🧩Hey ! young Detectives,are you ready to solve some spooky mystery with Riley ? Check the spooky video ☝️and solve the Number Puzzle with Riley to break the Phantom's Curse ?

• Rounding off numbers (to nearest 10, 100, 1000)              
• Estimation and approximation
• Roman Numerals
• 

1.Rounding Off Numbers

Rounding means making a number simpler but keeping it close to its original value.

Rounding to the Nearest 10

Look at the ones digit:

⭐If it’s 5 or more → round up (add 1 to the tens digit).

⭐If it’s 4 or less → round down (keep the tens digit the same).

Examples:

⭐47 → Ones digit is 7 (≥5), so 47 → 50.

⭐32 → Ones digit is 2 (<5), so 32 → 30.

Rounding to the Nearest 100

Look at the tens digit:

🚀If it’s 5 or more → round up (add 1 to the hundreds digit).

🚀If it’s 4 or less → round down.

Examples:

🚀368 → Tens digit is 6 (≥5), so 368 → 400.

🚀243 → Tens digit is 4 (<5), so 243 → 200

Rounding to the Nearest 1000

🪐Look at the hundreds digit:

🪐If it’s 5 or more → round up (add 1 to the thousands digit).

🪐If it’s 4 or less → round down.

Examples:

🪐5,678 → Hundreds digit is 6 (≥5), so 5,678 → 6,000

🪐3,421 → Hundreds digit is 4 (<5), so 3,421 → 3,000

2. Estimation & Approximation

🌈Estimation means making a smart guess close to the exact answer.

🌈Approximation means using rounded numbers to make math easier.

Example:

🌈Exact: 48 + 53 = 101

🌈Estimate: Round to nearest 10 → 50 + 50 = 100 (close to 101).

Uses:

🌈Quick calculations (e.g., shopping totals).

🌈Checking if an answer is reasonable.

3. Roman Numerals

Roman numerals use letters to represent numbers:

🐯  | Letter | I | V | X |  L   |  C  |   D   |   M   |

🐯  | Value | 1 | 5 |10 | 50 |100 | 500 | 1000 |

Rules:

Add if a smaller number is after a larger one:

🐯VI = 5 + 1 = 6

🐯XV = 10 + 5 = 15

Subtract if a smaller number is before a larger one:

🐯IV = 5 – 1 = 4

🐯IX = 10 – 1 = 9

Examples:

🐯12 = XII (10 + 1 + 1)

🐯34 = XXXIV (10 + 10 + 10 + 4)

🐯100 = C

Practice: Write these in Roman numerals:

🐯7 → VII

🐯29 → XXIX

Summary

🐯Rounding: Simplify numbers (check the next digit).

🐯Estimation: Quick, close guesses using rounding.

🐯Roman Numerals: Use letters (I, V, X, etc.) with add/subtract rules.

🕵️‍♀️ The Phantom Number Curse – Advanced Challenge

🧩 Part 1: Rounding Off to Break the Curse

The Phantom Number has trapped you in the Cave of Clues! Only by rounding numbers correctly can you escape!

1.The cave’s keypad shows 5,837.

🧩What is this number rounded to the nearest 10?

🧩What is it rounded to the nearest 100?

🧩What is it rounded to the nearest 1000?

🕵️Solution

• To the nearest 10: Look at the units digit (7). Since 7 ≥ 5, round up: 5,837 → 5,840.
• To the nearest 100: Look at the tens digit (3). Since 3 < 5, round down: 5,837 → 5,800.
• To the nearest 1000: Look at the hundreds digit (8). Since 8 ≥ 5, round up: 5,837 → 6,000.

2.Riley finds three scrolls: 3,685, 3,789, 3,245.

🧩Which of these, when rounded to the nearest 100, becomes 3,700?

• For 3,685: Tens digit is 8 (≥ 5), so round up: 3,685 → 3,700.
• For 3,789: Tens digit is 8 (≥ 5), so round up: 3,789 → 3,800.
• For 3,245: Tens digit is 4 (< 5), so round down: 3,245 → 3,200.
• Answer: 3,685.

