Estimation

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Answer Key & Explanations

Estimation · Grade 3 · Worksheet 1

1. A rectangular playground is drawn on a grid. The playground is 120 meters long and 85 meters wide. What is the total area of the playground in square meters? Answer: 10200 Solution: The formula for the area of a rectangle is length multiplied by width. The length is 120 meters and the width is 85 meters. Multiply the length by the width: 120 * 85.
   Full step-by-step solution

   Step 1: The formula for the area of a rectangle is length multiplied by width. Step 2: The length is 120 meters and the width is 85 meters. Step 3: Multiply the length by the width: 120 * 85. Step 4: First, calculate 100 * 85 = 8500. Step 5: Then, calculate 20 * 85 = 1700. Step 6: Add the two results: 8500 + 1700 = 10200. Step 7: The total area is 10200 square meters.

2. A school is collecting books for their library. Third graders collected 1,238 books and fourth graders collected 985 books. About how many books were collected in total? Round each number to the nearest hundred before adding. Answer: 2200 Solution: Round 1,238 to the nearest hundred. Since 238 is closer to 200 than 300, 1,238 rounds to 1,200. Round 985 to the nearest hundred.
   Full step-by-step solution

   Step 1: Round 1,238 to the nearest hundred. Since 238 is closer to 200 than 300, 1,238 rounds to 1,200. Step 2: Round 985 to the nearest hundred. Since 985 is closer to 1,000 than 900, 985 rounds to 1,000. Step 3: Add the rounded numbers: 1,200 + 1,000 = 2,200. The estimated total number of books collected is 2,200.

3. Liam is collecting cans for recycling. On Monday, he collected 127 cans. On Tuesday, he collected 94 cans. About how many cans did Liam collect in total? Round each number to the nearest ten before adding. Answer: 220 Solution: Identify the numbers given in the problem. Liam collected 127 cans on Monday and 94 cans on Tuesday. Round each number to the nearest ten.
   Full step-by-step solution

   Step 1: Identify the numbers given in the problem. Liam collected 127 cans on Monday and 94 cans on Tuesday. Step 2: Round each number to the nearest ten. - 127: The digit in the ones place is 7, which is 5 or more, so we round up. 127 rounded to the nearest ten is 130. - 94: The digit in the ones place is 4, which is less than 5, so we round down. 94 rounded to the nearest ten is 90. Step 3: Add the rounded numbers. 130 + 90 = 220. Step 4: State the final answer. So, Liam collected about 220 cans in total.

4. Hana is collecting donations for the school fun run. Her class raised 462 dollars from the first round and 358 dollars from the second round. About how much money did the class raise in total? Round each amount to the nearest hundred before estimating the sum. