⚙️ Pattern Machines

Two machines stamp out patterns in sync, pairs fly onto a grid, and parentheses become real containers.

REMEMBER: Math notation has grammar. Parentheses are containers — whatever is inside gets computed first, as one package. Without a container, × and ÷ happen before + and −, left to right. You can often read an expression without computing it: 3 × (18932 + 921) is simply three times the sum, whatever the sum is. When two patterns run side by side, line up the terms that were made at the same time — those corresponding terms become ordered pairs, and the pairs make a picture.

Part 1 · Run the Machines

Set a rule for each machine, then stamp terms. Every stamp makes one term on each machine at the same time — those two terms are corresponding, so they become an ordered pair (Machine A, Machine B) and fly onto the grid.

Machine A (x-coordinate)

Machine B (y-coordinate)

Ordered pairs (A, B)

Expression Grammar Lab

Type an expression. Parentheses ( ), brackets [ ], and braces { } are drawn as containers. Press Compute one package to open the innermost container — or, with no containers left, to do the next operation in grammar order.

You can type * for × and / for ÷. Division must come out whole.

Part 2 · Structure Spotting

Which expression is bigger? Do not compute — read the structure. Lock in your answer, then watch the reveal. Some rounds ask you to turn words into an expression, or to spot the relationship between two patterns.

Part 3 · The Machines

Three step-by-step machines. Each step says what to do and why.

Evaluate an expression in grammar order

    Say what an expression means — without computing it

      Two rules → two patterns → pairs → relationship

      Write rules like “start 2, add 4” or “start 1, multiply 2”.

        Part 4 · Machine Mechanic Quiz

        Ten questions. Each wrong answer tells you which machine to revisit.

        Question 1 of 10 Score: 0

        Word Box

        Expression
        A math phrase made of numbers and operations, like 2 × (8 + 7). It has no equals sign.
        Parentheses ( ) · Brackets [ ] · Braces { }
        Containers that say “do this part first, as one package.” When containers nest, the innermost opens first.
        Order of operations
        The grammar rule: containers first, then × and ÷ left to right, then + and − left to right.
        Evaluate
        Compute an expression to find its single value.
        Interpret (read without computing)
        Describe what an expression means from its structure: 3 × (18932 + 921) is three times a sum.
        Pattern · Term
        A list of numbers made by a rule; each number in the list is a term.
        Corresponding terms
        Terms in the same position in two patterns — the first with the first, the second with the second.
        Ordered pair (x, y)
        Two numbers in order. The first tells how far right, the second how far up, on the coordinate grid.
        Coordinate plane
        The grid made by a horizontal x-axis and a vertical y-axis meeting at the origin (0, 0).
        Free lessons, assessments & worksheets at WinElements.com  ·  Unlimited online practice at Sleedu.com