Guided Practice
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The Purpose of Guided Practice
Guided practice bridges the gap between learning concepts and applying them independently. In this lesson, you will work through representative questions with explicit step-by-step reasoning. The goal is to internalize the problem-solving process so you can replicate it on test day.
The Four-Step Problem-Solving Framework
Step 1: Understand the Question
- Read the question carefully before looking at answer choices
- Identify what the question is asking for
- Note any constraints or conditions
- Underline or circle key information
Step 2: Plan Your Approach
- Determine which concept or skill is being tested
- Recall relevant formulas, rules, or strategies
- Estimate what a reasonable answer might look like
- Decide whether to solve directly or use answer choices
Step 3: Execute Your Plan
- Work through the problem systematically
- Show your work to avoid careless errors
- Check each step before moving to the next
- Use scratch paper effectively
Step 4: Verify Your Answer
- Re-read the question to confirm you answered what was asked
- Check that your answer is reasonable
- If time permits, verify by substitution or alternative method
- Make sure you have not fallen for common traps
Time Management in Guided Practice
When practicing, track how long each question takes. Your goal is to build accuracy first, then speed. As you become more comfortable with question types, your pace will naturally improve.
Examples
Guided Example 1: Reading Comprehension
Passage excerpt: "The author argues that urban green spaces provide not only environmental benefits but also significant improvements to community mental health. Studies cited in the passage show a 23% reduction in reported stress levels among residents living within 500 meters of a park."
Question: Based on the passage, which statement best describes the relationship between urban parks and mental health?
(A) Urban parks are the primary cause of reduced stress.
(B) Proximity to green spaces correlates with lower reported stress.
(C) All residents benefit equally from urban parks.
(D) Environmental benefits are more important than mental health benefits.
Step-by-Step Solution:
Step 1 - Understand: The question asks about the relationship between parks and mental health as described in the passage.
Step 2 - Plan: Look for direct evidence in the passage. Avoid choices that go beyond what is stated.
Step 3 - Execute: The passage states "23% reduction in reported stress levels among residents living within 500 meters of a park." This shows correlation based on proximity.
Step 4 - Verify: (A) says "primary cause" - too strong. (C) says "equally" - not supported. (D) contradicts the passage. (B) accurately reflects the data.
Answer: (B)
Guided Example 2: Algebra Problem
Question: If 3x + 7 = 22, what is the value of 6x + 14?
Step-by-Step Solution:
Step 1 - Understand: We need to find the value of 6x + 14, given an equation with x.
Step 2 - Plan: Notice that 6x + 14 = 2(3x + 7). This is a shortcut! We could also solve for x first.
Step 3 - Execute: Since 3x + 7 = 22, then 2(3x + 7) = 2(22) = 44.
Step 4 - Verify: Check by solving for x: 3x = 15, so x = 5. Then 6(5) + 14 = 30 + 14 = 44. Confirmed!
Answer: 44
Guided Example 3: Grammar Question
Original: "The orchestra, along with the choir, are performing at the ceremony tonight."
Question: Which is the correct verb form?
(A) NO CHANGE
(B) is performing
(C) were performing
(D) have been performing
Step-by-Step Solution:
Step 1 - Understand: This is a subject-verb agreement question. The phrase "along with the choir" is a parenthetical element.
Step 2 - Plan: Identify the true subject. Phrases like "along with," "as well as," and "together with" do not change the number of the subject.
Step 3 - Execute: The subject is "orchestra" (singular). The verb must be singular: "is performing."
Step 4 - Verify: Remove the parenthetical: "The orchestra is performing at the ceremony tonight." This sounds correct.
Answer: (B)
Practice
Apply the four-step framework to these practice problems.
1. If 2y - 5 = 13, what is the value of 4y - 10?
Show Answer
Solution: Notice 4y - 10 = 2(2y - 5) = 2(13) = 26. Verification: 2y = 18, y = 9. Then 4(9) - 10 = 36 - 10 = 26.
2. A passage states: "Solar energy adoption has increased by 40% over the past decade, though initial installation costs remain a barrier for many homeowners." Which conclusion is best supported?
Show Answer
Best supported: Solar energy is growing in popularity despite cost obstacles. The passage shows growth (40% increase) but also acknowledges a limitation (cost barrier). Avoid conclusions that ignore either part of this balanced statement.
3. "The committee have decided to postpone the vote." Is this sentence correct in American English?
Show Answer
In American English, collective nouns like "committee" typically take singular verbs: "The committee has decided to postpone the vote." British English may use plural verbs with collective nouns.
4. A store sells notebooks for $3 each. With a 20% discount, how much would 5 notebooks cost?
Show Answer
Solution: Full price = 5 x $3 = $15. Discount = 20% of $15 = $3. Final price = $15 - $3 = $12.
5. "Despite the team's hard work, however, they still lost the game." What is wrong with this sentence?
Show Answer
The sentence contains redundant contrast words. "Despite" already indicates contrast, so "however" is unnecessary. Correct: "Despite the team's hard work, they still lost the game."
6. If the average of 5 numbers is 12, what is their sum?
Show Answer
Solution: Average = Sum / Count. So Sum = Average x Count = 12 x 5 = 60.
7. An author writes: "Critics dismissed the novel as pretentious, but readers embraced its unconventional narrative structure." What is the author's purpose?
Show Answer
The author's purpose is to contrast critical reception with popular reception. The "but" signals opposition between the critics' negative view and readers' positive response.
8. Simplify: 3(x + 4) - 2(x - 1)
Show Answer
Solution: 3x + 12 - 2x + 2 = x + 14. Be careful with the negative sign distributing to both terms in the second parentheses.
9. "The data suggests that exercise improves cognitive function." Is "suggests" or "suggest" correct?
Show Answer
Both can be correct depending on context. In American English, "data" is increasingly treated as singular: "The data suggests..." In scientific writing, "data" is often plural: "The data suggest..." The SAT/ACT generally accept "data suggests."
10. A car travels 150 miles in 3 hours. At this rate, how long will it take to travel 250 miles?
Show Answer
Solution: Rate = 150/3 = 50 mph. Time = Distance/Rate = 250/50 = 5 hours.
Check Your Understanding
Answer these questions to verify your mastery of the key concepts.
- Can you apply the four-step problem-solving framework consistently?
- Can you recognize patterns that allow shortcuts (like factoring out common terms)?
- Can you distinguish between what a passage states and what it implies?
- Can you identify and avoid common answer choice traps?
- Can you verify your answers using alternative methods?
If you answered "no" to any of these questions, review the corresponding section before moving on.
Next Steps
- Practice applying the four-step framework until it becomes automatic
- Time yourself on practice problems to build pacing awareness
- Move on to Review Your Mistakes to learn from errors