# Algebra II and Trigonometry Resources

## Five Level Study Method

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

• Go to the chapter in the text
• 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
• 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
• 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>

• Go to the chapter in the text
• 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

## Algebra II Problem Solving Method

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:

1. Use the supplementary problems to drive yourselves through this sequence for each type of problem.
2. Speed is of little use, if you are making mistakes.
3. Consistency is useless unless you are correct (i.e., Who wants to be consistently wrong?)
4. Proficiency has no meaning unless you can execute the algorithm (i.e., start, perform, complete, and present the solutions to the problems).
5. 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.
6. 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.