Built-in Paint tools can be used to color and annotate the grid. Some projects require more powerful tools.
Then, complete the transfer to Notes —
Use any drawing app that can import and edit a PDF --
Choosing a full-fledged graphic design program will give you more capabilities than Notes. One app we like and use is Graphic for iPad. It has an amazing amount of power for not much money and also works with an Apple Pencil. It has features like 'snapping to grid lines' that makes adding shapes easier. Also, Graphic for iPad can add lines, notes or even modify the shapes originally created in our app, for example, and even change line color or width.
Coloring a grid using Graphic for iPad
[Also available for the Apple Mac]
NOTE: We have no association with Graphic other than we use it.