how to present math in different angles which represents depth of subject,easiness,empowerment,basics,logic,analyze,view of subject from back,view from front.Give multiple e.g.s .(just 11th & 12th)

5/6=1/3-x please solve

i deposit 1,000 for 4 years a rate 2% nthe compounded annually how much money after 4years

Alice had an ending balance of $546.78, outstanding deposits totaling $412.39, and outstanding checks totaling $872.63. How much additional money does she need in her account to pay the telephone bill, which is $148.19?

To effectively present math from different angles that represent depth, easiness, empowerment, basics, logic, analysis, and various viewpoints, you can use the following strategies and examples for 11th and 12th-grade mathematics:

1. Depth of Subject: Introduce advanced concepts by linking them to real-world applications or historical contexts. For example, when teaching calculus, you could explain how Newton developed this branch of mathematics to describe the motion of planets.

2. Easiness: Break down complex topics into simpler step-by-step explanations and use visual aids. For instance, when teaching trigonometry, use diagrams and animations to demonstrate the relationships between angles and sides of triangles.

3. Empowerment: Encourage students to explore mathematical concepts independently by providing challenging problems and additional resources. For example, assign open-ended project work that allows students to apply their knowledge creatively.

4. Basics: Reinforce fundamental concepts by relating them to everyday situations. When teaching algebra, use examples such as calculating expenses or solving problems related to proportions and percentages.

5. Logic: Emphasize the logical reasoning behind mathematical concepts. One example is teaching the laws of logic and proof techniques, which are essential in disciplines like geometry or discrete mathematics.

6. Analysis: Teach students to analyze mathematical problems by providing opportunities for critical thinking. For instance, assign problems that require students to analyze patterns, make conjectures, and justify their solutions.

7. View of Subject from Back: Show the historical progression and development of the subject. For instance, when teaching geometry, highlight the contributions of ancient mathematicians like Euclid and explain how their insights shaped the subject.

8. View from Front: Present cutting-edge research and applications in mathematics to pique students' curiosity. For example, discuss how mathematicians use probability theory in fields like machine learning or finance.

9. Example for 11th grade: When teaching quadratic equations, compare them to real-world scenarios, such as modeling projectile motion or designing bridges.

10. Example for 12th grade: When teaching calculus, demonstrate how it is applied in physics to analyze motion, acceleration, and optimization problems.

11. Another example for 12th grade: In statistics, introduce the concept of hypothesis testing by analyzing survey data or conducting experiments.

By incorporating these strategies and examples, you can present math from multiple angles that cater to different learning styles and aspects of the subject, making it more engaging and comprehensive for students.