Curriculum placement
Grade 6. This describes the skill, not a learner estimate.
Equivalent expressions
Generate equivalent expressions using algebraic properties
Problem types
- Decide which expressions are equivalent
- Multiply into parentheses
- Choose the expression with a number factored out
- Mark the equivalent expressions
Builds on
- Expressions with variables
- Properties of addition and multiplication · Earlier idea
Splitting an array into two parts to multiply is the distributive property. With a letter in place of a number it shows two expressions are equivalent.
- The meaning of the equal sign · Earlier idea
Equal expressions have the same value whatever number replaces the letter, which extends the equal sign from numbers to expressions.
Leads to
- Expanding and factoring linear expressions
- Adding, subtracting, and multiplying polynomials
- Solving two-step equations · See it applied
Seeing $5(x+8)$ as one group multiplied by 5 is what lets an equation be divided by 5 in a single step; factoring a number out shows the common factor first.
- Proving a polynomial identity · Extend the idea
Equivalent expressions have equal values for every input, and a polynomial identity is such an equivalence.
Related skills
- Dependent and independent variables · Shared foundations
- Solving one-step equations · Shared foundations
Open the interactive map to explore lessons and skill connections.