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Primary 5 (Grade 5) Maths Study Notes

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

Notes for Primary 5 (Grade 5) maths. Each note explains one subject with worked examples and diagrams, and ends with problems to try, with their solutions.

Whole Numbers

  • Place Value to MillionsThe place value of each digit in numbers up to 10 million, how to read large numbers and write them in expanded form, for Primary 5 (Grade 5).
  • Writing & Representing NumbersHow to write numbers up to 10 million in words and in figures, and show them with number discs, with worked examples for Primary 5 (Grade 5).
  • Comparing & Ordering NumbersHow to compare and order numbers up to 10 million using place value and the signs > and <, and how to round large numbers, for Primary 5 (Grade 5).
  • Multiplying by 10, 100 and 1,000How to multiply a whole number by 10, 100 or 1000 by moving its digits along the place-value chart, with worked examples for Primary 5 (Grade 5).
  • Multiplying by Tens, Hundreds and ThousandsHow to multiply a whole number by 30, 400 or 5000: multiply by the single digit first, then by 10, 100 or 1000. Worked examples for Primary 5 (Grade 5).
  • Dividing by 10, 100 and 1,000How to divide a whole number by 10, 100 or 1000 by moving its digits along the place-value chart, with worked examples for Primary 5 (Grade 5).
  • Dividing by Tens, Hundreds and ThousandsHow to divide a whole number by 60, 300 or 4000: divide by 10, 100 or 1000 and by the single digit, in either order. For Primary 5 (Grade 5).
  • Order of OperationsWhich to do first when a sum mixes +, −, × and ÷: multiplication and division before addition and subtraction, left to right, for Primary 5 (Grade 5).
  • Order of Operations with BracketsHow to work out sums with brackets: what is inside the brackets first, then × and ÷, then + and −, with worked examples for Primary 5 (Grade 5).

Decimals

  • Multiplying Decimals by 10, 100 and 1000How to multiply a decimal by 10, 100 or 1000 by moving the decimal point to the right, with place-value charts and examples for Primary 5 (Grade 5).
  • Multiplying Decimals by Tens, Hundreds and ThousandsHow to multiply a decimal by 30, 400 or 5000: multiply by the single digit, then by 10, 100 or 1000, with worked examples for Primary 5 (Grade 5).
  • Dividing Decimals by 10, 100 and 1000How to divide a decimal by 10, 100 or 1000 by moving the decimal point to the left, with place-value charts and examples for Primary 5 (Grade 5).
  • Dividing Decimals by Tens, Hundreds and ThousandsHow to divide a decimal by 30, 400 or 5000: divide by the single digit and by 10, 100 or 1000, in either order, with examples for Primary 5 (Grade 5).
  • Converting MeasurementsHow to convert length, mass and volume in decimals by multiplying or dividing by 10, 100 and 1000, with worked examples for Primary 5 (Grade 5).
  • Decimal Word ProblemsWorked decimal word problems for Primary 5 (Grade 5): one-step, multi-step and bar model questions with full solutions, then practice problems to try.

Fractions

  • Addition and Subtraction of Mixed NumbersHow to add and subtract mixed numbers with different denominators, renaming a whole when needed, with worked examples for Primary 5 (Grade 5).
  • Multiplying a Fraction and a Whole NumberHow to multiply a fraction by a whole number and find a fraction of a set, with bar models and worked examples for Primary 5 (Grade 5).
  • Multiplying a Mixed Number and a Whole NumberHow to multiply a mixed number by a whole number: change it to an improper fraction, cancel, multiply and simplify, for Primary 5 (Grade 5).
  • Multiplying Two FractionsHow to multiply a fraction by a fraction: what "of" means, multiplying tops and bottoms, cancelling first, with diagrams for Primary 5 (Grade 5).
  • Division of Whole Numbers as FractionsWhy 2 ÷ 3 = 2/3: writing a division as a fraction, sharing wholes equally, and answers as mixed numbers, with pictures for Primary 5 (Grade 5).
  • Expressing Fractions as DecimalsHow to write a fraction as a decimal: by making tenths or hundredths, or by long division, and rounding recurring decimals, for Primary 5 (Grade 5).
  • Fraction Word ProblemsTen fraction word problems for Primary 5 (Grade 5) solved with bar models: adding, subtracting and multiplying fractions and mixed numbers, step by step.

