Learning path · Secondary / high-school algebra
High-school algebra
Work through the relationships behind secondary algebra. Reuse number skills, connect equations to graphs, and build toward systems and quadratics.
5 units · 8 skills
School context: Secondary / high-school algebra
For school-level algebra or equivalent independent study after basic arithmetic and fraction work. Course names, grade placement, and the order of topics differ between curricula.
What this path connects
- Solve and check a linear equation or system.
- Connect algebraic relationships to graphs and function notation.
- Interpret and check the roots of a factorable quadratic.
The learning sequence
See what each unit covers and open the skill you want to understand. The order gives you a route through the material.
Unit 1
Make the number work reliable
Review the signs and fractional values that appear inside algebraic steps. Fix these small uncertainties before they become difficult to trace.
- Signed numbersUse a number line to make sense of positive and negative numbers. Distinguish a value’s position from its distance from zero and explain changes in either direction.
- Equivalent fractionsExplain why different fractions can name the same number. Scale the numerator and denominator together and connect the calculation to equal parts of one whole.
- DecimalsRead tenths and hundredths as fractional units. Compare decimal values and align place values when adding or subtracting them.
Unit 2
Solve a single relationship
Use equality-preserving operations to isolate an unknown and check the proposed value in the original equation.
Unit 3
Connect symbols and graphs
Read a graph’s coordinates, scale, and rate of change. Use function notation to connect the displayed relationship to its rule.
- Graphs & coordinatesRead a graph as a relationship between quantities. Check axes and scale, connect points to an equation, and interpret the change between two points.
- Function notationRead f(x) as the output of a function at an input. Evaluate a rule carefully, check its domain, and connect notation to a table or graph.
Unit 4
Satisfy two relationships together
Choose substitution or elimination and verify that the resulting pair satisfies both equations.
Unit 5
Recognize a quadratic’s structure
Use a factorable example to connect products, roots, and the zero-product rule. Keep both candidate solutions in view.
Make the path useful to you
Respect the course’s notation and method
Bring the original question and the method expected by the teacher or course. Alternative methods are useful when their relationship is explained, not when they obscure what the assignment asks.
Keep areas separate from course labels
Algebra I, Algebra II, and integrated mathematics courses package overlapping ideas differently. This path organizes the first equation, graph, and system foundations; it does not claim to replace every topic in one of those courses.
Choose the next branch deliberately
Continue toward precalculus for further function and angle preparation, or toward linear algebra when systems, vectors, and matrices match the goal.
Explore related learning
Get closer to the step that matters.
See how the AI Tutor we’re developing can fit around questions, explanations, and guided practice within a learning path.