Given its many inbound and outbound interconnections with other resources, the 1600.io Digital SAT Math Orange Book can be used in several different ways as part of a structured math learning cycle. The most useful approaches are enumerated below.

Practice Test-Driven Learning Cycle:

A practice test-driven SAT Math learning cycle centers on the periodic taking of practice test sections. This is probably the most common approach used by both self-studiers and tutored students, as it is easily understood, provides progress tracking as a side-effect of taking tests periodically, and it's reasonably satisfying. 1600.io provides several potent resources that can be used to power this approach.

1. The student takes a practice math section from a released SAT and enters their answers into the corresponding Autoscoring Answer Form (AAF). If the student chooses not to use the AAF, and to score themselves manually, they can use the following procedure and then skip to step 5:
   1. The student launches our SAT Math Topic Explorer (SMTEx) and selects the test and section (calculator or no calculator). For each problem that requires additional learning, the student selects the test, section
2. The student submits their answer form, which is instantly scored for them.
3. The on-screen score report, in addition to showing the raw score and the scoring for each problem in the section, provides instant access to a video explanation for every problem, allowing the student to understand how the problem could be approached and solved.
4. The AAF score report also displays the precise topic(s) and sub-topic(s) that pertain to each problem. For a deeper understanding, the student can click a button to see the problem displayed in our SAT Math Topic Explorer (SMTEx), which will open with that problem preselected, showing a pie chart breakdown of how frequently similar problems have appeared on the SAT; this helps students understand the relative importance of mastering the relevant skills.
5. SMTEx offers two paths forward for skills improvement:
   1. A list is displayed of every problem from every released SAT that uses the same concepts and techniques as does the selected problem. Students can use this information to work additional real-test problems to reinforce their understanding and skills. SMTEx provides a direct link from each listed problem to the video explanation for that problem, so students can instantly check their understanding.
   2. If the student wants instruction on the topic(s) for the selected problem, with one click SMTEx will open the Digital SAT Math Orange Book to the exact page where the concept is explained. The student can then learn the concepts and techniques needed to solve that type of problem, and at the end of the explanatory text, they have the opportunity to work a set of original practice problems to check their learning and reinforce their new skills. Answers to these section quizzes can be entered into AAFs that can be opened simply by clicking a problem set's title. If the student wants additional practice, there is a large set of practice problems at the end of each chapter, also with an AAF just one click away. Every practice problem in the book has a set of explanatory tools in the Answer Bar atop the problem statement; students who need help can watch a video, read a pop-up written explanation, or open an interactive graph that demonstrates the concepts and shows how to arrive at the solution.
6. Once the student has utilized these various learning paths, and they have elevated their skills in the areas where they struggled on the diagnostic math section that started the cycle, they are ready to take another diagnostic math section to start the cycle once again.

Topic-Driven Learning Process:

Rather than rely on iterative use of diagnostic tests, the topic-driven learning process relies on a student or tutor to have a good grasp on the student's areas of weakness, so a prioritized itemization of those skills is made at the outset of the process (SMTEx can help with deciding the relative importance of the various skills).

1. The student looks up a math topic in the Digital SAT Math Orange Book and reads the instructional materials and follows the hyperlinks to expanded explanations, working any SkillDrills that are presented along the way; the SkillDrill video explanations help support this activity.
2. The student works the problems in the sub-topic problem sets and, if appropriate, the large chapter problem set is also worked. The student can click on the titles of those problem sets to open the appropriate AAFs to make scoring simple.
3. For any problems that gave the student trouble, they can use the tools in the Answer Bar above each problem to watch a video explanation, read a written solution, or interact with a graph.
4. If the student would like additional practice, they can click on the SMTEx link at the end of any sub-topic section, or they can click on any section or sub-section title, to open SMTEx to the relevant topic/sub-topic; SMTEx will display a list of every real-test problem that relates to the selected concepts. Students can use that listing as a source of additional exercise for the concepts they have been studying.

Comprehensive SAT Math Curriculum Approach:

For students who are generally weak in the math concepts and techniques within the scope of the SAT, or for students who are striving for very high math scores and who have the time and dedication to devote to that pursuit, a methodical, exhaustive use of the Orange Book can be optimal. In this model, the student works through the entire book, cover to cover.

1. The student reads the explanatory material in the current chapter, working through all the SkillDrills and watching the accompanying videos as needed to ensure understanding, and following the hyperlinks to expanded explanations.
2. The student works the problems in each sub-topic problem set and in the large chapter problem set. The student can click on the titles of those problem sets to open the appropriate AAFs to make scoring simple.
3. For any problems that gave the student trouble, they can use the tools in the Answer Bar above each problem to watch a video explanation, read a written solution, or interact with a graph.
4. If the student would like additional practice, they can click on the SMTEx link at the end of any sub-topic section, or they can click on any section or sub-section title, to open SMTEx to the relevant topic/sub-topic; SMTEx will display a list of every real-test problem that relates to the selected concepts. Students can use that listing as a source of additional exercise for the concepts they have been studying.

Students can punctuate this process with occasional assessments through practice test sections, but many students prefer to attack the math without interruption before engaging in test-based self-diagnostic activities to find gaps.