Students will learn how to determine whether a whole number is prime, composite, or neither. Before learning this, your students must be comfortable performing divisibility tests.
Do these Khan Academy exercises:
Next, students will investigate several number spirals. Start by exploring the spirals seen here. I think this would be done best by giving your students unshaded grids on sheets of paper or via software, then asking them to shade the square numbers, or shade the multiples of four, etc. After investigating various properties of these spirals, show them this video or relay the ideas therein.
Make LaTeX sheets for the number spirals, so teachers can print them. Later, develop software so that shading the spirals is as easy as clicking the mouse.
Conclude by leading this investigation:
Prime Cubes by JRMF
4.OA.B.4: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.