3.A stone tablet reads:
“I am a 4-digit number. When rounded to the nearest 100, I become 5,300.
When rounded to the nearest 1,000, I become 5,000.”

🧩What could the original number be? List 2 possibilities.

🕵️Solution

For nearest 100: Number must be in the range [5,250, 5,349] (since 5,250 ≤ x < 5,350 rounds to 5,300).

For nearest 1,000: Number must be in the range [4,500, 5,499] (since 4,500 ≤ x < 5,500 rounds to 5,000).

Intersection: [5,250, 5,349].

Two possibilities: 5,250 and 5,349 (any numbers in this range are valid, but these are clear examples).

4. The Phantom says:
“Round me to the nearest 10 and I become 6,850.
Round me to the nearest 100 and I’m still 6,900.”

🧩What number am I?

For nearest 10: Number must be in [6,845, 6,854] (since 6,845 ≤ x < 6,855 rounds to 6,850).

For nearest 100: Number must be in [6,850, 6,949] (since 6,850 ≤ x < 6,950 rounds to 6,900).

Intersection: [6,850, 6,854].

Possible numbers: 6,850, 6,851, 6,852, 6,853, 6,854.

Since the question asks for “the number,” the simplest or exact match (often implied in such puzzles) is 6,850 (satisfies both conditions directly).

🔮 Part 2: Estimation & Approximation – The Maze of Maybes

Only the right approximations can reveal the safe path through the Maze of Maybes!

5.Estimate: 398 + 1,213 + 689

🧩Round each to the nearest 100, then add.

🧩Is your estimate higher or lower than the actual sum?

6.Riley bought:

📌A sword for ₹178

📌A shield for ₹349

📌A scroll for ₹102

Estimate her total shopping cost by rounding to the nearest 10.

🧩Can she carry ₹600 to be safe?

🕵️Solution

Round to nearest 10

₹178: Units digit 8 (≥ 5), so 178 → 180.

₹349: Units digit 9 (≥ 5), so 349 → 350.

₹102: Units digit 2 (< 5), so 102 → 100.

Total estimate: 180 + 350 + 100 = 630.

Actual total: 178 + 349 + 102 = 629.

Can she carry ₹600? The estimated total (630) exceeds ₹600, and the actual total (629) also exceeds ₹600. Thus, no, ₹600 is not enough to be safe.

7.The Phantom threw 4 fireballs: 239 m, 412 m, 511 m, and 387 m.

Estimate the total distance (to nearest 100) he threw them.

Could he have thrown more than 1,500 m?

🕵️Solution

📝Round to nearest 100:

📝239: Tens digit 3 (< 5), so 239 → 200.

📝412: Tens digit 1 (< 5), so 412 → 400.

📝511: Tens digit 1 (< 5), so 511 → 500.

📝387: Tens digit 8 (≥ 5), so 387 → 400.

Total estimate: 200 + 400 + 500 + 400 = 1,500.

Actual total: 239 + 412 + 511 + 387 = 1,549.

More than 1,500 m? The actual total (1,549 m) is greater than 1,500 m, so yes, he could have thrown more than 1,500 m.

8.True or False:

🧩“Rounding up always gives a larger estimate.”

🧩“Estimation gives the exact answer.”

🧩“We round off to make calculations easier.”

🕵️Solution

📝“Rounding up always gives a larger estimate.” False. Rounding up individual numbers increases their value, but the estimate depends on whether numbers were rounded up or down. For example, rounding 412 down to 400 reduces the estimate.

📝“Estimation gives the exact answer.” False. Estimation approximates and rarely matches the exact sum (though it did in Q5 by coincidence).

📝“We round off to make calculations easier.” True. Rounding simplifies mental or quick calculations.

🏛️ Part 3: Roman Numerals – Unlock the Secret Tomb

🧩Decode the Roman clues to unlock the Phantom’s treasure chest!

9.What is the Roman numeral for:

🔍49

🔍87

🔍94

🔍159

🕵️Solution

Roman numerals: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000.

49=> 50 - 1 = XLIX (L - X = 50 - 10 = 40, + IX = 9) → XLIX.

87=>50 + 30 + 7 = LXXXVII (L = 50, XXX = 30, VII = 7) → LXXXVII.

