SAT Prep lesson 5&6

SAT Prep for Advanced ESL Students: Lesson 5 - Math Problem-Solving Strategies

Introduction

Welcome to Lesson 5 of our SAT prep series! In this session, we will focus on enhancing your math problem-solving skills. The SAT math section can be challenging, but with the right strategies, you can tackle even the toughest problems with confidence. We will explore key concepts, practice problem-solving techniques, and work through sample questions to boost your math skills.

Objectives

By the end of this lesson, you will:

• Understand the format and types of questions on the SAT math section.

• Learn effective problem-solving strategies for different question types.

• Practice solving sample SAT math problems with confidence.

• Develop techniques to manage your time effectively during the test.

Warm-Up Activity

Start with a quick math challenge! Solve the following problem within 5 minutes:

Problem:A rectangular garden has a length of 12 meters and a width of 8 meters. If a path of uniform width is constructed around the garden, reducing the area of the garden by 50 square meters, what is the width of the path?

Your Task:

• Write down your solution steps and final answer.

Understanding the SAT Math Section

The SAT math section consists of two main parts: Math Test – No Calculator and Math Test – Calculator Allowed. Here’s a breakdown of what you need to know:

1. Question Types

• Heart of Algebra: Linear equations, inequalities, and systems of equations.

• Problem Solving and Data Analysis: Ratios, percentages, probability, and data interpretation.

• Passport to Advanced Math: Quadratic equations, functions, and complex equations.

• Additional Topics in Math: Geometry, trigonometry, and complex numbers.

1. Format and Scoring

• Total Questions: 58 questions (45 in the No Calculator section, 13 in the Calculator section).

• Time Limit: 80 minutes for both sections combined.

• Scoring: Questions are scored based on the number of correct answers. There is no penalty for wrong answers, so guess if you’re unsure!

Problem-Solving Strategies

Let’s explore some effective strategies for tackling SAT math problems:

1. Understand the Problem

• Read the question carefully.

• Identify what is being asked and the information given.

1. Plan Your Approach

• Decide on the best method to solve the problem (e.g., algebraic manipulation, drawing diagrams, or using logical reasoning).

• Write down key equations or steps.

1. Solve Step-by-Step

• Work through the problem methodically.

• Check your calculations and ensure all steps are clear and logical.

1. Review Your Answer

• Verify that your answer makes sense in the context of the problem.

• Check for any mistakes or missed details.

Practice Activity: Solving Sample Problems

Let’s apply these strategies with some sample SAT math questions. Follow these steps:

1. Read the Problem Carefully: Understand what is being asked.

2. Choose a Strategy: Decide on the best method to solve the problem.

3. Solve Step-by-Step: Work through the problem and show all your steps.

Sample Problem 1:

Question:A triangle has angles in the ratio 3:4:5. What are the measures of the angles?

Options:

• a) 30°, 40°, 50°

• b) 45°, 60°, 75°

• c) 36°, 48°, 96°

• d) 36°, 54°, 90°

Solution Steps:

1. Let the angles be 3x3x3x, 4x4x4x, and 5x5x5x.

2. The sum of angles in a triangle is 180∘180^\circ180∘: 3x+4x+5x=1803x + 4x + 5x = 1803x+4x+5x=180

3. Solve for xxx: 12x=180  ⟹  x=1512x = 180 \implies x = 1512x=180⟹x=15

4. Calculate the angles: 3x=45∘,4x=60∘,5x=75∘3x = 45^\circ, \quad 4x = 60^\circ, \quad 5x = 75^\circ3x=45∘,4x=60∘,5x=75∘

Answer: b) 45°, 60°, 75°

Sample Problem 2:

Question:A rectangular prism has a volume of 216 cubic centimeters. If its length is 6 cm and its width is 9 cm, what is the height of the prism?

Options:

• a) 3 cm

• b) 4 cm

• c) 5 cm

• d) 6 cm

Solution Steps:

1. Use the volume formula for a rectangular prism: V=l×w×hV = l \times w \times hV=l×w×h.

2. Substitute the known values: 216=6×9×h216 = 6 \times 9 \times h216=6×9×h

3. Solve for hhh: 54h=216  ⟹  h=21654=454h = 216 \implies h = \frac{216}{54} = 454h=216⟹h=54216​=4

Answer: b) 4 cm

Vocabulary in Context

Understanding key math vocabulary is crucial. Let’s discuss some terms from the problems:

1. Ratio (noun): A relationship between two numbers indicating how many times one value contains or is contained within the other.

2. Volume (noun): The amount of space occupied by a three-dimensional object, measured in cubic units.

3. Prism (noun): A solid geometric figure with two identical ends and flat sides.

Activity: Use each term in a sentence related to the problems.

