Apprentice’s Spell Die
Wondrous Item, uncommon (requires attunement by a spellcaster)
This rough-hewn, die of bone is worn smooth at the edges. Its four runic inscriptions are stained dark from years spent in the pocket of a nervous young adept. Often crafted as an exercise by a student of the arcane, the runes on each of the four sides are imbued with the magical energy of its maker.
When the die is cast by a spellcaster, its own power can contribute to the strength of some types of spells.
As you cast a spell that has an “At Higher Levels” clause in its description, choose the spell slot level that you will use to cast the spell. Before any attack, saving throw, or damage rolls are made roll the Apprentice’s Spell Die as a somatic spell component of the original spell (use a d4 at the game table). Add a number of spell slot levels equal to the result on the die to the spell slot level you chose to cast your spell. Use the new, combined spell slot level to determine the effects of the spell, but only the original spell slot level is consumed. Once cast, the die remains inert and cannot be used again until the next midnight.
Strange Dice 
I like this idea, and I probably will use it in my game very soon. I’m curious about how it affects actual game play. It seems pretty powerful. One extra spell slot can really give the players a boost at a critical point, and that’s the minimum bonus. An additional two or three spell slots could potentially unbalance an encounter. Four spell slots? Well, I guess that’s why you became a wizard in the first place, isn’t it?
I’ll probably try something more like this: Roll 1d6. On a roll of 1, 2, or 3, add one spell slot to the spell you are casting. On a roll of 4 or 5, add two spell slots. On a roll of 6, add three spell slots.
To be honest, I’ve pretty much given up on balanced encounter design. 🙂 I wouldn’t say that I run a “high magic” game, but once my players level up to high single-digits and above, this just looks like another trick up their sleeves. I tried to use the ‘Pearl of Power’ (DMG 184) as the basis for the Die… it trades an action for a 3rd level spell slot (which can be used on any spell with no real time limit). The Die has the potential for an additional level, but its use is restricted.
I like magic items that feel like they have a real impact and a first level spell slot feels more like a minor buff to me than an infusion of power. If you want to minimize the frequency with which a level four spell slot hits the table, maybe tweak the recharge? Roll the die again at dawn to see if it recharged?