Learning goals
- Operation order decides which subexpression becomes a single value first.
- Parentheses and multiplication/division can change the whole result.
- A tree keeps the expression structure visible while calculating.
Order of Ops Tree
Collapse the expression in order
Collapse 4 + 6 × 3 by reducing the multiplication node before the final addition.
What this game shows · Order of Ops as a Tree
An expression is a tree, not a left-to-right list. PEMDAS picks which sub-tree collapses first. Watch 4 + 6 × 3 reduce: the multiplication node fires first, then the addition root.
- PEMDAS
- Parentheses, Exponents, Multiply/Divide, Add/Subtract.
- Sub-expression
- a node in the tree that becomes a single value when collapsed.
- Root collapse
- the final operation that produces the answer.
Aligned with CCSS 5.OA.A.1 (use parentheses, brackets, or braces in numerical expressions).
Order of operations tree
Collapse the deepest operation first, then collapse the root.
22
4 + 6 x 3
Collapse
0/2
Expression
Algebra readiness model
Who this demo helps, and where to practice next
Order of Ops Tree is built for students who need expression structure and balance before formal algebra. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Order of Ops Tree helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
How to play
- 1 Name the parts of the expression or equation before simplifying.
- 2 Change one side or one tile group and predict the effect.
- 3 Move to Grade 6 expressions or equations after the structure is visible.
Continue with guided practice
FAQ
Tap to expand Order of operations, as a tree.
01 What does PEMDAS mean? P-E-MD-AS
Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right). It is the agreed reading order.
02 Why does 4 + 6 × 3 = 22 and not 30? 22, not 30
Multiplication outranks addition. Collapse 6 × 3 = 18 first, then add to 4 → 22. Treating it left-to-right would give 30, which violates the convention.
03 When do parentheses change the answer? ( ) overrides
When they force a lower-priority operation to fire first. (4 + 6) × 3 = 30 instead of 22 — the parentheses promote addition above multiplication.
04 Which grade is this game for? Grades 5–6
Grades 5–6, aligned with CCSS 5.OA.A.1. Direct precursor to algebraic expression evaluation in middle school.