KAPDEC 

Grade 6 Mathematics 

Course Overview & Student Guide 

Aligned to the Common Core State Standards for Mathematics (CCSS-M), Grade 6 

What the course covers, what students will learn, what they should know by the end of the year, and how Kapdec helps them get there. 

kapdec.com 

1. Grade 6 at a Glance 

Grade 6 is the first year of middle-school math and the start of algebraic thinking. Under the Common Core standards, instructional time in Grade 6 focuses on four critical areas: 

The five domains 

Code	Domain	Standards	Kapdec modules
6.RP	Ratios & Proportional Relationships	3	Ratio & Proportion, Decimals
6.NS	The Number System	8	Whole Numbers, Playing With Numbers, Fractions, Decimals, Integers, Basic Geometrical Ideas
6.EE	Expressions & Equations	9	Knowing our Numbers, Whole Numbers, Expressions & Equations
6.G	Geometry	4	Polygon Perimeter, Area, and Volume, Basic Geometrical Ideas, Elementary Shapes
6.SP	Statistics & Probability	5	Data Handling and Analysis
Total	Five domains	29 standards	14 modules, 56 chapters (including enrichment)

Required fluencies by the end of Grade 6 

The standards name two skills students must do fluently (quickly and accurately): dividing multi-digit numbers using the standard algorithm (6.NS.2), and adding, subtracting, multiplying and dividing multi-digit decimals using the standard algorithm for each operation (6.NS.3). 

The learning objective in one sentence 

By the end of Grade 6, a student should be able to… 

• reason with ratios, rates and percents, compute fluently with fractions, decimals and negative numbers, write and solve one-step equations and inequalities, find area, surface area and volume, and summarize data using center and spread — and apply all of these to real-world problems. 

How Kapdec helps — the big picture 

• Micro-chapters: the entire grade is broken into 14 modules and 56 small, focused chapters, each mapped to the Common Core standards. 

• Thousands of questions at every level of difficulty: every chapter has a deep bank of practice questions, from basic to advanced. 

• Step-wise instructions: every question comes with a step-by-step solution, so students learn the method, not just the answer. 

• A tutor when needed: students can connect with a tutor of their choice in a Kapdec Smart Room for live help. 

2. How the Course Is Structured 

The course follows the Common Core design: grade → domains → clusters → standards. Kapdec organizes the grade into modules and small, focused chapters (micro-chapters), and attaches practice, solutions and tutoring to every chapter. 

Layer	What it means for the student
Grade	The full year of Grade 6 math.
Domain (5)	A large area of math, such as Ratios or Geometry.
Standard (29)	A specific skill the student is expected to learn, e.g., 6.NS.1 Divide fractions by fractions.
Kapdec module (14)	A group of related chapters, such as Integers or Ratio & Proportion, exactly as it appears in the Kapdec portal.
Kapdec chapter (56)	A short, focused lesson unit that teaches one idea at a time and maps to one or more standards.
Practice questions (every chapter)	Thousands of questions that progress from basic to advanced.
Step-wise solution (every question)	A worked solution that shows each step and the reason for it.
Tutor support (on demand)	Live help from a tutor of the student’s choice when they are stuck or want to go deeper.

The Kapdec learning path 

Every chapter follows the same simple, repeatable path. Students always know what to do next. 

• Step 1 — Learn the idea. Open the chapter in the Kapdec portal and study the concept using study notes, tips and e-books in the Kapdec Digital Library. 

• Step 2 — Practice at your level. Start with basic questions and move to harder ones as accuracy improves. Thousands of questions mean students never run out of fresh practice. 

• Step 3 — Check every step. After each answer, review the step-wise solution to see exactly where the reasoning was right or went wrong. 

• Step 4 — Get help. Still stuck? Use unlimited doubt clarification or book a session with a tutor of your choice in a Smart Room. 

• Step 5 — Prove mastery. Take an auto-graded test (with an optional time limit). Results feed the Grade Book so students, parents and teachers can see progress. 

3. Domain-by-Domain Guide 

Each domain below lists what it covers, the learning objectives (the Common Core standards, in plain language), the Kapdec chapters that cover them, what a student should know by the end of the grade, and how Kapdec helps achieve each objective. 

