Lower Secondary
Core mathematics for junior secondary learners, including algebra, geometry, and statistics.
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Choose the area you need, or begin with the recommended Algebra Foundations route.
Number Foundations
Build the fraction, decimal, percentage and ratio fluency that supports later algebra.
Converting Fractions, Decimals and Percentages
Learn how to convert between fractions, decimals, and percentages with easy steps and examples to master these essential math skills.
Mastering Fraction Operations
Learn how to add, subtract, multiply, and divide fractions step by step with clear examples, tips for simplifying, and mixed number strategies.
Ratios, Proportions and Rates
From bubble tea mixtures to MTR speeds — simplify ratios, share amounts by the parts method, master the unitary method, and handle rates, exchange rates, map scales and inverse proportion. Foundation lesson for Pre-IGCSE / Lower Secondary.
Divisibility Rules: 1 to 13 Guide
Learn the simple tricks to check if a number is divisible by any number from 1 to 13 without a calculator. Master divisibility rules today!
Algebra Foundations
Follow this sequence to build confident algebra habits step by step.
Intro to Algebra: Expressions, Equations & Inequalities
Learn the building blocks of algebra! This lesson explains expressions, equations, and inequalities with easy-to-follow examples and practice problems.
Like Terms vs. Unlike Terms: Simplifying Algebra
Learn the difference between like and unlike terms in algebra. Master how to identify, group, and simplify algebraic expressions easily.
The Minus Sign: 5 Classic Mistakes
Master the tricky minus sign in algebra by learning how to avoid common errors with brackets, substitution, and expanding expressions.
Factorising Quickly: Speed Up Your Algebra
Learn to factorise algebraic expressions quickly by spotting the Highest Common Factor (HCF). Master simple techniques for numbers and variables.
Fixing 5 Common Algebra Mistakes
Master algebra by correcting the 5 most common mistakes students make with variables, negatives, and powers. Learn to solve equations correctly.
Patterns and Sequences
Move from spotting a pattern to writing a rule for any term.
Data Handling
Describe and compare data using essential statistical measures.
More Lower Secondary Lessons
Explore other Lower Secondary material, including newly added lessons.
Recurring Decimals to Fractions
Make the infinite parts cancel A recurring decimal has a block of digits that repeats forever. Multiplying by suitable powers of ten gives two decimals with identical tails; subtraction removes those tails exactly. Read the repeating block British dots mark the first and last digits of the repeating block, or just one digit when it […]
Difference of Two Squares
Same terms, opposite signs Two brackets with matching terms and opposite signs have a useful shortcut: their mixed terms cancel. Why the middle terms disappear The pair $(a+b)(a-b)$ is called a conjugate pair. Expand all four products to see the cancellation. $(a+b)(a-b)=a^2-ab+ab-b^2$ $-ab+ab=0$ $(a+b)(a-b)=a^2-b^2$ Any real values of $a$ and $b$ work, including zero and […]
Perfect Square Expansion
Lesson focus A square with side length $a+b$ can be cut into four smaller regions. Their areas explain every term in a perfect square expansion. A square split into four pieces Start with a square whose side is $a+b$. Split each side into lengths $a$ and $b$ $a^2$ $ab$ $ab$ $b^2$ $a$$b$$a$$b$ Total area: $a^2+ab+ab+b^2=a^2+2ab+b^2$. […]
Algebraic Expressions: Expand, Simplify and Substitute
Lesson focus Algebra is a compact way to describe a changing quantity. Use brackets carefully, collect like terms, and replace letters with values accurately. Like terms and brackets Only terms with the same variable part can be collected. For example, $3x$ and $-7x$ are like terms, but $3x$ and $3x^2$ are not. Worked example Simplify […]
Numbers, Factors and Primes
Lesson focus Build precise number language before formal algebra and proof. Read the worked example, then use the practice and quiz to check your understanding. Factors and prime factorisation A factor divides a number exactly. A prime number is greater than 1 and has exactly two positive factors: 1 and itself. Example: $84=2^2[[cdot]]3[[cdot]]7$. Writing general […]
The Division Algorithm
Lesson focus Write whole-number division as divisor × quotient + remainder, then check that the remainder is valid. Read the worked example, then use the practice and quiz to check your understanding. Start with a familiar division Think about $137[[div]]12$. The answer is 11 remainder 5 because $12[[cdot]]11=132$ and there are 5 left over. Write […]
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