🏗️ Array Architect

Design buildings whose floor plans are multiplications. Snap them apart along place-value lines.

REMEMBER: A multiplication is an area. Break each factor into its tens and ones (or thousands, hundreds, tens, ones), and the big rectangle snaps into smaller rooms whose areas are easy multiplications. Add the rooms — that is the answer. This is the distributive property at work: (20 + 3) × (40 + 7) = 20×40 + 20×7 + 3×40 + 3×7. Before you build, estimate by rounding to the nearest ten so you know roughly where the answer should land.

Part 1 · The Blueprint Studio

Type a multiplication (up to 4-digit × 1-digit or 2-digit × 2-digit). The plaza splits along place-value lines into rooms. Reveal them one at a time and watch the ledger add up.

4-digit × 1-digit works, and so does 2-digit × 2-digit (or 3×1, 2×1). One factor must be 1 or 2 digits.

Estimate
?
Rooms revealed
0 of 0
Running total
0
Answer
?

Part 2 · Build-This Challenges

Predict before you build. Each challenge asks you to pick the answer, spot the partial product, or catch a mistake in someone else’s ledger.

Part 3 · The Machines

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

Multiply with an area model

    Multiply with partial products (the ledger)

      Estimate before you multiply

        Part 4 · Master Architect Quiz

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

        Question 1 of 10 Score: 0

        Word Box

        Factor · Product
        In 23 × 47 = 1,081, the numbers 23 and 47 are factors; 1,081 is the product.
        Array · Area model
        A rectangle whose length and width are the factors. The area is the product.
        Place-value decomposition
        Splitting a number into its places: 47 = 40 + 7 (four tens and seven ones).
        Partial product
        One of the pieces of the answer: 20 × 40, 20 × 7, 3 × 40, 3 × 7 — each a friendly multiplication.
        Distributive property
        a × (b + c) = a × b + a × c. Why you can split a factor into place-value chunks and multiply each part.
        Ledger
        The list where partial products are stacked and then summed: the written form of the area model.
        Estimate
        An approximate answer using rounded factors, useful for checking reasonableness.
        Reasonableness
        Does the answer sit near the estimate? If not, look for a lost or extra zero.
        Free lessons, assessments & worksheets at WinElements.com  ·  Unlimited online practice at Sleedu.com