Practice Questions

Apply the problem-solving strategies to these sample SAT math questions:

1. Question:The area of a circle is 36π36\pi36π square inches. What is the radius of the circle?

• a) 3 inches

• b) 6 inches

• c) 9 inches

• d) 12 inches

1. Question:If x2+6x+9=0x^2 + 6x + 9 = 0x2+6x+9=0, what is the value of xxx?

• a) -3

• b) 3

• c) -6

• d) 6

Discussion and Review

Discuss your answers with a partner or in a group. Share your solution methods and reasoning. Provide feedback to each other, focusing on clarity, strategy, and problem-solving approaches.

Homework Assignment

For homework, solve the following problems and prepare to discuss your solutions in the next class:

1. Problem 1:A triangle has angles in the ratio 2:3:4. What are the measures of the angles?

2. Problem 2:A cylinder has a radius of 5 cm and a height of 12 cm. What is its volume? Use π≈3.14\pi \approx 3.14π≈3.14.

Conclusion

Mastering math problem-solving strategies is essential for the SAT. By understanding the question, planning your approach, solving step-by-step, and reviewing your answers, you can tackle any math problem with confidence. Keep practicing these strategies, and you’ll be well-prepared for the math section of the SAT.

Stay tuned for Lesson 6, where we will focus on improving your reading comprehension and essay writing skills. Keep up the great work, and happy studying!

Additional Resources

• Khan Academy SAT Math Practice

• College Board SAT Math Practice

• SAT prep books and online math exercises

You’re making great progress! See you in the next lesson!

SAT Prep for Advanced ESL Students: Lesson 6 - Advanced Reading Comprehension and Essay Writing

Introduction

Welcome to Lesson 6 of our SAT prep series! In this session, we will dive into advanced reading comprehension strategies and essay writing techniques. We will explore how to analyze complex texts, develop compelling arguments, and write clearly and effectively. These skills are crucial for the reading and writing sections of the SAT, so let’s get started!

Objectives

By the end of this lesson, you will:

• Master advanced reading comprehension strategies for complex texts.

• Learn how to analyze and critique passages effectively.

• Develop techniques for writing well-structured, persuasive essays.

• Practice responding to sample SAT reading and essay prompts with confidence.

Warm-Up Activity

Start with a quick reading exercise. Read the following short passage and write a brief summary:

Passage:"In recent decades, the debate over the impact of technology on society has intensified. While some argue that technology has improved quality of life by increasing efficiency and connectivity, others contend that it has led to a decline in social skills and mental health. The rise of social media and digital communication has changed how people interact, often reducing face-to-face interactions and increasing feelings of isolation. As technology continues to evolve, it is essential to consider both its benefits and drawbacks to find a balanced approach that enhances human well-being."

Your Task:

• Write a summary of the main points in one paragraph.

Advanced Reading Comprehension Strategies

To excel in the reading section, you need to master these advanced strategies:

1. Critical Reading

• Analyze the Author’s Argument: Look for the thesis, evidence, and reasoning. Evaluate the strength and relevance of the arguments presented.

• Understand the Context: Consider the historical, cultural, or social context of the passage. This can provide deeper insight into the author’s perspective

and purpose.

1. Identify Key Details

• Main Ideas vs. Supporting Details: Distinguish between the central arguments and the supporting evidence or examples.

• Highlight Key Points: Mark important sentences and phrases that summarize the main ideas or provide crucial evidence.

1. Infer Meaning

• Context Clues: Use the surrounding text to infer the meaning of unfamiliar words or phrases.

• Read Between the Lines: Look for implied meanings and unstated assumptions.

1. Synthesize Information

• Connect Ideas: Relate information from different parts of the passage to form a comprehensive understanding.

• Summarize and Paraphrase: Practice summarizing paragraphs in your own words to reinforce understanding.

Practice Activity: Analyzing a Complex Passage

Let’s apply these strategies to a sample reading passage. Follow these steps:

1. Read the Passage Carefully: Take your time to understand the text.

2. Identify the Main Idea: What is the author’s primary argument?

3. Highlight Key Details: Mark important points and evidence.

4. Infer and Synthesize: Make connections and draw conclusions from the text.

Sample Passage:

"The rapid advancement of artificial intelligence (AI) is reshaping industries and societies around the globe. Proponents argue that AI has the potential to revolutionize healthcare, education, and transportation, leading to unprecedented efficiency and innovation. However, critics warn of the potential risks, including job displacement, ethical concerns, and the exacerbation of social inequalities. As AI technology continues to evolve, it is crucial to develop robust policies and regulations that ensure its benefits are widely shared and its risks mitigated."

Your Task:

• Identify the main argument of the passage.

• List two key details that support the argument.

