Patterns & Algebra
Sequences, rules, unknowns and equations.
- 33
- Games
- 35
- Worksheets
- 7
- Grades covered
What You'll Learn
Patterns and algebra are the same subject at two ages. Continuing a sequence of shapes, spotting that a number pattern goes up in fours, and describing the rule — that is algebraic thinking, years before a letter appears in place of a number.
When x does arrive, it is best understood as a name for something not yet known rather than a new kind of object. A child who has spent years describing rules in words usually finds the notation a convenience. A child who meets letters cold tends to experience algebra as a set of arbitrary moves, which is where the reputation comes from.
Practise Patterns & Algebra Through Games
Interactive practice with instant feedback — free, ad-free and playable in the browser.
5-7 · arcade
Odd Number Blaster
Children tap the odd numbers while even numbers drift past, building odd and even recognition.
5-7 · arcade
Number Pop Arcade
Children pop the smallest number each time to put numbers in order, building number sequencing.
8-10 · puzzle
Number Sequence Grid
Complete number sequences on a grid inside an ancient puzzle vault, filling missing values to unlock each chamber, for ages 8 to 10.
8-10 · builder
Symmetry Axis Builder
Select every line of symmetry of crystal shapes in a mirror kingdom, then check your balanced design, for ages 8 to 10.
8-10 · drag-drop
Decimal Sort Drag
Order decimals from smallest to largest on a deep sea research mission, for ages 8 to 10.
11-12 · speed
Two-Step Equation Blitz
Solve two-step equations against a friendly timer in a quantum reactor control center, for ages 11 to 12.
11-12 · puzzle
Pythagoras Logic Grid
Complete Pythagorean triples on a grid in an ancient geometry archive, finding each missing side, for ages 11 to 12.
11-12 · escape
Cipher Algebra Escape
Decode a chain of algebra ciphers to unlock secure systems in a cyber intelligence facility, for ages 11 to 12.
11-12 · speed
Index Laws Speed Quiz
Simplify index and exponent expressions against a timer in a digital power core, for ages 11 to 12.
11-12 · quiz
Standard Form Quiz
Convert numbers to and from standard form on a deep space science vessel, for ages 11 to 12.
11-12 · escape
Inequality Chain Escape
Solve a chain of inequalities to unlock a high security logic vault, for ages 11 to 12.
11-12 · drag-drop
Index Law Drag Sort
Sort expressions by which index law applies in a data classification nexus, for ages 11 to 12.
Showing 12 of 33. Browse all games
Practise Patterns & Algebra With Printable Worksheets
Every worksheet prints as a clean A4 PDF with a separate answer key.
5-7 · graph
Number Patterns Graph
Read a bar graph that shows a growing number pattern and answer the questions. A Grade 2 data worksheet with answer keys.
5 levels · PDF + answer key
5-7 · true-false
Is This Shape Symmetrical? True/False
Decide whether statements about a shape's symmetry are true or false. A Grade 2 geometry reasoning worksheet with answer keys.
5 levels · PDF + answer key
8-10 · true-false
Symmetry Properties True/False
Decide whether statements about shapes and their lines of symmetry are true or false. A Grade 4 geometry worksheet with answer keys.
5 levels · PDF + answer key
11-12 · fill-in
Expanding Brackets Fill-in
Expand single and double brackets and write the simplified expression. A Grade 7 algebra worksheet with five levels and answer keys.
5 levels · PDF + answer key
11-12 · fill-in
Factorising Expressions Fill-in
Factorise algebraic expressions by taking out the highest common factor. A Grade 7–8 algebra worksheet with answer keys.
5 levels · PDF + answer key
11-12 · multiple-choice
Pythagoras MCQ
Find the hypotenuse of a right-angled triangle using Pythagoras, choosing from four options. A Grade 7–8 geometry worksheet with answer keys.
5 levels · PDF + answer key
11-12 · match
Algebra Expression Match
Match each verbal description to its correct algebraic expression. A Grade 6–7 algebra worksheet with answer keys.
5 levels · PDF + answer key
11-12 · number-line
Coordinates in 4 Quadrants
Identify the coordinates of points plotted in all four quadrants. A Grade 6–7 coordinate geometry worksheet with answer keys.
5 levels · PDF + answer key
11-12 · fill-in
Forming and Solving Equations Fill-in
Write an equation from a worded description, then solve it. A Grade 7 algebra worksheet with answer keys.
5 levels · PDF + answer key
11-12 · fill-in
Index Notation Fill-in
Write numbers and expressions in index form and apply the index laws. A Grade 7–8 indices worksheet with answer keys.
5 levels · PDF + answer key
11-12 · grid
Linear Sequences Grid
Complete arithmetic sequence tables by finding the missing terms. A Grade 7 sequences worksheet with answer keys.
5 levels · PDF + answer key
11-12 · grid
nth Term Grid
Find the nth term rule of an arithmetic sequence from its table. A Grade 7–8 sequences worksheet with answer keys.
5 levels · PDF + answer key
Showing 12 of 35. Browse all worksheets
Patterns & Algebra by Grade
Patterns & Algebra appears across several grades on this site, with the skills becoming more advanced over time. Jump to a grade page for a broader set of activities at that level.
How to Use Patterns & Algebra Practice
Ask "what is the rule?" long before you ask for an equation. Being able to say "it goes up by four each time, starting at seven" is the whole idea; writing it as 4n + 3 is only notation for something already understood.
The equals sign is worth checking specifically. Many children read it as "the answer comes next" rather than "both sides are the same", and that misreading is what makes equation-solving feel arbitrary. Questions like "7 + □ = 5 + 6" surface it quickly.
Want a broader overview?
Browse Math by Grade for a full set of age-appropriate activities rather than a single strand.
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Frequently Asked Questions
- Recognising and continuing patterns, describing sequence rules, finding missing values, and using letters to represent unknowns in expressions and equations.
- Because they are the same reasoning at different ages. Continuing a pattern and solving an equation both involve finding and using a rule; the second just writes it more formally.
- Pattern work begins in the earliest years. Letters standing for unknowns typically appear around the start of middle school, though placement varies between school systems.
- Many children read = as "write the answer here" rather than "these two sides are equal". Problems like 7 + □ = 5 + 6 reveal it quickly, and fixing that reading makes equations far less arbitrary.
- Ask them to describe patterns in words and to find missing numbers in sentences like 3 + □ = 10. That is the same thinking, without the notation.
- One needing two operations to solve — 3x + 4 = 19 requires subtracting 4 and then dividing by 3. They usually follow once one-step equations are comfortable.
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