🎯 Estimation and Rounding - Grade 3
Understanding Estimation and Rounding!
Rounding makes numbers simpler and easier to work with! Estimation gives us a close answer quickly without doing exact calculations!
Why do we estimate?
• To get quick answers
• To check if our exact answer makes sense
• To solve problems when we don't need exact numbers
🔄 Rounding Numbers
What is Rounding?
Rounding means changing a number to the nearest ten, hundred, or thousand to make it easier to work with!
Rounding Rules:
If the digit is 0, 1, 2, 3, or 4
→ Round DOWN (keep the digit the same)
If the digit is 5, 6, 7, 8, or 9
→ Round UP (add 1 to the digit)
Rounding to the Nearest Ten:
Look at the ones digit to decide!
Example 1: Round 34 to the nearest ten
Look at ones digit: 4 (less than 5)
Round DOWN: \(34 \rightarrow 30\) ✓
Example 2: Round 47 to the nearest ten
Look at ones digit: 7 (5 or more)
Round UP: \(47 \rightarrow 50\) ✓
Example 3: Round 85 to the nearest ten
Look at ones digit: 5 (5 or more)
Round UP: \(85 \rightarrow 90\) ✓
Rounding to the Nearest Hundred:
Look at the tens digit to decide!
Example 1: Round 234 to the nearest hundred
Look at tens digit: 3 (less than 5)
Round DOWN: \(234 \rightarrow 200\) ✓
Example 2: Round 567 to the nearest hundred
Look at tens digit: 6 (5 or more)
Round UP: \(567 \rightarrow 600\) ✓
Example 3: Round 850 to the nearest hundred
Look at tens digit: 5 (5 or more)
Round UP: \(850 \rightarrow 900\) ✓
Rounding to the Nearest Thousand:
Look at the hundreds digit to decide!
Example 1: Round 2,340 to the nearest thousand
Look at hundreds digit: 3 (less than 5)
Round DOWN: \(2,340 \rightarrow 2,000\) ✓
Example 2: Round 4,678 to the nearest thousand
Look at hundreds digit: 6 (5 or more)
Round UP: \(4,678 \rightarrow 5,000\) ✓
💡 Remember: 5 or more, give it a shove! 4 or less, let it rest!
💰 Round Money Amounts
Rounding Money:
We can round money to the nearest rupee, ten rupees, or hundred rupees!
Round to the Nearest Rupee:
Look at the paise (decimal part) to decide!
Example 1: Round ₹45.30 to the nearest rupee
Look at paise: 30 (less than 50)
Round DOWN: ₹45.30 → ₹45 ✓
Example 2: Round ₹78.75 to the nearest rupee
Look at paise: 75 (50 or more)
Round UP: ₹78.75 → ₹79 ✓
Round to the Nearest Ten Rupees:
Example: Round ₹234 to the nearest ten rupees
Look at ones digit: 4 (less than 5)
Round DOWN: ₹234 → ₹230 ✓
Round to the Nearest Hundred Rupees:
Example: Round ₹567 to the nearest hundred rupees
Look at tens digit: 6 (5 or more)
Round UP: ₹567 → ₹600 ✓
🧩 Rounding Puzzles
What are Rounding Puzzles?
Rounding puzzles ask you to find numbers that round to a certain value! You need to think backwards!
Type 1: Find All Numbers That Round to a Value
Question: Which numbers round to 40 when rounded to the nearest ten?
Think:
• Numbers from 35 to 44 round to 40
• 35, 36, 37, 38, 39, 40, 41, 42, 43, 44
Answer: Any number from 35 to 44 ✓
Type 2: Find the Smallest and Largest Numbers
Question: A number rounds to 300 when rounded to the nearest hundred. What are the smallest and largest possible numbers?
Think:
• Numbers from 250 to 349 round to 300
Smallest: 250
Largest: 349 ✓
Quick Reference:
| Rounds To | Number Range |
|---|---|
| 30 (nearest ten) | 25 to 34 |
| 200 (nearest hundred) | 150 to 249 |
| 3000 (nearest thousand) | 2500 to 3499 |
➕ Estimate Sums
What is Estimating Sums?
Estimating sums means finding an approximate answer for addition by rounding the numbers first!
