Algebra has several topics - We can break them into smaller units – For Example, this is how a tutorial for Equations may look like.

Level 1. Test for Knowledge - Say Equations - This test uses bloom's verbs to construct question that test prior knowledge - theory questions on linear equations. Define a linear equation??

Level 2. Test of Comprehension - Ability to use prior knowledge + Comprehend new information- Here we add tutorials that explain all types of Equations with examples. The task here is whether the student can comprehend this new material. So there needs to be a test, again using bloom’s verbs.

Level 3. Test of Application - Ability to apply the theory from Levels 1 and 2.

Example : A child has a total of 75 coins comprising $1 and $2 coins. If the total value of the money with the child is $95, how many more $1 coins does the child have?

A successful student needs to be able to tell that this problem can be solved using a linear equation.

Level 3 can have 5 questions on each equation type as described in the example above.

Level 4-6 Test of Analysis, Synthesis and Evaluation (Problem Solving skills)

This levels test the ability to solve previously unseen questions in a timed environment.

We will introduce a Data Sufficiency Question or a Problem Solving question. We introduce the the Polya Method - Understand, Plan, Solve, Evaluate

1. Students who study history must study geography, but cannot study science; students can

study geography and science. If 22 students study history, 40 study geography, 42 study

science, and 16 study both geography and science, how many students study at least one

of these three subjects?

a. 60

b. 58

c. 74

d. 72

e. 66

This question tests your ability to develop linear equations and solve them simultaneously.

Some more info - http://problemsolving.engin.umich.edu/open/blooms/index.htm