⚙️ Expression Machines

Same value, new shape — machines that rebuild expressions without changing what they're worth.

REMEMBER: Like terms have the exact same variable part — only like terms can be combined. A number outside parentheses must multiply everything inside. Two expressions are equivalent when they give the same value for every x.

Part 1 · See It as Tiles

The expression a(x + b) is a rectangle: a rows, and each row holds one x-tile plus b unit tiles. Slide the numbers and watch the two forms describe the same tiles. Then plug in a number for x to prove they match.

Rows (a): 3 Unit tiles per row (b): 2

Try a value for x

Part 2 · Equivalent... or Impostor?

Two expressions walk into the machine. Are they truly equivalent, or is one an impostor hiding a classic mistake? Commit to your answer first — then the machine substitutes x = 2 and x = 10 to expose the truth.

EXPRESSION A

EXPRESSION B

Correct calls: 0

Part 3 · Run the Machines

Three machines, three jobs. Feed in your own numbers — each machine prints every step and the why, then checks its own work.

Choose a machine

Build the expression ax + b + cx + d. Negatives welcome — type them right in.

a (first x term)

b (first number)

c (second x term)

d (second number)

Build the expression a(bx + c). Try a negative a to see the sign flip in action!

a (outside)

b (with x, inside)

c (number, inside)

Build the expression px + q with whole numbers. The machine hunts for the greatest common factor.

p (with x)

q (number)

Part 4 · Machine Master Quiz

Question 1 of 10 Score: 0

📗 Word Box

Expression: A math phrase built from numbers, letters, and operations — like 3x + 5. It has no equals sign.
Term: One piece of an expression, separated by + or − signs. In 3x + 5, the terms are 3x and 5.
Like terms: Terms with the exact same variable part. 4x and 2x are like terms. 4x and 4 are NOT.
Coefficient: The number multiplying a variable. In 7x, the coefficient is 7. A plain x has a hidden coefficient of 1.
Constant: A term that's just a number, with no variable. It never changes — that's why it's called constant.
Distributive property: The rule a(b + c) = ab + ac. The outside number multiplies EVERY term inside the parentheses.
Greatest common factor (GCF): The biggest number that divides evenly into all the terms. It's the number you pull out when factoring.
Equivalent expressions: Expressions that look different but give the same value for every x — same tiles, new arrangement.

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

	x = 2	x = 10
A gives
B gives