The Connect mode in the Numbers game pertains to place values.
The way that Osmo interprets your tiles depends on which mode you are playing.
In Count and Add mode, all the tiles visible to Osmo will simply be added up to form the total.
In Connect and Multiply modes, tiles that are close to one another take on a special meaning.
In Connect mode, they are joined together to form a bigger number. For example, a 3 tile and a 6 tile placed next to each other will be interpreted as 36.
In Multiply mode, the same tiles would be multiplied, forming 18. Any tiles that are placed away from a group of closely placed tiles will be added, just like in Count or Add mode. Further, a 2 tile placed away from the 3 and 6 tiles would bring the total up to 38 for Connect mode and 20 for Multiply mode.
Remember, you can have more than 2 tiles forming a close group too. Also, you can have several close groups and several "away" tiles in a single move for maximum flexibility in forming numeric totals.
Please note that the Words game can also be used to teach place values�(through the custom-made albums); see, e.g., this album: