Apply the category of knowledge by recalling formulas and fundamental theorems of algebra, such as the quadratic formula.
Demonstrate "comprehension" by explaining fundamental algebraic concepts, such as what a variable or equation is. To draw on the example from Step 1, show comprehension by articulating when and how the quadratic formula is applied (beyond merely restating it.)
Demonstrate "application" by applying theories and formulas to an actual algebraic problem. For example, you can apply the concept of a variable by solving for x in the hypothetical equation 12=2x + 6.
Conduct an "analysis" of an algebraic problem or, more broadly, of algebra itself. You can take a complex equation and analyze what it's asking to solve, its component parts, its form. Consider, for example, the problem x^2 - 4x + c=0, where you have to solve for c in the quadratic equation. The analysis category stresses more the deconstruction of the underlying concepts rather than the mathematical solution.
Demonstrate "synthesis" by synthesizing the algebraic knowledge you have acquired into a novel form. Associated key words for this category include "construct," "create" and "document." For example, you could synthesize algebraic concepts and problems into a word problem of your own creation.
Draw on the "evaluation" category by taking a step back and looking at algebra, and algebra projects, from a distance. Evaluate answers you have given for algebra problems (in algebra, check your solution for a variable by inputting its value back into the original equation).