In Gcompris, we already have a simplified Hanoi tour game. To complete this concept, we need a real Hanoi tower game with the real rules. See also 
DONE: Implemented in GCompris 7.1
For young kids, we could create an activity where they must classify object from larger to smaller, and so on. The size classification could be based on the real-life sizes. For example, a car is larger than a light bulb, but the actual images could be equal size.
We could also have classification based on shape, e.g. round apples and wheels, and rectangular books and doors.
Could teach also "in front of" and "behind" concept.
Modify Well balance the scales to make it a substractive activity: Putting e.g. masse 9 and a punct on left side , masse 13 on right side.
Make the scale work like a real scale (tilt to one side when it's heavier on one side than the other).
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We could also create a new situation : The Magician
The magician holds a hat.
He tells (pictograms) "7 rabbits" for eg.
A number of rabbits come out of the hat, but not all.
The "?" sign appears on the hat.
The user has to click the number of remaining rabbits in the hat before they come out and he is congratulated.
Marc Brun is working on this activity.
A symmetrical drawing activity, with various forms of symmetries. See this example.
See this game (and also the GNOME game glightoff). This has interesting mathematical properties.
A la "Rosegarden" - with more simple features, just drag n' drop notes on a score and hit play button.
In that activity, we could add :
- filling incomplete tables
- choosing the right heading for rows and columns of an already filled-in table
Take code from gtans, putting a simplified ui. DONE In GCompris Release 7.2
Based on the gnucap simulator as the backend, we can create a simplified electric simulator. Bruno is working on it.
Like Dr.Geo does, we can provide an interactiv geometry activity. Of course we have to make it much simpler and stick to point, line, segment, perpendicular, parallel and circle.
Here some ideas to steal. TicTacToe and others variants of same game (QuinzeVainc, Sentier, Mots and Lettres].