Sequences, rules, unknowns and equations.
Spotting the rule in a pattern — 3, 7, 11, 15 goes up by 4 — is the same thinking algebra writes with symbols. Algebra then uses letters for unknown numbers, so a puzzle like "something plus 5 is 12" becomes x + 5 = 12, solved by keeping both sides of the equals sign balanced.
One error to watch for: reading the equals sign as "the answer comes next". For example, filling 3 + 4 = □ + 5 with 7 instead of 2.
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.
Interactive practice with instant feedback — free, ad-free and playable in the browser.
5-7 · arcade
Children tap the odd numbers while even numbers drift past, building odd and even recognition.
5-7 · arcade
Children pop the smallest number each time to put numbers in order, building number sequencing.
8-10 · puzzle
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
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
Order decimals from smallest to largest on a deep sea research mission, for ages 8 to 10.
11-12 · speed
Solve two-step equations against a friendly timer in a quantum reactor control center, for ages 11 to 12.
11-12 · puzzle
Complete Pythagorean triples on a grid in an ancient geometry archive, finding each missing side, for ages 11 to 12.
11-12 · escape
Decode a chain of algebra ciphers to unlock secure systems in a cyber intelligence facility, for ages 11 to 12.
11-12 · speed
Simplify index and exponent expressions against a timer in a digital power core, for ages 11 to 12.
11-12 · quiz
Convert numbers to and from standard form on a deep space science vessel, for ages 11 to 12.
11-12 · escape
Solve a chain of inequalities to unlock a high security logic vault, for ages 11 to 12.
11-12 · drag-drop
Sort expressions by which index law applies in a data classification nexus, for ages 11 to 12.
Showing 12 of 33. Browse all games
Every worksheet prints as a clean A4 PDF with a separate answer key.
5-7 · 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
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
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
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
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
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
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
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
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
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
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
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 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.
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.
Browse Math by Grade for a full set of age-appropriate activities rather than a single strand.
Browse Math by GradeThe Parent Dashboard shows XP, streaks and accuracy for games played in this browser — no account and no personal details asked for.
View Parent DashboardChoose a game, print a worksheet, or explore another math skill.