Steps:
1. Round each number
2. Add the rounded numbers
3. Write "about" or "approximately"
Examples:
Example 1: Estimate to Nearest Ten
Estimate: \(37 + 54\)
Step 1: Round to nearest ten
\(37 \rightarrow 40\)
\(54 \rightarrow 50\)
Step 2: Add rounded numbers
\(40 + 50 = 90\)
Answer: About 90 ✓
(Exact answer: 91)
Example 2: Estimate to Nearest Hundred
Estimate: \(234 + 567\)
Step 1: Round to nearest hundred
\(234 \rightarrow 200\)
\(567 \rightarrow 600\)
Step 2: Add rounded numbers
\(200 + 600 = 800\)
Answer: About 800 ✓
(Exact answer: 801)
Example 3: Three Numbers
Estimate: \(43 + 78 + 62\)
Step 1: Round to nearest ten
\(43 \rightarrow 40\)
\(78 \rightarrow 80\)
\(62 \rightarrow 60\)
Step 2: Add rounded numbers
\(40 + 80 + 60 = 180\)
Answer: About 180 ✓
(Exact answer: 183)
📖 Estimate Sums: Word Problems
How to Solve:
- Read the problem - Understand what's being asked
- Find the numbers - Identify the values to add
- Round each number - Choose nearest ten or hundred
- Add the rounded numbers - Find the sum
- Write your estimate - Use "about" or "approximately"
Examples:
Example 1: Shopping
Maya wants to buy a book for ₹58 and a pen for ₹23. Estimate the total cost.
Step 1: Round to nearest ten
₹58 → ₹60
₹23 → ₹20
Step 2: Add
₹60 + ₹20 = ₹80
Answer: The total cost is about ₹80. ✓
Example 2: Distance
Ravi walks 345 meters to school and 278 meters to the park. Estimate the total distance.
Step 1: Round to nearest hundred
345 → 300
278 → 300
Step 2: Add
300 + 300 = 600
Answer: The total distance is about 600 meters. ✓
➖ Estimate Differences
What is Estimating Differences?
Estimating differences means finding an approximate answer for subtraction by rounding the numbers first!
Steps:
1. Round each number
2. Subtract the rounded numbers
3. Write "about" or "approximately"
Examples:
Example 1: Estimate to Nearest Ten
Estimate: \(87 - 34\)
Step 1: Round to nearest ten
\(87 \rightarrow 90\)
\(34 \rightarrow 30\)
Step 2: Subtract rounded numbers
\(90 - 30 = 60\)
Answer: About 60 ✓
(Exact answer: 53)
Example 2: Estimate to Nearest Hundred
Estimate: \(678 - 234\)
Step 1: Round to nearest hundred
\(678 \rightarrow 700\)
\(234 \rightarrow 200\)
Step 2: Subtract rounded numbers
\(700 - 200 = 500\)
Answer: About 500 ✓
(Exact answer: 444)
📖 Estimate Differences: Word Problems
Examples:
Example 1: Comparison
A movie theater has 567 seats. If 234 seats are filled, estimate how many seats are empty.
Step 1: Round to nearest hundred
567 → 600
234 → 200
Step 2: Subtract
600 - 200 = 400
Answer: About 400 seats are empty. ✓
Example 2: Money
Priya has ₹485. She spends ₹178 on groceries. Estimate how much money she has left.
Step 1: Round to nearest hundred
₹485 → ₹500
₹178 → ₹200
Step 2: Subtract
₹500 - ₹200 = ₹300
Answer: Priya has about ₹300 left. ✓
✖️ Estimate Products
What is Estimating Products?
Estimating products means finding an approximate answer for multiplication by rounding the numbers first!