3.1  Ratios & Proportional Relationships (6.RP) 

A brand-new domain in Grade 6. Students learn to describe how two quantities relate using ratios, unit rates and percents, and use these ideas to solve real-world problems. 

Learning objectives 

Standard	The student will…
6.RP.1	Understand the concept of a ratio and use ratio language to describe a relationship between two quantities (e.g., “for every 2 wings there is 1 beak”).
6.RP.2	Understand the concept of a unit rate a/b associated with a ratio a:b (b ≠ 0) and use rate language (e.g., “$5 per pound”).
6.RP.3	Use ratio and rate reasoning to solve real-world problems: tables of equivalent ratios, unit pricing and constant speed, percent of a quantity, and converting measurement units.

Kapdec chapters that cover these objectives 

Kapdec module	Chapters included
Ratio & Proportion	Ratios Proportions Unitary Method
Decimals	Decimals in Measurements (unit conversions)

By the end of Grade 6, the student can… 

• Write the ratio of 12 boys to 18 girls as 12:18 = 2:3 and explain what it means. 

• Find a unit rate: if 4 notebooks cost $10, one notebook costs $2.50. 

• Complete a table of equivalent ratios and use it to solve a problem. 

• Find 30% of 80 and solve “24 is 40% of what number?” 

• Convert 2.5 kilometers to meters using ratio reasoning. 

How Kapdec helps achieve the 6.RP objectives 

• The Ratio & Proportion module moves step by step from ratios, to proportions, to the Unitary Method, so students build one idea on the next. 

• Practice starts with simple ratio language and builds up to multi-step word problems on unit pricing, speed and percents. 

• Step-wise solutions show how to set up a ratio table or find the unit rate before solving. 

• Tutors in Smart Rooms connect ratios to everyday situations such as shopping, recipes and travel. 

3.2  The Number System (6.NS) 

Students complete their understanding of fraction division, become fluent with multi-digit division and decimal operations, and extend the number line to include negative numbers. 

Learning objectives 

Standard	The student will…
6.NS.1	Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions (e.g., (2/3) ÷ (3/4) = 8/9).
6.NS.2	Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3	Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.4	Find the greatest common factor of two whole numbers ≤ 100 and the least common multiple of two whole numbers ≤ 12; use the distributive property to express a sum with a common factor.
6.NS.5	Understand that positive and negative numbers describe quantities with opposite directions or values (temperature, elevation, credits/debits) and explain the meaning of 0.
6.NS.6	Understand a rational number as a point on the number line; extend number lines and coordinate axes to include negative numbers and recognize opposites.
6.NS.7	Understand ordering and absolute value of rational numbers, and interpret them in real-world contexts.
6.NS.8	Solve real-world problems by graphing points in all four quadrants of the coordinate plane, including distances between points with the same first or second coordinate.

Kapdec chapters that cover these objectives 

Kapdec module	Chapters included
Whole Numbers	Whole Numbers & the Number Line
Playing With Numbers	Classification of Numbers Divisibility of Numbers Division of Multi-Digit Numbers Factors & Multiples, Introduction Prime Factorization Greatest Common Factor (GCF), HCF Least Common Multiple (LCM)
Fractions	Introduction Types of Fractions Comparing Fractions Addition & Subtraction of Fractions Multiplication and Division of Fractions
Decimals	Introduction Fractions & Decimals Comparing Decimals Addition & Subtraction of Decimals
Integers	Introduction to Integers Addition & Subtraction of Integers Absolute Value of Numbers
Basic Geometrical Ideas	Graphing Ordered Pairs

By the end of Grade 6, the student can… 

• Compute 2/3 ÷ 3/4 = 8/9 and solve “How many 3/4-cup servings are in 2/3 of a cup?” 

• Fluently divide 8,742 ÷ 31 with the standard algorithm (a required Grade 6 fluency). 

• Fluently compute 12.6 × 0.35 and 45.9 ÷ 1.5 (a required Grade 6 fluency). 

• Find GCF(24, 36) = 12 and LCM(6, 8) = 24, and write 36 + 8 as 4(9 + 2). 

• Place −3, 0 and 2.5 on a number line and explain that |−7| = 7. 

