Sum-difference-multiple bar model
Pull the gold bonus gap out of a larger vault, then split the remaining blue energy into equal units. This animated 和差倍 game turns bar modeling into a vault puzzle.
A sum-difference-multiple problem asks students to compare two hidden quantities by difference and by times-as-many. This game turns the comparison into two vault bars: remove the gold difference first, then split the remaining blue bar into equal units.
Aligned with CCSS 3.OA.A.1 and 2.OA.A.1 for representing word problems with equal groups and unknowns.
Olympiad bar model
Remove the extra gold gap first. What remains must be split into equal blue units.
Olympiad thinking model
Gem Vault Balance is built for students who need a visual way to decode multi-step puzzle structure. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Gem Vault Balance 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.
Learning goals
How to play
Continue with guided practice
A word problem where two quantities are related by a difference and a multiple, such as "A is 3 times B plus 12." The bar model shows both relationships at once.
The extra gap is not part of the equal repeated units. Once it is removed, the remaining larger bar can split into same-size parts.
One unit = (larger quantity - difference) / multiple. The smaller quantity is one unit; the larger is multiple units plus the gap.
Grades 3-5 as an Olympiad-style extension of equal groups and two-step word problems.
