**SCAN-IN {with pencil and paper} <Snorkeling>**

- Read the table of contents for the chapter and place the sequence of topics in your memory
- Go to the chapter in the text
- Sequentially: For each section, read and understand the section’s heading
- Skip to this section’s “SOLVED PROBLEMS” and “Supplementary Exercises” at the end of the chapter
- Read over each category and the types of problems that you will be expected to solve for this section
- Quickly read the “SOLVED PROBLEMS” and “Supplementary Exercises” and consider:
- The commonalities of the groups of problems
- The unique characteristics of individual problems

- The commonalities of the groups of problems
- Quickly skim-read over the section’s narrative
- Look at the material’s content, framework, and the dynamics of the calculations (they are called algorithms) {Note: By problem dynamic (or flow) I mean how the problem’s information is sequentially used, combined and calculated (i.e., derived) with various thought-tools to reach the correct answer
- Understand the main points of each subsection [leaving the finer points for the “Read” and “Intensely Study” phases]

- Repeat this entire process for each section until the chapter is complete

**READ-IN {with pencil and paper} <Deep Snorkeling>**

- Go to beginning of the chapter and read each section
- Understand the meaning and relationships between each major section and its minor sections
**Taking your time, read everything comfortably: text, graphics, formula staging, and complementary notes**- Read each section’s examples and solutions, making certain that you understand how each problem is solved
- Go to the “Solved Problems” at the end of the chapter that correspond to the section that you are reading
- Read the solved problems for your section. If anything seems unclear, go back to your reading and pencil in a big star with a question mark to remind you to concentrate on this area during the next two stages
- Go to the “Supplementary Exercises” at the end of the chapter that correspond to your current section.
- Classing the problems as “easy”, “medium”, and “challenging” try to solve one easy and one medium problem, noting any difficulties that you may encounter, in your notebook and with a “starred question mark lightly penciled in your book” for later clarification

- Repeat this entire process until the chapter is complete

**INTENSELY STUDY {with pencil and paper} <SCUBA diving>**

- Go to the beginning of the chapter and intensely read each section, understanding each phrase of each line of text
- Investigate and understand each new action in the mathematical formula in the order of occurrence
- Consider why and how each action was done
- Consider, in the back of your mind, how you can apply this principle, method, or tool in similar problems

- Investigate and understand each new action in the mathematical formula in the order of occurrence
- Go to the “SOLVED PROBLEMS” section at the end of the chapter that corresponds to your study area
- Study the solved problems so that you can do them yourself, without the book in front of you

- Test yourself with the “Supplementary Exercises” section that corresponds to your study area
- Try one “easy”, two “medium”, and three “challenging” problems for this section. Be prepared to hand these in to Courtney or Ernest on the following Saturday.

**READ-OUT {with pencil and paper} <Deep Snorkeling>**

- Go to beginning of the chapter and read each section
- Understand the meaning and relationships between each major section and its minor sections
**Taking your time, read everything comfortably:**text, graphics, formula staging, and complementary notes- Read each section’s examples and solutions, making certain that you understand how each problem is solved
- Go to the “Solved Problems” at the end of the chapter that correspond to the section that you are reading
- Read the solved problems for your section. If anything seems unclear, go back to your reading and pencil in a big star with a question mark to remind you to concentrate on this area during the next two stages
- Go to the “Supplementary Exercises” at the end of the chapter that correspond to your current section.
- Classing the problems as “easy”, “medium”, and “challenging” try to solve one easy and one medium problem, noting any difficulties that you may encounter, in your notebook and with a “starred question mark lightly penciled in your book” for later clarification

- Repeat this entire process until the chapter is complete

**SCAN-OUT {with pencil and paper} <Snorkeling>**

- Quickly read the table of contents for the chapter and place the sequence of topics in your memory
- Go to the chapter in the text
**Sequentially:**For each section, remember your understanding the section’s heading- Skip to this section’s “SOLVED PROBLEMS” and “Supplementary Exercises” at the end of the chapter
- Read over each category and the types of problems that you are expected to be able to solve for this section
**Quickly**read the “SOLVED PROBLEMS” and “Supplementary Exercises” and reinforce:- The commonalities of the groups of problems
- The unique characteristics of individual problems

- Quickly skim-read over the section’s narrative
- Review the material’s content, framework; and the dynamics of the calculations
- You now understand all of the major, minor, and miniscule points of each subsection

- Repeat this entire process for each section until the chapter is complete

**BACKGROUND -- BUILDING INTELLIGENCE:** We tend to learn in stages from notion to effective-&-efficient capability [e.g., from curiously watching the bird fly to knowingly designing and expertly flying the plane yourself].

Step 1 **Notional**

Step 2 **Conceptual**

Step 3 **Familiar**

Step 4 **Comprehensible**

Step 5 **Executable**

Step 6** Proficient **(assess, comprehend, approach, execute, verify, present)

[Practice, practice, practice! {Just like a musical instrument}]

Step 7 **Effective and Efficient** (perfection and speed)

[Practice, practice, practice! {Just like a musical instrument}]

Step 8 **Justifiably Confident**: Ready to “ace” college admission, achievement, and placement examinations!

**ALGEBRA AND TRIGONOMETRY PROBLEM SOLUTION APPROACH:**

**Step 1:** Notion: Carefully read and determine exactly what the problem asks.

**Step 2:** Concept: Recognize the type of problem and general solution alternatives

**Step 3:** Approach: Decide what thought tools & instruments (e.g., calculator, ruler, and/ or protractor) you may need to solve this type of problem__Pivot 1:__ Determine applicable algorithms {algorithm – the sequence of mathematical steps we use to solve a problem}__Pivot 2:__ Choose the most efficient algorithm__Pivot 3:__ Choose the correct tools & instruments__Pivot 4:__ Structure, configure, and sequence an intelligible solution

**Step 4:** Execution:** Neatly write **a traceable algorithm in a vertical sequence of comprehensible steps. Provide comments explaining each step on the right hand side of your work – short definitive phrases will suffice

**Step 5: **Verification: Verify that your solution is correctly calculated

**Step 6:** Presentation: Present the solution with a border and the label “Answer”.

Notion, Concept, Familiarity, Execution (capability), Proficiency (consistently correct), Efficiency (speed) & Confidence (no doubts about your abilities). [NCFEPEC]

Take one step at a time, in the correct direction:

- Use the supplementary problems to drive yourselves through this sequence for each type of problem.
- Speed is of little use, if you are making mistakes.
- Consistency is useless unless you are correct (i.e., Who wants to be consistently wrong?)
- Proficiency has no meaning unless you can execute the algorithm (i.e., start, perform, complete, and present the solutions to the problems).
- Addressing an unfamiliar concept usually leads to the use of a more challenging algorithm that, in turn leads to the wrong answer, or takes too long to get the answer.
- Without a sound notion and conception of a problem and its solution, you are lost in a dark and dangerous forest, at midnight, without the moon or start to guide you safely home.