Multiplication and Division Games

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 Students build their own equal groups by dragging counters into group slots they create themselves. The Foundations of Multiplication mode has students make and fill a set number of groups. The Foundations of Division mode gives students a pool of counters to share equally — covering both partitive division (how many in each group?) and measurement division (how many groups?).

Best for: Grades 2–4, early multiplication and division introduction, Tier 2 intervention.

 Choose either Foundations of Multiplication or Foundations of Division from the menu. In Multiplication mode, read the prompt — for example, "Make 3 groups of 4" — then click Add a Group to create each group oval, and drag counters from the bank into each one. When all groups are filled equally, click Check Groups and then drag the correct answer into the equation to complete it. In Division mode, a pool of counters is given and students add their own groups, then share the counters equally across them. Click Check Groups when all counters are placed, then complete the division equation.

The goal is for students to experience what equal groups and fair sharing actually mean before they work with abstract equations — building the conceptual foundation that multiplication facts rest on.

Students reason from a partially screened image to find a missing factor, then — in Level 2 — connect that multiplication equation directly to a division equation using labeled drop zones. The draggable screen unlocks once the correct answer is found, revealing the full image as confirmation.

Best for: Grades 3–5, connecting multiplication and division, students ready to formalize the inverse relationship.

Choose Level 1 or Level 2 from the menu. In both levels, an image appears showing either equal groups or an array with most of it hidden behind a draggable purple screen. One group or one row is always visible — students use that information and the total shown on the screen to reason out the missing factor, then drag the correct number into the equation. Once the answer is checked correctly, the screen unlocks and can be dragged away to reveal the full image. In Level 2, after the missing factor equation is solved, a division equation appears below it — students complete it by dragging the correct numbers into drop zones labeled groups, in each group, and total, connecting the multiplication they just did directly to its inverse. The skip-count number line at the top supports students who need it.

The goal is to move students from finding a missing factor toward understanding why that same situation can be expressed as a division equation — making the inverse relationship between multiplication and division explicit and visual rather than just procedural.

These games are built on the same research foundation as the Multiplicative Thinking Intervention Program.

The CRA framework is one of the most validated approaches in elementary math intervention. A 2025 meta-analysis found an effect size of nearly 1.0 across 30 studies, and the IES Practice Guide recommends CRA for Tier 1 and Tier 2 math support. Equal groups and array models are the conceptual foundation of that framework — research by Flores and Hinton (2019) found significant gains in both multiplication skill and conceptual understanding when CRA was applied to elementary multiplication, including for students with learning disabilities.

The shift from counting to multiplicative thinking is the central developmental challenge these games address. Students who still rely on counting strategies to solve multiplication problems have not yet made that shift. Connecting skip counting, equal group models, and the number line in the same instructional context accelerates that transition and deepens understanding of why multiplication works — not just what answer it produces.