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Balance Forge

A strategic addition and subtraction forge. Share numbered ingots across competing orders: a correct pair can still leave another order impossible. Plan ahead, Undo freely and balance the whole forge. Three challenges, number ranges up to 1,000 and fresh practice puzzles.

Mental additionMental subtractionNumber bondsStrategic planning
Game guide

Strategic addition & subtraction · no timer

Balance Forge

One tray. Every order. Choose wisely.

Think like a master smith

A correct pair isn’t always a good plan. Each ingot can fill just one order. Plan ahead, forge a pair, and save what the others need.

  1. Choose an order.
  2. Tap two numbered ingots.
  3. Forge the pair. Balance every order.

Three orders share the tray. Keep the whole plan in mind. Bigger numbers change the arithmetic; the challenge level changes the planning.

Your forge collection

0 / 8 complete

Undo is free. Tap a chosen ingot again to deselect it. Progress saves on this device only. No timer, speed penalty or mastery score.

Leave this puzzle?

Your unfinished plan will be lost. Completed collection badges are saved.

Balance Forge guide

How Balance Forge supports maths practice

Share one tray of numbered ingots across two, three or four addition and subtraction orders. A mathematically correct pair can still leave another order impossible. Plan the whole puzzle, with no timer and free Undo.

How to play

  1. Choose Apprentice (two orders), Smith (three) or Master (four), and a separate number range. Learn to play offers a short interactive first lesson.
  2. Select an unfinished order, then tap two available number ingots. Tap again to deselect; changing order keeps your pair selected.
  3. Add to the target or find the stated difference. For differences, the larger number comes first.
  4. Forge pair to spend those ingots. They cannot be used in another order. Incorrect pairs spend nothing.
  5. Look ahead at the other orders. Undo freely if your plan leaves no way to finish.
  6. Reset all, beside Undo, immediately restores every ingot and order in the same puzzle without a confirmation popup.
  7. Fill every order, enjoy the celebration, then View results. Replay and the next puzzle are at the top of the results.

Skills practised

  • Addition and number bonds
  • Subtraction differences and inverse relationships
  • Equality and reasoning with constraints
  • Planning with shared numerical resources

Teacher notes

  • This untimed game supports planning and whole-class discussion. Ask pupils why one correct pair preserves more options than another.
  • Undo supports reasoning, not a mastery score. Wrong pairs are distinguished from valid pairs that block later orders.
  • Number ingots with the same value are separate resources. No dragging is needed; all actions support touch and keyboard.
  • Challenge changes the number of competing orders; number range changes arithmetic size. Each challenge/range has eight collection puzzles. Fresh practice is generated and solver-checked, with no collection badges.
  • Preferences and collection badges save on this device only and can be cleared in Privacy. Storage restrictions do not prevent play. The game does not increment public counters or collect pupil identities.