• Plot (−2, 4) and find the distance between (−2, 4) and (5, 4). 

How Kapdec helps achieve the 6.NS objectives 

• Playing With Numbers builds divisibility, factors, GCF and LCM before students need them for fractions, so nothing feels sudden. 

• Fractions and Decimals chapters review earlier skills first, then lead into fraction division and decimal operations. 

• Integers chapters introduce negative numbers on the number line and absolute value through real-life contexts like temperature and money. 

• Step-wise solutions break long division into Divide → Multiply → Subtract → Bring down, one step per line. 

• Unlimited doubt clarification and tutors help when a student is stuck on a specific step. 

3.3  Expressions & Equations (6.EE) 

Students move from arithmetic to algebra. They write and evaluate expressions with variables and exponents, generate equivalent expressions, and solve one-step equations and inequalities. 

Learning objectives 

Standard	The student will…
6.EE.1	Write and evaluate numerical expressions involving whole-number exponents.
6.EE.2	Write, read and evaluate expressions in which letters stand for numbers, using terms such as sum, term, product, factor, quotient and coefficient.
6.EE.3	Apply the properties of operations to generate equivalent expressions (e.g., 3(2 + x) = 6 + 3x).
6.EE.4	Identify when two expressions are equivalent.
6.EE.5	Understand solving an equation or inequality as finding which values make it true; use substitution to check.
6.EE.6	Use variables to represent numbers and write expressions when solving real-world or mathematical problems.
6.EE.7	Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q.
6.EE.8	Write an inequality of the form x > c or x < c to represent a constraint, recognize it has infinitely many solutions, and show them on a number line.
6.EE.9	Use variables to represent two quantities that change in relationship to one another (dependent and independent variables), and analyze the relationship with graphs, tables and equations.

Kapdec chapters that cover these objectives 

Kapdec module	Chapters included
Knowing our Numbers	Order of Operations: BODMAS Rule / PEMDAS Rule
Whole Numbers	Properties of Whole Numbers Patterns in Whole Numbers
Expressions & Equations	Introduction to Variables Expressing with Variables Equations, Simplification Inequalities and Simplification

By the end of Grade 6, the student can… 

• Evaluate 2³ + 4 × (6 − 1) = 28 using the order of operations. 

• Evaluate 3x² + 5 when x = 2. 

• Show that 3(2 + x) and 6 + 3x are equivalent. 

• Solve x + 7 = 15 and 4x = 28, and check by substitution. 

• Write x ≥ 13 for “you must be at least 13” and show it on a number line. 

• Describe how distance depends on time with a table, a graph and d = 60t. 

How Kapdec helps achieve the 6.EE objectives 

• Order of Operations and Properties of Whole Numbers come first, so students have the rules they need before working with variables. 

• The Expressions & Equations module moves from what a variable is, to writing expressions, to solving equations and inequalities. 

• Practice starts with plain numerical expressions and builds up to real-world problems that students must translate into equations. 

• Step-wise solutions show every move used to isolate the variable, so students see why each step keeps the equation balanced. 

3.4  Geometry (6.G) 

Students find areas of triangles, special quadrilaterals and other polygons, find volume with fractional edge lengths, draw polygons on the coordinate plane, and use nets to find surface area. 

Learning objectives 

Standard	The student will…
6.G.1	Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes.
6.G.2	Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes, and show this matches V = l × w × h and V = b × h.
6.G.3	Draw polygons in the coordinate plane given the coordinates of their vertices; use coordinates to find side lengths.
6.G.4	Represent three-dimensional figures using nets made of rectangles and triangles, and use the nets to find surface area.

Kapdec chapters that cover these objectives 

Kapdec module	Chapters included
Polygon Perimeter, Area, and Volume	Area Perimeter Area of Triangle, Quadrilateral Volume of Right Rectangular Prism, Unit Cubes
Basic Geometrical Ideas	Points, Lines & Curves 2-D Shapes, Polygons Graphing Ordered Pairs
Elementary Shapes	3-Dimensional Shapes

By the end of Grade 6, the student can… 

• Find the area of a triangle with base 10 cm and height 6 cm (30 cm²) and of a trapezoid by splitting it into shapes. 