Percentage

  • Per CentWhat per cent means: parts of a hundred, shown on a 100-square grid, and why all the parts of a whole add up to 100%, for Primary 5 (Grade 5).
  • Conversions between Fractions, Decimals and PercentagesHow to change a percentage to a fraction or a decimal and back again, with the rule for each and worked examples for Primary 5 (Grade 5).
  • Percentage Part of a WholeHow to find what percentage one quantity is of another, and a quantity from a percentage, with worked examples and practice for Primary 5 (Grade 5).
  • GST, Discount and Annual InterestPercentage in money questions for Primary 5 (Grade 5): how to work out GST, a discount and annual interest, with worked examples and practice problems.
  • Percentage in Pie ChartsHow to read a pie chart with percentages or fractions, find a missing part and work out how many from the total, for Primary 5 (Grade 5).

Rate

  • Understanding RateWhat rate means, how to find the rate for one unit and how to use it, with worked examples, tables and practice problems for Primary 5 (Grade 5).
  • Rate Word ProblemsRate word problems for Primary 5 (Grade 5): reading rate tables, parking and postage charges in steps, and multi-step questions, with full solutions.

Area of Triangle

  • Base and Height of a TriangleHow to find the height of a triangle for any base: always at right angles to the base, and sometimes outside the triangle, for Primary 5 (Grade 5).
  • Area of a TriangleWhy the area of a triangle is half of base times height, and how to use it for acute, right-angled and obtuse triangles, for Primary 5 (Grade 5).
  • Area of Composite FiguresHow to find the area of figures made of triangles, rectangles and squares by adding or subtracting areas, with worked examples for Primary 5 (Grade 5).

Volume

  • Understanding Volume with Unit CubesWhat volume is and how to find it by counting unit cubes, layer by layer, in solids built of cubes, with pictures for Primary 5 (Grade 5).
  • Volume in Cubic Centimetres and Cubic MetresMeasuring volume in cubic centimetres (cm³) and cubic metres (m³): what each unit is and when to use it, with examples for Primary 5 (Grade 5).
  • Volume of Cubes and CuboidsHow to find the volume of a cube or cuboid with length × breadth × height, and why it works, with worked examples for Primary 5 (Grade 5).
  • Volume of LiquidsVolume of liquid in litres and millilitres: 1 litre = 1000 ml = 1000 cm³, and water in a tank or container, with examples for Primary 5 (Grade 5).
  • Volume Word ProblemsVolume word problems for Primary 5 (Grade 5): water in a tank, filling a tank, pouring between containers and fractions of a tank, solved step by step.

Angles

  • Angles on a Straight LineWhy angles on a straight line add up to 180° and how to find an unknown angle on a line, with diagrams and practice for Primary 5 (Grade 5).
  • Angles at a PointWhy angles at a point add up to 360°, a complete turn, and how to find an unknown or equal angles at a point, for Primary 5 (Grade 5).
  • Vertically Opposite AnglesWhen two straight lines cross, the angles opposite each other are equal: how to spot them and use them, with diagrams for Primary 5 (Grade 5).
  • Finding Unknown AnglesUsing angles on a straight line, angles at a point and vertically opposite angles together to find unknown angles, for Primary 5 (Grade 5).

Triangles

  • Types of TrianglesEquilateral, isosceles and right-angled triangles, and acute- and obtuse-angled ones: their sides and angles, with diagrams for Primary 5 (Grade 5).
  • Angle Sum of a TriangleWhy the three angles of a triangle add up to 180° and how to find the third angle, in any triangle and in isosceles ones, for Primary 5 (Grade 5).
  • Finding Unknown Angles in TrianglesFinding unknown angles in triangles, with extended sides and with two triangles side by side, worked step by step for Primary 5 (Grade 5).

Quadrilaterals

  • Properties of a ParallelogramThe sides and angles of a parallelogram: opposite sides parallel and equal, opposite angles equal, and how to find unknown angles, for Primary 5 (Grade 5).
  • Properties of a RhombusThe sides and angles of a rhombus: four equal sides, opposite angles equal, and how to find unknown angles in a rhombus, for Primary 5 (Grade 5).
  • Properties of a TrapeziumThe sides and angles of a trapezium: one pair of parallel sides, and the two angles on each slanted side adding up to 180°, for Primary 5 (Grade 5).
  • Finding Unknown Angles in Four-Sided FiguresFinding unknown angles in parallelograms, rhombuses and trapeziums, using their properties step by step, with practice for Primary 5 (Grade 5).