This assignment can turn out very differently depending upon whether black and white or color film is used -- try them both and see which you like better!
ShapeThis can be approached from an artistic perspective, where the shapes in your composition are the subjects themselves. Or, you can use shapes to enhance the actual subjects in your frame. Try back-lighting to produce a silhouette, or using side-lighting and choosing a "clean" background to emphasize the shapes of your subjects. (A fun exercise is to see what kinds of objects are recognizable merely by their silhouettes. Also, shadows often create very interesting and beautiful shapes).
FormThis is where you try to accentuate the fact that you're photographing three-dimensional objects. Side-lighting will assist you with this task, as will camera angle and composition. (My favorite subjects for this are trees -- side-lit so that half the trunk is lit, and the other half is in shadow).
TextureAgain, try taking abstract shots that have texture as their subject, and also try to incorporate texture into photographs of other subjects. Side-lighting will often exaggerate textures, but try using light in other ways as well. (Try rocks and pebbles -- perhaps moist from a stream or the ocean).
PatternBy now you're probably aware that incorporating these design elements into your photographs makes them more interesting and vibrant. Once again, for pattern, try abstract compositions where the pattern is the message, and also photographs where patterns are made a part of your composition. Patterns to look for include natural as well as human-made. (Be on the lookout for spider webs, tall grasses, walls, formal gardens…..).
Also, try to include more than one design element in a particular photograph.