• Find the volume of a box that is 2½ × 3 × 4 units. 

• Draw a rectangle with vertices (1, 1), (1, 4), (5, 4), (5, 1) and find its side lengths. 

• Draw the net of a rectangular prism and use it to find surface area. 

How Kapdec helps achieve the 6.G objectives 

• Polygon Perimeter, Area, and Volume takes students from basic area and perimeter to triangles, quadrilaterals and volume with unit cubes. 

• Basic Geometrical Ideas and Graphing Ordered Pairs connect shapes to the coordinate plane. 

• Step-wise solutions show how to split a complex shape into rectangles and triangles and add the areas. 

• Tutors can share interactive visuals in Smart Rooms to make nets and 3-D shapes easy to picture. 

3.5  Statistics & Probability (6.SP) 

Another new domain. Students learn to ask statistical questions, describe a data set by its center and spread, and display data with dot plots, histograms and box plots. 

Learning objectives 

Standard	The student will…
6.SP.1	Recognize a statistical question as one that anticipates variability in the data (e.g., “How old are the students in my school?”).
6.SP.2	Understand that a set of data has a distribution that can be described by its center, spread and overall shape.
6.SP.3	Recognize that a measure of center summarizes all values with a single number, while a measure of variation describes how values vary.
6.SP.4	Display numerical data in plots on a number line, including dot plots, histograms and box plots.
6.SP.5	Summarize numerical data sets: number of observations, what was measured, measures of center (median, mean) and variability (interquartile range, mean absolute deviation), and relate the choice of measure to the shape of the data.

Kapdec chapters that cover these objectives 

Kapdec module	Chapters included
Data Handling and Analysis	Data Handling Pictograph A Bar Graph Histogram Measures of Center & IQR Box Plots

By the end of Grade 6, the student can… 

• Tell the difference between “How tall am I?” and “How tall are the students in my class?” 

• Find the mean and median of 4, 7, 7, 9, 13. 

• Find the interquartile range and draw a box plot for a data set. 

• Build a histogram from grouped data and describe its shape. 

• Explain when the median is a better summary than the mean. 

How Kapdec helps achieve the 6.SP objectives 

• Data Handling and Analysis moves from familiar pictographs and bar graphs to histograms, measures of center, IQR and box plots. 

• Practice uses real-world data sets so students learn to read and question data, not just calculate. 

• Step-wise solutions show how to order data, find quartiles and build a box plot one step at a time. 

• Grade Book reports let teachers and parents see which statistics skills a student has mastered. 

3.6  Foundation & Enrichment Chapters 

The Kapdec Grade 6 syllabus also includes chapters that strengthen number sense and go beyond the Grade 6 standards, such as symmetry and geometric constructions. They build confidence and give students a head start on Grade 7 geometry. 

Kapdec module	Chapters included
Knowing our Numbers	Playing with Digits Estimation of Numbers Roman Numerals
Elementary Shapes	Angles Triangles Quadrilaterals Circle
Symmetry	Introduction & Types of Symmetry
Practical Geometry	Construction of Circle Construction of Perpendicular Bisector Construction of Angles

How Kapdec helps with foundation and enrichment 

• Students can use the number-sense chapters to fill gaps before starting ratios and algebra. 

• Students who master the Grade 6 chapters early can continue straight into the geometry enrichment chapters. 

• The same practice questions, step-wise solutions and tutor support are available for every one of these chapters. 

4. Habits of a Strong Math Thinker 

Alongside content, Common Core expects students to build eight Standards for Mathematical Practice. These are the habits that turn “getting answers” into real understanding. 

Mathematical Practice	How Kapdec supports it
1. Make sense of problems and persevere	Questions that grow gradually harder build stamina; tutors coach persistence instead of giving the answer.
2. Reason abstractly and quantitatively	Advanced word problems ask students to move between real situations and numbers.
3. Construct arguments and critique reasoning	Step-wise solutions model clear reasoning; Smart Room sessions let students explain their thinking aloud.
4. Model with mathematics	Real-world questions on ratios, unit rates, area and data connect math to everyday life.
5. Use tools strategically	Ratio tables, number lines, coordinate grids and box plots appear throughout practice and study notes.
6. Attend to precision	Auto-graded tests reward exact answers, correct units, correct signs and correct decimal placement.
7. Look for and make use of structure	Chapters reveal structure, such as the distributive property and equivalent ratios, one at a time.
8. Look for regularity in repeated reasoning	Thousands of practice questions help students notice shortcuts and general methods.