• Infer one potential unstated concern about AI that the author might have.

Essay Writing Techniques

Writing a well-structured, persuasive essay is a key skill for the SAT. Follow these steps to craft an effective essay:

1. Understand the Prompt

• Carefully read the essay prompt.

• Identify the task: Are you asked to analyze, argue, or describe?

1. Plan Your Essay

• Introduction: Briefly introduce the topic and state your thesis or main argument.

• Body Paragraphs: Each paragraph should focus on a single point, supported by evidence and examples.

• Conclusion: Summarize your main points and restate your thesis in a new way.

1. Develop Your Argument

• Use Clear Topic Sentences: Start each paragraph with a clear statement of the point you’re making.

• Incorporate Evidence: Use quotes, data, and examples to support your argument.

• Analyze and Explain: Don’t just present evidence—explain how it supports your argument.

1. Revise and Edit

• Check for Clarity and Coherence: Ensure your essay flows logically from one point to the next.

• Proofread for Grammar and Spelling: Correct any errors to improve readability.

Practice Activity: Responding to an Essay Prompt

Let’s practice writing an essay based on a sample prompt. Follow these steps:

1. Read the Prompt Carefully: Understand what is being asked.

2. Outline Your Essay: Plan your introduction, body paragraphs, and conclusion.

Sample Essay Prompt:

"Read the following passage and analyze how the author builds an argument to persuade the audience. Discuss the use of evidence, reasoning, and stylistic or persuasive elements."

Passage:

"In a world increasingly dominated by technology, it is essential to consider its impact on our daily lives. While technology offers numerous benefits, including improved communication and access to information, it also poses significant challenges. One major concern is the potential loss of privacy, as personal data is collected and shared without consent. Additionally, the reliance on digital devices can lead to decreased face-to-face interactions, affecting social skills and relationships. To harness the benefits of technology while mitigating its drawbacks, we must adopt a balanced approach that prioritizes both innovation and ethical considerations."

Writing Your Essay

Introduction:

• Introduce the topic of technology’s impact on daily life.

• State your thesis: The author argues for a balanced approach to technology, highlighting both benefits and challenges.

Body Paragraphs:

1. First Point: The benefits of technology in communication and information access.

• Evidence: Mention specific examples or statistics from the passage.

• Analysis: Explain how these benefits improve daily life.

1. Second Point: The challenges of privacy and data security.

• Evidence: Reference details or quotes from the passage.

• Analysis: Discuss the implications of privacy loss and the need for ethical considerations.

1. Third Point: The impact of technology on social interactions.

• Evidence: Highlight any evidence or examples provided in the passage.

• Analysis: Analyze how decreased face-to-face interactions affect social skills and relationships.

Conclusion:

• Summarize your main points and restate your thesis.

• Emphasize the importance of a balanced approach to technology.

Practice Questions

Let’s test your understanding with some sample questions:

1. How does the author use evidence to support the argument in the passage?

• a) By presenting opposing views

• b) Through anecdotal stories

• c) By citing examples of technology’s benefits and challenges

• d) By describing historical trends

1. Which of the following best describes the author’s tone in the passage?

• a) Indifferent

• b) Persuasive and balanced

• c) Critical and dismissive

• d) Formal and academic

1. What is the primary purpose of the passage?

• a) To entertain readers with stories about technology

• b) To argue for a balanced approach to technology use

• c) To provide a historical account of technological advancements

• d) To criticize current technological practices

Discussion and Review

Discuss your essay with a partner or in a group. Share your thesis, main points, and any challenges you faced while writing. Provide feedback to each other, focusing on clarity, argument strength, and use of evidence.

Homework Assignment

For homework, write an essay responding to the following prompt:

Prompt:"Read the following passage and analyze how the author builds an argument to persuade the audience. Discuss the use of evidence, reasoning, and stylistic or persuasive elements."

Passage:

"Climate change is one of the most pressing issues of our time, demanding immediate and sustained action. The increasing frequency of extreme weather events, rising sea levels, and shifting ecosystems are clear indicators of a changing climate. Scientists agree that human activities, particularly the burning of fossil fuels, are the primary drivers of these changes. To address this crisis, we must transition to renewable energy sources, implement energy-efficient practices, and support policies that reduce carbon emissions. Collective action at both individual and governmental levels is essential to mitigate the impacts of climate change and ensure a sustainable future for generations to come."

Conclusion

Advanced reading comprehension and essay writing skills are crucial for the SAT. By mastering critical reading strategies, planning your essays effectively, and practicing your writing, you can excel in these sections. Keep honing these skills, and you’ll be well-prepared for the test.

Stay tuned for the next lesson, where we will continue to build on these skills and explore new strategies. Keep up the great work, and happy studying!