94=> 100 - 10 + 4 = XCIV (C - X = 90, + IV = 4) → XCIV.

159=> 100 + 50 + 9 = CLIX (C = 100, L = 50, IX = 9) → CLIX.

10.Fill in the blanks to continue the Roman sequence
XX, XXX, ____, ____, LX

🕵️Solution

• Sequence: XX = 20, XXX = 30, ?, ?, LX = 60.
• Pattern: Numbers increase by 10 (20, 30, 40, 50, 60).
• Blanks: 40 = XL, 50 = L.

11.Riley finds a puzzle
“I am a Roman numeral.
Multiply me by 2 and you get C.
Divide me by 5 and you get X.”

🔍What Roman numeral am I?

🕵️Solution

Let the Roman numeral represent number N.

Multiply by 2 = C: C = 100, so 2N = 100 → N = 50.

Divide by 5 = X: X = 10, so N ÷ 5 = 10 → N = 50.

Both conditions give N = 50. Roman numeral for 50 is L.

Answer: L.

12.Match the Phantom’s traps to their values:

🔍Trap I: XCIV

🔍Trap II: LXXXVIII

🔍Trap III: LIX

🔍Trap IV: CXIII

Match them to

88, 113, 59, 94

🕵️Solution

Trap I (XCIV) = 94

Trap II (LXXXVIII) = 88

Trap III (LIX) = 59

Trap IV (CXIII) = 113

💡 Bonus Phantom Riddle (Cross-topic)

13.I was rounded to the nearest 100 and became 1,500.
     But when rounded to the nearest 1,000, I became 2,000.
     I am less than 2,000, but greater than 1,450.
     My Roman numeral is MDCC.”

🧩Am I cursed or wrongly calculated? Explain the mistake!

🕵️Solution

🪄Lets Solve some intersting Real World Task Problems !!

📖Nearest 100 = 1,500: Number is between 1,450 and 1,549.

📖Nearest 1,000 = 2,000: Number is between 1,500 and 2,499.

📖Less than 2,000, greater than 1,450: Number is between 1,500 and 1,999.

📖Roman numeral MDCC: M = 1,000, D = 500, C = 100, C = 100 → 1,000 + 500 + 200 = 1,700.

Check 1,700:

Nearest 100: Tens digit 0 (< 5), rounds down to 1,500.

Nearest 1,000: Hundreds digit 7 (≥ 5), rounds up to 2,000.

Range: 1,700 > 1,450 and < 2,000.

Roman numeral: 1,700 = MDCC (matches).

Answer: 1,700.

📚Phantom’s Budget: A Six Digit Code Adventure

🧩Objective: Help the Phantom plan a mysterious party by calculating the total budget using 4-, 5-, and 6-digit numbers. Practice addition and estimation to crack the code!

🧩Instructions: The Phantom is hosting a secret party and needs your help to manage the budget. Solve the problems below in your notebook, showing all steps (e.g., line up numbers by place value, add step-by-step). Submit your answers via the online platform by uploading a photo/PDF of your work or entering answers in the provided form. Be a Codebreaker detective and double-check your calculations!

🧩Scenario: The Phantom’s party requires decorations, food, and entertainment. Each item has a cost, and you need to add them to find the total budget. Use the clues to solve the mystery of the total cost.

🧩Task Questions

1. Decorations Budget:
   • The Phantom buys spooky lanterns for ₹3,456 and glowing banners for ₹2,789.
   • a) What is the total cost of decorations? Show your addition step-by-step.
   • b) Estimate the total by rounding each cost to the nearest 100. Is your estimate close to the actual total? Explain.
2. Food Budget:
   • The Phantom orders mystic pizzas for ₹12,345 and enchanted drinks for ₹8,901.
   • a) Calculate the total cost of food. Show your work.
   • b) Estimate the total by rounding each cost to the nearest 1,000. Compare your estimate to the actual total.
3. Entertainment Budget:
   • The Phantom hires a magician for ₹45,678 and a music band for ₹23,456.
   • a) Find the total cost of entertainment. Show all steps.
   • b) If the Phantom adds a fireworks show for ₹10,000, what is the new total for entertainment?
4. Total Party Budget:
   • Add the totals from decorations (Q1), food (Q2), and entertainment (Q3, including fireworks).
   • a) What is the total party budget? Show your addition.
   • b) Is the total budget a 5-digit or 6-digit number? Write it in words (Indian system).
   • c) Compare your total to ₹100,000. Is it greater or less? Explain.

