Here a two great websites that provide lots of great pattern problems.
These patterns can be used with elementary students (if you just ask number questions) through advanced algebra (if you include questions about functions).
Mathematics is often described as the study of patterns. That is exactly what Spotting Numbers and Visual Patterns do.
The interplay of geometry and numbers and algebraic thinking in these questions puts the learner squaring at the core of mathematical reasoning. Quite frankly, it doesn’t get much better than this! (OK, my opinion.)
Questions to Ask
Here are some questions. As a general rule, For Elementary: a-b; Middle School: a-d; Algebra: a-e
a. How many *** are in next figure?
b. How many *** are in next figure after that?
c. How many *** are in pattern n = 10?
d. How many *** are in pattern n = 43?
e. Generalize: How many *** are in pattern n?