Curriculum placement
Algebra 1. This describes the skill, not a learner estimate.
Why each equation step is valid
Justify each equation transformation by equality-preserving operations
Problem types
- Justify each step
- Assume a solution, then check
- Choose the property behind each step
- Name the property that justifies a step of completing the square
- Judge the first steps of completing the square
- Solve a linear equation and justify each step
Builds on
- Linear equations with variables on both sides
- Solving two-step equations · Earlier idea
Choosing the equation after one step is the move whose reason equation-reasoning names: each step is a property of equality applied to both sides.
Leads to
- Why elimination keeps the same solutions
- Proving a polynomial identity · See it applied
A polynomial identity is shown by a chain of steps that each keep the expression equal.
- Pythagorean and angle-sum identities · See it applied
Proving a trigonometric identity is a chain of equal expressions, each step justified by a property.
Related skills
- The meaning of the equal sign · Related idea
Each step in solving an equation must keep both sides equal, which is the balance idea of the equal sign.
- Rearranging a formula · Shared foundations
- A graph as the solution set · Shared foundations
- Linear equations from constraints · Shared foundations
- Systems of linear equations · Shared foundations
Open the interactive map to explore lessons and skill connections.