Scales are essential to learning any instrument, but there are three in particular that I believe to be imperative when you are first learning the violin. If you know these one-octave scales and the finger patterns that accompany them, you will be much more comfortable playing in these common keys.
The first scale you should know is A Major. We have three sharps in the key of A - F#, C#, and G#. For this scale, we stay between the A and E strings.
Tip: Practice going up and down this scale, and try adding your own rhythms!
The second scale you should be familiar with is D Major, which has two sharps - F# and C#. As you can see, we are borrowing two sharps from A Major, and leaving the G# behind. For this scale, we stay between the D and A strings.
Tip: Practice long bows for this scale, and pay special attention to creating a strong, beautiful tone.
The third and final scale we are talking about today is G Major, which has only one sharp, and that's F#. For this scale, we stay between the G and D strings, and continue the finger pattern we have used for the last two scales.
Tip: Practice going up and down this scale, and be sure to keep your right elbow elevated while easing into the lower strings.
One piece of advice I can give for learning these scales is to ensure that you know the names of the notes you are playing. The best way to practice this is to simply say each note aloud, one at a time, before playing it. That way you are making the mental connection between the name of the note, and the pitch you are hearing.
While knowing the finger pattern and finger numbers used within a scale can be helpful at first, it is not recommended to rely on these methods alone. Knowing the notes will allow you to figure out the finger pattern pretty quickly if you happen to forget, but knowing only the finger pattern or finger numbers will not necessarily help you with the note names. Additionally, familiarity with the musical alphabet is incredibly transferrable, and will help to strengthen your music-reading ability, which will in turn help you to learn music much more quickly.