📐 Grade 6 Mathematics

Ratios, the number system, algebraic expressions, geometry, and statistics — the six domains that build the mathematical foundation every student carries into Grade 7 and beyond.

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What You Learn in Grade 6 Math

Grade 6 Mathematics marks a significant shift in how students think about numbers. For most of elementary school, Math was about computing with whole numbers — adding, subtracting, multiplying, dividing. In Grade 6, the focus moves to relationships between quantities. Why does doubling a recipe require doubling every ingredient? Why does a 20% discount cost less on a cheaper item? These are ratio and proportional thinking questions, and they are where Grade 6 Math begins.

The second major shift is the introduction of variables. Students move from "solve 3 + ? = 7" to "evaluate 3 + x when x = 4" and then to "write an expression that represents the total cost of n items at $3 each." This is the beginning of algebra, and the students who master it in Grade 6 find all future math dramatically easier.

Geometry in Grade 6 is more rigorous than in earlier grades — students calculate area of triangles, parallelograms, and complex composite shapes, and extend this thinking into surface area and volume of 3D solids. Statistics introduces the idea of a distribution: not just "what is the average?" but "how spread out is the data, and what does that tell us?"

The curated videos on this page are ranked using a quality score that accounts for channel reputation, view count, like ratio, and instructional clarity. The video ranked #1 for each topic is the single best explanation available — start there, and use the others for additional practice and alternative explanations if you need them.

Topic 1

Ratios & Proportional Relationships

Understanding ratios as comparisons, equivalent ratios, ratio tables, unit rates, and applying proportional reasoning to real-world problems including percent calculations.

📚 Study Notes

Key Concepts

  • A ratio compares two quantities — write as 3:4, 3/4, or "3 to 4"
  • Equivalent ratios are created by multiplying or dividing both parts by the same number
  • Unit rate = value per 1 unit (e.g., $2 per apple, 60 km per hour)
  • Percent means "out of 100" — convert fraction → decimal → percent
  • Use a ratio table to find missing values in proportional problems
📐 Key formulas: Unit rate = total ÷ number of units  |  Percent = (part ÷ whole) × 100  |  Cross-multiply to solve a/b = c/d → ad = bc
💡 Remember: "Per" always means divide. "Miles per hour" = miles ÷ hours. When you see "per 1", you're finding the unit rate.
Topic 2

The Number System

Division of fractions by fractions, operations with multi-digit decimals, understanding negative numbers on the number line, and ordering rational numbers.

📚 Study Notes

Key Concepts

  • To divide fractions: Keep the first fraction, Change ÷ to ×, Flip the second fraction (KCF)
  • Negative numbers are less than zero — the farther left on the number line, the smaller
  • Absolute value |n| = distance from zero — always positive or zero
  • When multiplying/dividing decimals, count total decimal places in the factors
  • To order rational numbers, convert all to decimals first
📐 Fraction division: a/b ÷ c/d = a/b × d/c  |  Absolute value: |−7| = 7, |7| = 7  |  Negative × Negative = Positive
💡 Remember: KCF — Keep, Change, Flip. Keep the first fraction exactly as is, change ÷ to ×, then flip (reciprocal) the second fraction.
Topic 3

Expressions & Variables

Writing and reading algebraic expressions, evaluating expressions by substitution, identifying parts of an expression (term, coefficient, constant, factor).

📚 Study Notes

Key Concepts

  • Variable: a letter that represents an unknown number (e.g., x, y, n)
  • Coefficient: the number multiplied by the variable (in 7x, the coefficient is 7)
  • Constant: a number with no variable (in 3x + 5, the constant is 5)
  • Evaluate: substitute the given value for the variable, then follow order of operations
  • Like terms have the same variable AND same exponent — only like terms can be combined
📐 Order of operations (PEMDAS): Parentheses → Exponents → Multiply/Divide → Add/Subtract  |  "5 less than twice n" = 2n − 5 (not 5 − 2n)
💡 Remember: "Less than" flips the order! "5 less than n" = n − 5, not 5 − n. Always read the whole phrase before writing the expression.
Topic 4

Equations & Inequalities

Solving one-step equations using substitution and properties of equality. Writing and solving inequalities. Understanding the difference between an equation and an inequality.

📚 Study Notes

Key Concepts

  • Equation: two expressions set equal (x + 3 = 10) — one solution
  • Inequality: uses <, >, ≤, ≥ — usually infinite solutions, shown on a number line
  • Solve by doing the inverse operation to both sides to isolate the variable
  • "At least" means ≥  |  "At most" means ≤  |  "More than" means >
  • Check your answer by substituting it back into the original equation
📐 Inverse operations: + and − are inverses  |  × and ÷ are inverses  |  To solve x + 7 = 15: subtract 7 from both sides → x = 8
💡 Remember: Whatever you do to one side of an equation, you MUST do to the other side. The equals sign is a balance — keep it balanced!
Topic 5

Geometry: Area & Surface Area

Area of triangles, quadrilaterals, and polygons by composing/decomposing shapes. Surface area of 3D figures using nets. Volume of right rectangular prisms.

📚 Study Notes

Key Concepts

  • Area of a triangle = ½ × base × height (height must be perpendicular to base)
  • Area of a parallelogram = base × height (NOT base × slant side)
  • Decompose complex shapes into triangles and rectangles, then add areas
  • Surface area = total area of all faces (use the net to see all faces)
  • Volume of a rectangular prism = length × width × height
📐 Formulas: Triangle: A = ½bh  |  Rectangle: A = lw  |  Parallelogram: A = bh  |  Volume: V = lwh  |  Units: area = units², volume = units³
💡 Remember: A triangle is exactly half a parallelogram — that's why the formula has ½. If you forget the triangle formula, draw a parallelogram and cut it in half diagonally.
Topic 6

Statistics & Data

Statistical questions, measures of centre (mean, median, mode), measures of variability (range, IQR, MAD), and displaying data in dot plots, histograms, and box plots.

📚 Study Notes

Key Concepts

  • Mean: sum of all values ÷ count (affected by outliers)
  • Median: middle value when ordered (not affected by outliers)
  • Mode: most frequent value (a data set can have multiple modes or none)
  • Range = max − min  |  IQR = Q3 − Q1 (middle 50% spread)
  • Use a histogram to see the shape/distribution of data
📐 Mean: sum ÷ n  |  Median: middle value (or average of two middles for even count)  |  Range: max − min  |  IQR: Q3 − Q1
💡 Remember: Use median (not mean) when there are outliers — like reporting typical house prices. One billionaire in a neighbourhood makes the mean misleading but not the median.

💡 Study Strategies for Grade 6 Math

✏️

Show all steps. In Grade 6, the working is as important as the answer. Practise writing out every step, even for problems that feel easy — it builds the habits you need for harder topics.

🔢

Master fractions first. Fraction division is the most commonly failed topic at the start of Grade 6. Spend extra time here — everything else builds on it.

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Use number lines. Every time you work with negative numbers or fractions, draw a number line. It prevents sign errors and makes ordering problems visual and intuitive.

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Practise word problems. At least one-third of Grade 6 Math assessments involve real-world contexts. Translate the situation into an equation before solving — don't skip this step.

🎬 Grade 6 Math Videos

Top-ranked videos for Grade 6 Mathematics — starting with the highest-quality picks first.

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