Algebra

25 Skills in Mathematics. 25 are ready to try — three verified questions each, no account needed.

Ready to try

Ages 10–11
Equations with Two Unknowns
Find pairs of numbers that satisfy an equation with two unknowns (e.g. find pairs (a, b) where a + b = 10 or 2a + b = 15)
10 verified questions on this shelf
Ages 10–11
Linear number sequences
Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule
10 verified questions on this shelf
Ages 10–11
Number Pattern Relationships
Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane
10 verified questions on this shelf
Ages 10–11
Systematic Listing
Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options)
9 verified questions on this shelf
Ages 10–11
Using Simple Formulae
Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))
21 verified questions on this shelf
Ages 10–11
Writing Algebraic Equations
Express missing number problems algebraically using letters for unknowns; translate word problems into equations
128 verified questions on this shelf
Ages 11–12
Algebraic Notation
Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently
12 verified questions on this shelf
Ages 11–13
Algebraic Transformations
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations
120 verified questions on this shelf
Ages 11–12
Collecting Like Terms
Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence
153 verified questions on this shelf
Ages 11–12
Coordinates (age 11+)
Plot and read coordinates in all four quadrants of the Cartesian plane, using positive and negative x- and y-values to describe positions precisely
10 verified questions on this shelf
Ages 11–13
Expanding Single Brackets
Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers
53 verified questions on this shelf
Ages 11–12
Expressions & Equations Vocabulary
Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)
13 verified questions on this shelf
Ages 11–14
Generating Sequences
Generate terms of a sequence from a term-to-term rule (e.g., 'add 3 each time') or a position-to-term rule (e.g., '2n + 1'), and identify whether a sequence is arithmetic, geometric, or neither
13 verified questions on this shelf
Ages 11–14
Numbers on a number line
Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations
35 verified questions on this shelf
Ages 11–14
Solving Linear Equations
Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients
173 verified questions on this shelf
Ages 11–12
Substituting into Formulae
Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations
479 verified questions on this shelf
Ages 12–13
Factorising Expressions
Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)
12 verified questions on this shelf
Ages 12–14
Linear Function Graphs
Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context
34 verified questions on this shelf
Ages 12–14
Nth-Term Rules
Find the nth-term expression for an arithmetic sequence by identifying the common difference and the zero-term, and use it to determine any term in the sequence or test whether a given number belongs to the sequence
10 verified questions on this shelf
Ages 12–14
Plotting Linear Graphs
Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line
25 verified questions on this shelf
Ages 12–14
Simple formulae
Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable
12 verified questions on this shelf
Ages 13–14
Estimating answers (age 13+)
Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts
22 verified questions on this shelf
Ages 13–14
Expanding Double Brackets
Expand products of two or more binomials, e.g., (x + 3)(x - 2) = x² + x - 6, using the grid method or FOIL; simplify the result by collecting like terms
9 verified questions on this shelf
Ages 13–14
Quadratic Graphs
Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions
11 verified questions on this shelf
Ages 13–14
Simultaneous Equations
Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations
13 verified questions on this shelf

Skill names and descriptions include the Marble Skill Taxonomy © Generative Spark, Inc. (withmarble.com), licensed under ODbL 1.0 (database) and CC BY-SA 4.0 (content). Practice questions are GlowGrades's own, each checked by independent verifiers that must agree before a child ever sees it.