutes
- 12 seats per section
- Homework is assigned
- Teacher feedback given during class, Formal grades, Teacher feedback offered on homework
- Materials
The teacher will provide all the materials.
5th Grade Math: Making Mathematical Connections
$325.00
This course follows a concrete-pictorial-abstract approach, helping fifth graders build genuine mathematical understanding through hands-on experiences, visual models, and gradual progression to abstract thinking. Our live classes complement the online curriculum with connection-building activities, spiral review, encouragement, and biblical connections that help students see God’s perfect order and design in mathematics.
Section Options / Enroll:
- Description
- Lesson Schedule
- Class Intro Video
- A Biblical Worldview
- Philosophy of Teaching: Mathematics
- The Lemons-Aid Way
- Teacher Bios
- Outschool
- Request a Section
Description
Connecting all the Pieces
Picture this: Your fifth grader encounters a complex real-world problem about planning a school fundraiser. Instead of panicking, they become a mathematical detective, confidently drawing connections across everything they’ve learned. They use ratios to compare different fundraising options, convert percentages to fractions to calculate profits, apply area formulas to determine booth sizes, and create coordinate graphs to track progress over time. When asked how they solved such a complex problem, they smile and explain, “I just connected the math I already know!” This is the dream outcome for students in their final year of elementary mathematics—the ability to see math as one beautiful, interconnected system rather than isolated procedures to memorize.
Course Description
Our 5th Grade Math course helps students make crucial mathematical connections through an online curriculum enhanced by our expert live instruction. Students master advanced computational skills, discover deep mathematical relationships, and develop sophisticated problem-solving abilities in a nurturing, Christ-centered environment.
This course follows a concrete-pictorial-abstract approach, helping fifth graders build genuine mathematical understanding through hands-on experiences, visual models, and gradual progression to abstract thinking. Our live classes complement the online curriculum with connection-building activities, spiral review, encouragement, and biblical connections that help students see God’s perfect order and design in mathematics.
Our students meet and exceed state standards, and they score well on standardized tests.
Fifth-grade math prepares students for middle school by strengthening their understanding of fractions, decimals, geometry, and algebraic thinking while developing confidence in solving complex, multi-step problems. Throughout the year, students learn to:
- Read, write, compare, and round whole numbers and decimals
- Develop a deeper understanding of place value through the thousandths
- Add, subtract, multiply, and divide whole numbers and decimals using efficient strategies and standard algorithms
- Solve multi-step real-world problems involving all four operations
- Add and subtract fractions with unlike denominators
- Multiply and divide fractions and mixed numbers
- Write, evaluate, and simplify numerical expressions using the order of operations
- Calculate the volume of rectangular prisms and apply volume concepts to real-world situations
- Graph points on the coordinate plane and solve problems using ordered pairs
- Classify two-dimensional figures based on their properties
- Explain mathematical reasoning using models, strategies, and precise mathematical language
How It Works
Asynchronous Learning (Daily): Students work through online lessons 4-5 days per week, progressing through tutorials and practice exercises independently.
Live Classes: Our expert teachers lead a 45-minute live class once per week, focusing on:
- Direct instruction of new material with modeling and guided practice
- Re-teaching concepts based on student questions and online performance
- Spiral review of previously learned skills
- Intensive practice with multi-digit algorithms
- Advanced problem-solving strategies
- Biblical connections and prayer time
- Encouragement and confidence building
Assessment & Communication:
- Complete grading of all online work and assessments
- Regular progress monitoring and parent updates
*There is a 2-day per week live class option available to pod learners. With this option, students do not have required homework. If interested, reach out to su*****@********id.com for more details.
Social, Emotional & Spiritual Growth
Building Mathematical Confidence: We understand that fifth grade is when students either see mathematics as a connected, logical system or view it as disconnected procedures to memorize. Our connection-building approach emphasizes how all mathematical concepts work together to create a beautiful, unified understanding. Students learn that with God’s help and systematic thinking, they can DO HARD THINGS and see the deep relationships that make mathematics both powerful and beautiful.
Faith Integration: Students discover that God is a God of relationships through the beautiful connections between fractions and decimals, the logical relationships in geometric properties, and the proportional relationships in ratios. We begin each class with prayer, thanking God for minds capable of seeing these deep mathematical connections. As students explore how different mathematical concepts relate to each other, they learn that “God is not a God of disorder but of peace” (1 Corinthians 14:33) and see how mathematical relationships reflect His perfect design throughout creation.
Developing Advanced Mathematical Thinking: At this pivotal age, we intentionally build sophisticated mathematical reasoning through making explicit connections between concepts. Students learn that mathematics is not a collection of isolated procedures but a unified system where each concept strengthens and illuminates the others.
In 5th Grade Math, we help each student discover the beautiful relationships that bind all mathematics together, creating the deep understanding and sophisticated mathematical thinking they need for success in middle school and beyond, while helping them see the beauty of God’s unified design in the interconnected nature of mathematical truth.
Semester A
Unit 1: Whole Number Arithmetic
Evaluate numerical expressions using the order of operations, and apply long division to larger dividends and two-digit divisors.
