Content review: Find the Boundary
Status: Published — approved by the creator. Mastery threshold 80% (provisional).
Checkpoint 1 of 6
Find the included boundary
The number line shows the inequality; in this context, guests must be nonnegative whole numbers.
Input : → Output :
From original
- Title, wording, choices, answer key
- Hint (checkpoints 1–4)
- Generic correct / “Not yet” feedback; Checkpoint 4 cost feedback
⚠ Reconstructed — needs approval
- Choice-specific wrong-answer feedback and misconception tags
- Checkpoint 2 split into four separate matches
- Checkpoint 5: retries allowed after the first attempt (creator decision)
Step 1 · Which number line represents x ≤ 5?
You may bring no more than 5 guests. Let x be the number of guests. Which number line represents x ≤ 5?
- A. Number line: open circle at 5, shaded left
- B. Number line: closed circle at 5, shaded left ✓
- C. Number line: closed circle at 5, shaded right
- D. Number line: open circle at 5, shaded right
Answer: Number line: closed circle at 5, shaded left
✓ Correct: Correct. Continue when you are ready.
✗ If A: The shading is right, but an open circle leaves out 5. “No more than 5” allows exactly 5 guests.
✗ If C: The circle is closed, but the shading goes the wrong way. “No more than” means 5 or fewer.
✗ If D: Both parts need another look: “no more than 5” includes 5 (closed circle) and smaller values (shade left).
Checkpoint 2 of 6
Read the inequality words
Match each phrase to its symbol.
Input : → Output :
From original
- Title, wording, choices, answer key
- Hint (checkpoints 1–4)
- Generic correct / “Not yet” feedback; Checkpoint 4 cost feedback
⚠ Reconstructed — needs approval
- Choice-specific wrong-answer feedback and misconception tags
- Checkpoint 2 split into four separate matches
- Checkpoint 5: retries allowed after the first attempt (creator decision)
Step 1 · No more than
Match “No more than” to its symbol.
- A. <
- B. ≤ ✓
- C. >
- D. ≥
Answer: ≤
✓ Correct: Correct. Continue when you are ready.
✗ If A: Check whether “no more than” includes the boundary number itself.
✗ If C: Check the direction: does “no more than” allow larger or smaller values?
✗ If D: Check the direction: does “no more than” allow larger or smaller values?
Step 2 · At least
Match “At least” to its symbol.
- A. <
- B. ≤
- C. >
- D. ≥ ✓
Answer: ≥
✓ Correct: Correct. Continue when you are ready.
✗ If A: Check the direction: does “at least” allow larger or smaller values?
✗ If B: Check the direction: does “at least” allow larger or smaller values?
✗ If C: Check whether “at least” includes the boundary number itself.
Step 3 · Fewer than
Match “Fewer than” to its symbol.
- A. < ✓
- B. ≤
- C. >
- D. ≥
Answer: <
✓ Correct: Correct. Continue when you are ready.
✗ If B: Check whether “fewer than” includes the boundary number itself.
✗ If C: Check the direction: does “fewer than” allow larger or smaller values?
✗ If D: Check the direction: does “fewer than” allow larger or smaller values?
Step 4 · More than
Match “More than” to its symbol.
- A. <
- B. ≤
- C. > ✓
- D. ≥
Answer: >
✓ Correct: Correct. Continue when you are ready.
✗ If A: Check the direction: does “more than” allow larger or smaller values?
✗ If B: Check the direction: does “more than” allow larger or smaller values?
✗ If D: Check whether “more than” includes the boundary number itself.
Checkpoint 3 of 6
Change the constraint
A concert venue expects at least 500 people to attend. Let p be the number of people.
Input : → Output :
From original
- Title, wording, choices, answer key
- Hint (checkpoints 1–4)
- Generic correct / “Not yet” feedback; Checkpoint 4 cost feedback
⚠ Reconstructed — needs approval
- Choice-specific wrong-answer feedback and misconception tags
- Checkpoint 2 split into four separate matches
- Checkpoint 5: retries allowed after the first attempt (creator decision)
Step 1 · Attendance constraint
A concert venue expects at least 500 people to attend. Let p be the number of people. Which inequality matches that expectation?
- A. p ≤ 500
- B. p > 500
- C. p ≥ 500 ✓
- D. p < 500
Answer: p ≥ 500
✓ Correct: Correct. Continue when you are ready.
✗ If A: “At least 500” is a minimum, so p can be 500 or larger.
✗ If B: “At least” includes 500 itself.
✗ If D: “At least 500” is a minimum: 500 and larger numbers.
