🔧 Expression Builder Workshop

Build expressions like machines, stack exponent towers, and put twin expressions on trial.

REMEMBER: An exponent counts copies being multiplied — 2³ = 2×2×2 = 8, never 2×3. A letter stands for a number, and an expression is a recipe for computing with it: exponents first, then × and ÷, then + and −. Two expressions are equivalent only if they match for EVERY value of the variable — one lucky match proves nothing.

Part 1 · The Exponent Tower

An exponent is a construction order: stack this many copies and multiply. Choose a base and crank the exponent — each new floor multiplies by the base again. Watch how fast the tower grows... and compare it to the multiplication trap.

Base

Exponent: 3

Part 2 · The Twin-Testing Rig

Two expressions claim to be the same machine. Commit your verdict — equivalent or not — then the rig feeds both machines the same test numbers and compares every output. Watch out: some impostors match on the first test or two!

Correct verdicts: 0

Part 3 · Workshop Machines

Three machines keep the workshop honest. Each prints its steps and names the rule it's using.

Pick an expression — the machine evaluates it in the lawful order and shows what the left-to-right shortcut would have wrecked.

Expression

Words in, algebra out — with the parts named and a test value pushed through.

Phrase

Test value: n =

The cube formulas V = s³ and A = 6s² — substitute, exponents FIRST, then multiply.

Edge length s

Part 4 · Master Builder Quiz

Question 1 of 10 Score: 0

📗 Word Box

Variable: A letter standing for a number — sometimes one specific unknown, sometimes any number at all.
Expression: A recipe for computing, built from numbers, variables, and operations — like 3n − 5. (No equals sign — that would make an equation.)
Base & exponent: In 2³, the base 2 is what gets copied, and the exponent 3 counts the copies being MULTIPLIED: 2 × 2 × 2.
Power: The whole package: 2³ is "the third power of 2," and its value is 8.
Coefficient: The number multiplying a variable: in 4x + 7, the coefficient is 4. (The 7 is a constant term.)
Term: A piece of an expression separated by + or −: the expression 4x + 7 has two terms, 4x and 7.
Equivalent expressions: Expressions that output the same number for EVERY input, like 3(2 + x) and 6 + 3x. Properties prove it; substitution tests it.
Order of operations: The agreed sequence: grouping symbols, then exponents, then × and ÷ (left to right), then + and − (left to right).

Free lessons, assessments & worksheets at WinElements.com · Unlimited online practice at Sleedu.com