Articles: category
Learning maths
Maths ideas, methods and worked examples, explained step by step.
Learning maths · 8 min read
Keep mixing up area and volume formulas? Group plane and solid formulas to remember them
Area and volume formulas are easy to confuse. It is usually not a memory problem but a failure to sort plane figures and solid figures separately. The common formulas are grouped below, with unit conversion and common mistakes explained, and worked examples showing how to choose a formula, substitute numbers and check the answer.
Learning maths · 11 min read
Common Reasons for Getting Percentage Change Wrong, and the Correct Method (with Compound Change Examples)
Questions on percentage increase and decrease are often answered wrongly, mostly because students identify the wrong "original quantity" or confuse percentage points with percentages. This article explains the formula for percentage change, how to calculate two successive changes, and how primary to Form 6 students and parents can practise, with several worked examples of calculating percentage change, and introduces Sprout Classroom's free maths course.
Learning maths · 7 min read
Why do we "flip and multiply" when dividing by fractions? Explaining the reasoning with diagrams
Children often ask: why do we flip the divisor and multiply when dividing by a fraction? This article uses diagrams and step-by-step demonstrations to explain the reasoning behind "dividing by a fraction is the same as multiplying by its reciprocal", and brings together common mistakes and practice methods. It is suitable for Primary 5 to Primary 6 students and parents to read together.
Learning maths · 6 min read
Quadratic Function Graphs: Steps to Find the Vertex, Axis of Symmetry and Intercepts from the Equation
Many students see a quadratic function and think only of memorising formulas. In fact, as long as you work through it step by step, finding the axis of symmetry, vertex and intercepts from the equation lets you draw the parabola reliably. This article uses S4 to S6 quadratic functions as examples, demonstrates the full steps, and explains common mistakes and revision methods.
Learning maths · 10 min read
Mixed numbers and improper fractions: what they mean and how to convert between them, with pictures
Can never tell mixed numbers and improper fractions apart? Following the Education Bureau primary maths curriculum, this guide uses pie charts and a number line to explain what each one means, sets out the steps for turning improper fractions into mixed numbers and back, explains why mixed numbers must become improper fractions before multiplying or dividing, and lists common mistakes and ways to practise, for parents and students to read together.
Learning maths · Updated · 4 min read
Solving inequalities: when does the sign flip? Linear, compound "and"/"or" and quadratic inequalities, with examples
The most common mistakes with inequalities are forgetting to flip the sign after multiplying or dividing by a negative number, and mixing up "and" with "or". Following the Education Bureau curriculum documents, this guide covers junior secondary linear inequalities and the senior compound inequalities, quadratic inequalities and linear programming, with worked examples, which parts are non-foundation and where they appear in the HKDSE, plus ways to check and the key terms in Chinese and English.
Learning maths · Updated · 10 min read
How to find the equation of a straight line: point-slope, two-point, slope-intercept and general form, with examples
The equation of a straight line is a compulsory senior secondary maths topic, which the Education Bureau suggests teaching in the first term of Secondary 4. This guide follows the curriculum documents: the distance, mid-point, slope and point-of-division (section) formulas; finding a line from a point and a slope, two points or two intercepts; reading slope and intercepts from the general form; and where two lines meet, with ways to check your answer.
Learning maths · 9 min read
Factors and Multiples: How to Tell Them Apart — Common Factors, Common Multiples, HCF and LCM Explained with Examples
The four terms factor, multiple, common factor and common multiple are easily confused. This article explains each one with concrete examples and shows the usual methods for finding the highest common factor and the lowest common multiple, helping primary pupils build clear concepts.
Learning maths · 5 min read
Adding and Subtracting Fractions with Unlike Denominators: Steps for Finding a Common Denominator, Examples and Practice Tips
Not sure how to find a common denominator when adding or subtracting fractions with unlike denominators? This article walks through finding a common denominator, converting the fractions and calculating step by step, with common mistakes and practice tips for P4 to P6 students and parents.
Learning maths · 8 min read
3D trigonometry: can't see which triangle to use? Three steps to extract the plane triangle
When doing 3D trigonometry questions, once the diagram is three-dimensional you don't know which triangle to use. This article sets out a practical set of steps: first find the right angles and known sides, then extract the plane triangles one at a time, and finally state the reason for each step. It also explains how to practise this 'extracting the diagram' skill when revising and with a tutor.
Learning maths · 4 min read
How to calculate standard deviation, step by step
The standard deviation formula, five steps to calculate it by hand, worked examples for a list and a frequency table, and population σ versus sample s.
Learning maths · 5 min read
What is math olympiad? Primary questions with solutions
What math olympiad means, the common primary olympiad question types, and six original questions with step-by-step solutions.
Learning maths · 6 min read
Similar triangle reasons and how to write the proof
The three reasons for similar triangles in the Hong Kong syllabus, how to set out the proof line by line, three worked examples and the RHS and SSA traps.