How to Play

🎬 Begin the Adventure

Choose your mode of play: Multiplication for clean products, Division for equal groups, Division + Remainder for trickier leftovers, or Mixed for a lively assortment of everything. Select your grid size (10×10 or 12×12), then press Start Session to launch the challenges.

📘 Read the Equation, Watch the Grid Transform

A new equation appears at the top of the screen, and the grid reorganizes itself. Columns snap into place to match the second factor or divisor. Rows fill gracefully from left to right. Your task is to tap the cell that completes the fact:

• Multiplication: Find the final square in the completed rectangle—the product.
• Division: Locate the last square of the final full row—the quotient.
• Remainders: Identify the first square beyond the last complete row—the starting point of the leftovers.

Correct answers trigger gentle animations and move you forward. Incorrect taps provide subtle cues to try again without punishing the learner. The flow continues smoothly until all prompts are solved.

Press Reset Session at any time to begin anew, switch modes, or experiment with a different grid size. Each fresh run offers a new mix of numbers and shapes, keeping the experience lively and unpredictable.

Study Notes

🧩 Arrays Reveal the Hidden Structure of Facts

By allowing the grid to reshape itself each round, Multiples Grid invites learners to view arithmetic not as disjointed facts, but as visual patterns with meaning. Multiplication becomes an area model: rows and columns forming a rectangle whose final square represents the product. Division becomes a journey along the grid’s rows until the equal groups run out. And remainder problems display their extra “stray squares,” making leftovers concrete and intuitive.

↔️ Unified Space for Multiplication and Division

One of the game’s strengths is that multiplication, division, and remainders all occur in the same grid space. The layout shifts, but the numbers never leave the learner—this consistency helps students understand how the same array can tell multiple mathematical stories. Quotients emerge naturally from full rows, just as products emerge from complete rectangles.

🗣️ Build Confidence Through Verbal Reasoning

For classrooms or tutoring sessions, encourage learners to state their reasoning aloud before tapping. “Three groups of four gives twelve,” or “Five fits into twenty only four times,” or “Two squares are left over.” This habit strengthens conceptual fluency and helps students form durable mental models of grouping and arrays.

🎓 A Gateway to Deeper Number Sense

Because each round highlights structure rather than speed alone, Multiples Grid serves as a bridge to more advanced ideas— factorization, partitioning, area models, and proportional reasoning. It gently nudges students toward noticing patterns and relationships that extend far beyond the single problem they’re solving.