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Primary 6 (Grade 6) Maths Study Notes

Every topic explained step by step, with worked examples and problems to try

Notes for Primary 6 (Grade 6) maths. Each note explains one subject with worked examples and diagrams, and ends with problems to try, with their solutions.

Fractions

  • Dividing a Fraction by a Whole NumberHow to divide a fraction by a whole number by sharing it into equal parts, with bar models, worked examples and practice for Primary 6 (Grade 6).
  • Dividing a Whole Number by a FractionHow to divide a whole number by a fraction: counting how many parts fit, then multiplying by the reciprocal, with examples for Primary 6 (Grade 6).
  • Dividing a Fraction by a FractionHow to divide a fraction by a fraction by multiplying by the reciprocal, with diagrams, worked examples and word problems for Primary 6 (Grade 6).
  • Dividing Fractions: Word ProblemsWord problems on dividing fractions for Primary 6 (Grade 6): one-step, multi-step and harder questions with bar models and full worked solutions.

Ratio

  • Introduction to RatiosWhat a ratio is and how to write one: why order matters, part-to-part and part-to-whole ratios, and ratios of three quantities, for Primary 6 (Grade 6).
  • Equivalent RatiosWhat equivalent ratios are and how to write a ratio in its simplest form using the highest common factor, with worked examples for Primary 6 (Grade 6).
  • Finding Equivalent RatiosHow to scale a ratio up or down and find a missing number in a pair of equivalent ratios, with tables and worked examples for Primary 6 (Grade 6).
  • Finding New RatiosHow to combine two ratios into one and work with ratios of three quantities, with bar models and worked examples for Primary 6 (Grade 6) maths.
  • Fraction and RatioHow a fraction and a ratio say the same thing: A is 2/3 of B means A : B = 2 : 3, and back again, with bar models for Primary 6 (Grade 6).
  • Ratio Word ProblemsRatio word problems for Primary 6 (Grade 6) solved with bar models: a total given, a difference given and harder problems, each worked step by step.

Percentage

  • Finding the Whole Given a Part and the PercentageHow to find the whole when a part and its percentage are given, using the unitary method and bar models, with worked examples for Primary 6 (Grade 6).
  • Percentage IncreaseHow to find a percentage increase and the new value after an increase, with bar models, tables and worked examples for Primary 6 (Grade 6) maths.
  • Percentage DecreaseHow to find a percentage decrease, the new value after a decrease and the original value, with bar models and worked examples for Primary 6 (Grade 6).
  • Percentage Word ProblemsPercentage word problems for Primary 6 (Grade 6): GST and discount, parts of a whole, remainders and mixed amounts, each solved step by step with models.

Algebra

  • Writing Algebraic ExpressionsHow to use a letter for an unknown number and write algebraic expressions for adding, subtracting, multiplying and dividing, for Primary 6 (Grade 6).
  • Simplifying Algebraic ExpressionsHow to simplify algebraic expressions by collecting like terms, with bar models, common mistakes and worked examples for Primary 6 (Grade 6) maths.
  • Evaluating Algebraic ExpressionsHow to find the value of an algebraic expression by putting a number in place of the letter, with worked examples and practice for Primary 6 (Grade 6).
  • Solving Algebraic EquationsHow to solve simple algebraic equations in Primary 6 (Grade 6): one-step and multi-step equations, bar models and word problems, with worked solutions.

Average

  • Finding the AverageWhat an average is and how to find it: total ÷ number of items, with levelling pictures, bar graphs and worked examples for Primary 6 (Grade 6).
  • Finding Total ValueHow to find the total when the average and the number of items are given (total = average × number of items), with examples for Primary 6 (Grade 6).
  • Finding the Number of ItemsHow to find the number of items when the total and the average are given (number = total ÷ average), with bar models and examples for Primary 6 (Grade 6).
  • Average Word ProblemsAverage word problems for Primary 6 (Grade 6): a missing value, two groups combined and changes to an average, each solved step by step with models.

Circles

  • Parts of a CircleThe centre, radius and diameter of a circle and how they are related (diameter = 2 × radius), with diagrams and practice for Primary 6 (Grade 6).
  • Area of a CircleHow to find the area of a circle from its radius or its diameter using π × r × r, with worked examples and practice problems for Primary 6 (Grade 6).
  • Perimeter of a Semicircle and a Quarter CircleHow to find the perimeter of a semicircle, a quarter circle and a three-quarter circle: the curved part plus the straight edges, for Primary 6 (Grade 6).
  • Area of a Semicircle and a Quarter CircleHow to find the area of a semicircle, a quarter circle and a three-quarter circle, with formulas, worked examples and practice for Primary 6 (Grade 6).
  • Circumference of a CircleHow to find the circumference of a circle from its diameter or radius using π, and the radius from the circumference, for Primary 6 (Grade 6).
  • Area and Perimeter of Composite FiguresArea and perimeter of figures made of circles, semicircles, quarter circles, squares and triangles, worked step by step for Primary 6 (Grade 6).

Volume of Cube and Cuboid

  • Finding an Edge of a Cube or CuboidHow to find an unknown length, breadth or height of a cuboid, or the edge of a cube, from its volume, with worked examples for Primary 6 (Grade 6).
  • Finding the Area of One FaceHow to find the area of one face of a cube or cuboid from its volume, and a length from a face area, with worked examples for Primary 6 (Grade 6).
  • Word Problems: Volume of Cube and CuboidVolume word problems for Primary 6 (Grade 6): water in tanks, rising and falling water levels, and time to fill a tank, each solved step by step.