Looking at scales in varying interval degrees is a great way to make scales more interesting. A good place to start is by looking at an interval called a third. The below exercises are based on 3rds and are great for learning scales, harmony, intervals and the fretboard all at the same time. You also can make them as interesting as you like when you apply varying rhythms.
The exercises below show the music and tab for Ascending/Descending 3rds as well as Ascending/Descending "stacked" 3rds . The rhythm is written in eighth notes. For a beginner feel free to use quarter notes at a nice and slow tempo.
The exercises and others like it can be found/explained at:
When you get to "Stacked" 3rds (i.e. true stacked thirds would essentially be triads), you'll be playing the same quality/type of intervals, but you'll also be arpeggiating all the chords for the key of C. So you'll be working on melody and harmony at the same time. For example, the 1st triplet is C-E-G (C Major) the 2nd triplet is D-F-A (D minor), so on and so forth.
When you get the single note melody practice down, try to play the exercise as triads instead of single note arpeggios. So if you playe C-E-G all at once you'd be playing the C major triad, then if you ascended a third and played E-G-B, you'd be playing an E minor triad. Use that method to move up and down the scale and you'll start finding your basic triads all over the neck and you may even start hearing some pieces of songs or writing your own.
Lastly, the exercises show the C major scale in 7th position, try playing the exercises in different positions to improve your fret-board dexterity. Also, some of the triads aren't possible in this position. If you find yourself practicing a specific scale, like C for example, find a beginner song in that key. A good one for the wife and kids in the key of C might be, "Somewhere Over the Rainbow". Let me know if you can't find a good version, I'll write one out for you.