🧩Submission Instructions

• Notebook Users: Write your answers in your notebook, showing all addition steps and explanations. Take a clear photo or scan and upload as a PDF/image via the platform’s assignment tool.
• Digital Users: Enter your final answers (e.g., totals for each question) in the platform’s form or type them in a document and upload.
• Bonus: Share one challenge you faced while adding (e.g., carrying over digits) on the platform’s discussion board for extra Codebreaker points!

🧩Time Estimate: 10 minutes

Some Interesting Picture Examples

🏀Roxy needs to round 42 to the nearest 10.

🏀Look at the number line in the picture. Which option is correct?

A) 40
B) 50
C) 30
D) 60

✅ Correct Answer: A) 40

Because:

• The difference between 42 and 40 is 2

• The difference between 42 and 50 is 8

• So, 42 rounds to 40 when rounding to the nearest 10.

🏀Check this numberline

🛹 “Which numbers round to the nearest 100?”

🛹“Which of these numbers are closer to the next 10?”

Lets see:

✅ Question 1: “Which numbers round to the nearest 100?”

This means: which numbers are closer to the next multiple of 100 (i.e., 100, 200, 300, etc.) than the one before.

We check if the number is more than halfway (≥ 50) past a hundred.

✔️ Answers:

123 → 100 ❌ (closer to 100, not next 100)

248 → 200 ❌ (still under 250, rounds down)

361 → 400 ✅

499 → 500 ✅

✅ Correct answers: 361, 499
(These round up to the next 100)

✅ Question 2: “Which of these numbers are closer to the next 10?”

This means numbers that are more than halfway past the previous 10 (e.g., 38 → 40).

We look at the unit digit (ones place)

If it’s 5–9 → rounds up

If it’s 0–4 → rounds down

✔️ Answers:

57 → rounds to 60 ✅

123 → rounds to 120 ❌

248 → rounds to 250 ✅

361 → rounds to 360 ❌

499 → rounds to 500 ✅

✅ Correct answers: 57, 248, 499
(These are closer to the next 10)

🐇✨“Roman Numeral Road with Roxy the Rabbit”

🗨️ Roxy the Rabbit is pointing at a sign on the Roman Road. The sign shows:LXXV

 What is the number shown on this Roman sign?

✅ Correct Answer:

B) 75

✳️ Q4: Match the Roman Numerals to Their Values

✅ Answer:

LXXV → 75

XX → 20

XC → 90

L → 50

✳️ Q5: Arrange in Ascending Order

Arrange the following Roman numerals from smallest to greatest:

XX, L, XC, LXXV

✅ Answer:
XX (20), L (50), LXXV (75), XC (90)

🏰Roman Temple Treasure Hunt

Question: Roxy the Rabbit found the numeral "CXC" on a temple tablet. What number does it represent?

• A) 150
• B) 190
• C) 170
• D) 180

Feedback:

• Correct: “Well done! CXC = 190 because C (100) + XC (90) = 100 + 90 = 190.”

Question: “Roxy found another clue CLX . What number is it?

A) 150                B) 160            C) 170             D) 180

Feedback:

• “Awesome! CLX = 160 because C (100) + L (50) + X (10) = 160.”

Question: Roxy found a temple tablet with "CC" marking the number of Roman soldiers. What  number does "CC" represent? How many groups of 50 soldiers could Roxy form with this number?

Answer: “Excellent! CC = 200 because C (100) + C (100) = 200, and 200 ÷ 50 = 4 groups.”

Question: Roxy spots another tablet with "CXC" near the treasure. What Arabic number does "CXC" represent? Choose the correct option or type your answer.

• A) 180
• B) 190
• C) 200
• D) 210

Correct: “Well done! CXC = 190 because C (100) + XC (90) = 100 + 90 = 190.”