Section 1: Order of Operations & Expressions
- Order of Operations
- Exponents: Expand/Condense (Whole Number Base)
- Write Expressions from Words (Whole Number) L1
- Identify Quantities and Operations (Whole Number)
- Match Context to Equation (Whole Number)
Section 2: Long Division
- Long Division, Whole Number, No Remainder
- Long Division, Whole Number, Remainder
- Convert Remainder to Fraction
- Long Division, Whole Number, Remainder as Fraction
Unit 2: Decimals
Extend place value concepts to the thousandths. Add, subtract, multiply, and divide decimals to solve contextual problems.
Section 1: Decimal Place Value
- Base Ten Blocks, Decimal Representation L2
- Base Ten Blocks, Identify Decimal L2
- Decimals from Words to Standard Form L2
- Identify Place Value, Decimal L2
- Identify Value of Digit, Decimal L2
- Expanded, Standard, and Written Form (Decimals)
- Multiplication/Division by 10 (Decimals)
- Multiplication/Division by Powers of 10
- Times Greater, Base Ten Concept (Decimal) Level 1
- Times Greater, Base Ten Concept (Decimal) Level 2
Section 2: Order & Round Decimals
- Place Decimals on a Number Line
- Order Decimals
- Order Decimals and Mixed Numbers
- Round Numbers (Level 1)
- Select All That Round To (Decimals)
Section 3: Add & Subtract Decimals
- Two-Digit Decimal Addition L1
- Two-Digit Decimal Addition L2
- Addition Algorithm, Two-Digit Decimals
- Two-Digit Decimal Subtraction L1
- Two-Digit Decimal Subtraction L2
- Subtraction Algorithm, Two-Digit Decimals
- Decimal Word Problems: Addition
- Decimal Word Problems: Subtraction
Section 4: Multiply & Divide Decimals
- Base Ten Blocks, Decimal Multiplication (Guided)
- Whole Number vs. Decimal Multiplication
- Area Model, Whole Number × Decimal
- Equivalent Expressions (Decimal Multiplication)
- Multiplication Algorithm, Decimal, 2-Digit × 1-Digit
- Scaling Decimal Division L1
- Decimal Divided by Whole Number
- Money Model, Decimal Division
- Long Division, Decimal Divisor, Whole Quotient
- Long Division, Decimal Divisor, Whole Quotient L2
Section 5: Decimal Word Problems
- Decimal Word Problems: Add, Subtract, Multiply
- How Much Change? Level 2
- How Much Change? Level 3
- Match Context to Expression (Decimal)
Semester B
Unit 3: Fractions: Multiplication & Division
Multiply and divide fractions with and without visual representations.
Section 1: Fair Share / Fraction of a Group
- Find Fractional Part of a Group L1
- Find Fractional Part of a Group L2
- Find Whole from Fractional Part L1
- Find Whole from Fractional Part L2
- Fractional Fair Share
- Fractional Fair Share L2
Section 2: Multiply Fractions
- Fractions, Equivalent Expressions
- Fractions, Equivalent Expressions L2
- Fraction of a Fraction (Guided)
- Multiplying Fractions with Area Model (Guided)
- Multiply Fractions
- Area of Rectangles (Fractions)
Section 3: Divide Fractions
- Fraction of a Fraction (Guided)
- Fraction Division (Tape Diagram) Matching
- Fraction Division (Tape Diagram)
- Divide Fractions
Unit 4: Fractions: Addition & Subtraction
Use common denominators to add and subtract fractions and mixed numbers with unlike denominators.
Section 1: Fraction Equivalence & Simplification
- Equivalent Fractions (Scale Up)
- Equivalent Fractions (Scale Down)
- Equivalent Fractions (Scale Down) L2
- Equivalent Fractions (Scale Up/Down)
- Equivalent Fractions (Scale Up/Down) L2
- Simplifying Fractions
Section 2: Add & Subtract Fractions
- Add Fractions Visually (Unlike Denominators)
- Rewrite Fractions with Common Denominator
- Add/Subtract Fractions (Guided) L1
- Add/Subtract Fractions (Guided) L2
- Add/Subtract Fractions (Positive)
- Fraction Word Problems
- Interpret Line Plots
Section 3: Mixed Numbers
- Convert Improper Fractions and Mixed Numbers Visually
- Convert Improper Fractions and Mixed Numbers
- Multiply Mixed Numbers
- Regroup Mixed Numbers (Addition)
- Reason to Add/Subtract Mixed Numbers L1
- Reason to Add/Subtract Mixed Numbers L2
Unit 5: Geometry
Introduce the coordinate plane and the volume of rectangular prisms using unit cubes. Classify triangles and quadrilaterals based on their sides and angles.
Section 1: Volume
- Volume of Unit Cubes
- Volume of Rectangular Prisms Visually
- Volume of Rectangular Prisms (Unit Cubes)
- Volume of Rectangular Prisms
- Volume of Rectangular Prisms L2
- Volume of Composite Prisms
- Volume of Composite Prisms L2
Section 2: Coordinate Plane
- Plotting Points (Quadrant 1)
- Battleship Game (Quadrant 1)
- Interpret Coordinates in Context (Quadrant 1)
- Plot and Find the Area and Perimeter of Rectangles (Quadrant 1)
Section 3: Shapes
- Scalene, Isosceles, and Equilateral Triangles
- Acute, Right, and Obtuse Triangles
- Identify Rectangles
- Classify Quadrilaterals by Appearance
- Statements About Quadrilaterals L1
- Statements About Quadrilaterals L2
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.
We have adopted The Master’s Seminary Doctrinal Statement.
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.
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!
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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