Checkpoint 4 of 6
Test the landscaping plan
A landscaping team budgets $3,000. Each tree costs $15 and each bag of grass seed costs $3. Let t be trees and g be bags.
Input : → Output :
From original
- Title, wording, choices, answer key
- Hint (checkpoints 1–4)
- Generic correct / “Not yet” feedback; Checkpoint 4 cost feedback
⚠ Reconstructed — needs approval
- Choice-specific wrong-answer feedback and misconception tags
- Checkpoint 2 split into four separate matches
- Checkpoint 5: retries allowed after the first attempt (creator decision)
Step 1 · Does (100, 200) satisfy the budget?
Does (100, 200) satisfy the budget?
- A. Yes ✓
- B. No
Answer: Yes
✓ Correct: Correct. Continue when you are ready.
✗ If B: Check the costs: (100, 200) costs $2,100, which is within $3,000. (600, 200) costs $9,600, which exceeds $3,000.
Step 2 · Does (600, 200) satisfy the budget?
Does (600, 200) satisfy the budget?
- A. Yes
- B. No ✓
Answer: No
✓ Correct: Correct. Continue when you are ready.
✗ If A: Check the costs: (100, 200) costs $2,100, which is within $3,000. (600, 200) costs $9,600, which exceeds $3,000.
Checkpoint 5 of 6
On your own: write the constraint
On your own · no hints. Tickets cost $5 for students and $10 for adults. A group can spend no more than $200. Let x be student tickets and y be adult tickets. Assume nonnegative whole-number ticket counts. Your first answer counts toward first-try accuracy; you may retry after it. This is practice — the final mastery check comes later.
Input : → Output :
From original
- Title, wording, choices, answer key
- Hint (checkpoints 1–4)
- Generic correct / “Not yet” feedback; Checkpoint 4 cost feedback
⚠ Reconstructed — needs approval
- Choice-specific wrong-answer feedback and misconception tags
- Checkpoint 2 split into four separate matches
- Checkpoint 5: retries allowed after the first attempt (creator decision)
Step 1 · 1. Choose the constraint
Choose the constraint.
- A. 5x + 10y ≥ 200
- B. 5x + 10y < 200
- C. 5x + 10y ≤ 200 ✓
- D. 10x + 5y ≤ 200
Answer: 5x + 10y ≤ 200
✓ Correct: Correct. Continue when you are ready.
✗ If A: “No more than $200” is a maximum, so the total must be at most 200.
✗ If B: “No more than $200” allows spending exactly $200.
✗ If D: Check which price goes with which variable: x is student tickets ($5), y is adult tickets ($10).
Step 2 · 2. Choose the boundary equation
Choose the boundary equation.
- A. 5x + 10y = 200 ✓
- B. 5x + 10y = 0
- C. x + y = 200
- D. 10x + 5y = 200
Answer: 5x + 10y = 200
✓ Correct: Correct. Continue when you are ready.
✗ If B: The boundary uses the same total as the constraint: replace ≤ with =, keeping 200.
✗ If C: The boundary keeps the costs: 5 per student ticket and 10 per adult ticket.
✗ If D: Check which price goes with which variable.
Step 3 · 3. Can the group buy 20 student tickets and 4 adult tickets?
Can the group buy 20 student tickets and 4 adult tickets?
- A. Yes ✓
- B. No
Answer: Yes
✓ Correct: Correct. Continue when you are ready.
✗ If B: Substitute: 5(20) + 10(4) = 100 + 40 = 140. Is $140 within the $200 limit?
Step 4 · Explain your choices
Explain how the costs and the spending limit support your choices.
Answer: Written explanation — saved for teacher review, not auto-scored
✓ Correct: Explanation saved. Your teacher will review it.
✗ Incorrect: Write at least a sentence explaining your choices.
Checkpoint 6 of 6
A note to Future Me
Your teacher will review your reflection; it is not automatically scored.
Input : → Output :
From original
- Title, wording, choices, answer key
- Hint (checkpoints 1–4)
- Generic correct / “Not yet” feedback; Checkpoint 4 cost feedback
⚠ Reconstructed — needs approval
- Choice-specific wrong-answer feedback and misconception tags
- Checkpoint 2 split into four separate matches
- Checkpoint 5: retries allowed after the first attempt (creator decision)
Step 1 · Future Me…
Write a note to Future Me about what a boundary, solution, or inequality means. Use at least one of those words and include a mathematical example.
Answer: Written explanation — saved for teacher review, not auto-scored
✓ Correct: Reflection saved. Your teacher will review it; it is not automatically scored.
✗ Incorrect: Write your note to Future Me before continuing.
Final independent mastery check
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