Is there a way to unlock a mode in Osmo Numbers without playing all the levels before it?

You can use the "Unlock All Modes" option in the settings menu of Numbers Education (the original version of the app) to unlock the first level of the "Add", "Connect" and "Multiply" levels. You can open the settings menu by tapping the screen once to bring up the settings button (a gear shaped icon) in the top left corner. Tap the settings button and then tap on "Unlock All Modes" near the bottom left of your screen.

The new Osmo Numbers app has a Mode Wizard, where you can adjust the difficulty at any time.

Find more information in our PDF guides to the new Osmo Numbers app and Osmo Numbers Education (the original version of the app).