Steps:
1. Round each number
2. Multiply the rounded numbers
3. Write "about" or "approximately"
Examples:
Example 1: One-digit × Two-digit
Estimate: \(4 \times 28\)
Step 1: Round to nearest ten
\(4 \rightarrow 4\) (no change needed)
\(28 \rightarrow 30\)
Step 2: Multiply rounded numbers
\(4 \times 30 = 120\)
Answer: About 120 ✓
(Exact answer: 112)
Example 2: Two-digit × Two-digit
Estimate: \(23 \times 48\)
Step 1: Round to nearest ten
\(23 \rightarrow 20\)
\(48 \rightarrow 50\)
Step 2: Multiply rounded numbers
\(20 \times 50 = 1000\)
Answer: About 1000 ✓
(Exact answer: 1104)
Example 3: Larger Numbers
Estimate: \(6 \times 234\)
Step 1: Round to nearest hundred
\(6 \rightarrow 6\) (no change needed)
\(234 \rightarrow 200\)
Step 2: Multiply rounded numbers
\(6 \times 200 = 1200\)
Answer: About 1200 ✓
(Exact answer: 1404)
📖 Estimate Products: Word Problems
Examples:
Example 1: Repeated Groups
A box contains 18 pencils. If there are 7 boxes, estimate the total number of pencils.
Step 1: Round to nearest ten
7 → 7 (no change)
18 → 20
Step 2: Multiply
7 × 20 = 140
Answer: There are about 140 pencils. ✓
Example 2: Cost
One notebook costs ₹42. If Ravi buys 8 notebooks, estimate the total cost.
Step 1: Round to nearest ten
8 → 8 (no change)
₹42 → ₹40
Step 2: Multiply
8 × ₹40 = ₹320
Answer: The total cost is about ₹320. ✓
🎯 Estimate Sums, Differences and Products: Word Problems
How to Decide Which Operation:
• Look for key words:
- "total", "altogether" → Addition
- "left", "remaining", "how many more" → Subtraction
- "each", "per", "groups of" → Multiplication
• Then round and calculate!
Mixed Examples:
Example 1: Addition Problem
A library has 345 fiction books and 278 non-fiction books. Estimate the total number of books.
Key word: "total" → Addition
Round: 345 → 300, 278 → 300
Calculate: 300 + 300 = 600
Answer: About 600 books ✓
Example 2: Subtraction Problem
A farmer had 567 apples. He sold 234 apples. Estimate how many apples are left.
Key word: "left" → Subtraction
Round: 567 → 600, 234 → 200
Calculate: 600 - 200 = 400
Answer: About 400 apples left ✓
Example 3: Multiplication Problem
One bus can carry 48 passengers. If there are 6 buses, estimate the total number of passengers.
Key word: "each bus" → Multiplication
Round: 6 → 6, 48 → 50
Calculate: 6 × 50 = 300
Answer: About 300 passengers ✓
Example 4: Multi-Step Problem
A school has 28 students in each class. There are 5 classes. They receive 67 new books. Estimate the total number of students and books combined.
Step 1: Find total students (Multiplication)
28 → 30, 5 → 5
30 × 5 = 150 students
Step 2: Add books (Addition)
150 + 67 → 150 + 70 = 220
Answer: About 220 students and books combined ✓
📝 Important Rules Summary
Rounding Rules:
0, 1, 2, 3, 4 → Round DOWN
5, 6, 7, 8, 9 → Round UP
Estimation Steps:
1. Round each number
2. Perform the operation (+, −, ×)
3. Write "about" or "approximately"
Place Value for Rounding:
Nearest Ten: Look at ones digit
Nearest Hundred: Look at tens digit
Nearest Thousand: Look at hundreds digit
💡 Quick Learning Tips
- ✓ Remember: 5 or more, give it a shove! 4 or less, let it rest!
- ✓ Always look at the digit to the RIGHT of the place you're rounding to
- ✓ Estimation gives a CLOSE answer, not the exact answer
- ✓ Use "about" or "approximately" when writing estimated answers
- ✓ Round to tens for smaller numbers, hundreds for larger numbers
- ✓ For rounding puzzles, work backwards from the rounded number
- ✓ Estimate to check if your exact answer makes sense
- ✓ Key words help you choose the operation (total, left, each)
- ✓ Round money to nearest rupee, ten, or hundred
- ✓ Numbers 25-34 round to 30 when rounding to nearest ten
- ✓ Numbers 250-349 round to 300 when rounding to nearest hundred
- ✓ Estimation makes math faster and easier!
- ✓ Always round BEFORE you calculate when estimating
- ✓ Practice rounding every day to get faster!
- ✓ Use estimation in real life - shopping, measuring, counting!