5. Suggested Year Plan 

A sample pacing guide for a full school year. Schools and families can adjust the order; Kapdec’s chapters can be taken in any order. 

Quarter	Focus	Kapdec modules
Q1 (Aug–Oct)	Number sense, order of operations, factors and multiples; multi-digit division	Knowing our Numbers; Whole Numbers; Playing With Numbers
Q2 (Nov–Jan)	Fraction division; decimal operations; ratios, rates and percents	Fractions; Decimals; Ratio & Proportion
Q3 (Feb–Mar)	Negative numbers, absolute value, coordinate plane; expressions, equations and inequalities	Integers; Basic Geometrical Ideas; Expressions & Equations
Q4 (Apr–Jun)	Area, surface area and volume; statistics; enrichment geometry; year-end review	Polygon Perimeter, Area, and Volume; Elementary Shapes; Data Handling and Analysis; Symmetry; Practical Geometry; review

How Kapdec helps keep the year on track 

• Auto-graded tests at the end of each chapter show whether a student is ready to move on. 

• The Grade Book gives a quick snapshot of performance across every chapter. 

• Mixed review sets in Q4 revisit earlier chapters so skills stay fresh before Grade 7. 

6. End-of-Grade Readiness Checklist 

Students (and parents) can use these “I can” statements to check readiness for Grade 7. 

Ratios & Proportional Relationships 

• I can use ratio language to describe how two quantities relate. 

• I can find and use unit rates, including unit prices and speed. 

• I can use tables of equivalent ratios to solve problems. 

• I can find a percent of a number and the whole from a part and a percent. 

• I can convert measurement units using ratio reasoning. 

The Number System 

• I can divide fractions by fractions and solve word problems. 

• I can divide multi-digit numbers fluently using the standard algorithm. 

• I can add, subtract, multiply and divide decimals fluently. 

• I can find the GCF and LCM and use the distributive property. 

• I can place positive and negative numbers on a number line and find absolute value. 

• I can plot points in all four quadrants and find distances between them. 

Expressions & Equations 

• I can write and evaluate expressions with exponents and variables. 

• I can write equivalent expressions using properties of operations. 

• I can solve one-step equations such as x + p = q and px = q. 

• I can write and graph simple inequalities. 

• I can describe how one variable depends on another with a table, graph and equation. 

Geometry 

• I can find the area of triangles, quadrilaterals and other polygons. 

• I can find the volume of a rectangular prism with fractional edge lengths. 

• I can draw polygons on the coordinate plane and find side lengths. 

• I can use nets to find surface area. 

Statistics & Probability 

• I can recognize a statistical question. 

• I can find the mean, median and interquartile range of a data set. 

• I can display data in dot plots, histograms and box plots. 

• I can describe a data set by its center, spread and shape. 

7. Why Kapdec 

Kapdec’s World School is an e-learning marketplace that connects students and tutors in one easy-to-use platform. For Grade 6 math, everything a student needs is in one place: 

• Micro-chapters — the full grade broken into 14 modules and 56 small, standard-aligned chapters. 

• Question bank — thousands of questions per grade, from basic to advanced. 

• Step-wise solutions — every question explained step by step. 

• Digital Library — over 1 million STEM resources, including e-books, study notes, tips and practice questions. 

• Tutors of choice — personalized, one-on-one or small-group sessions with a tutor the student selects. 

• Smart Rooms — live online classrooms that also keep students connected to their tutor beyond the session. 

• Auto-graded tests and Grade Book — instant results and a clear view of progress for students, parents and teachers. 

• Founding Mentors — top university students who support learners and model a love of STEM. 

Get started 

• Visit kapdec.com, choose Grade 6 Mathematics, and begin with the first module, Knowing our Numbers — or book a tutor to build a personalized plan. 

Standards source: Common Core State Standards for Mathematics, Grade 6 (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010). Standards are paraphrased for readability.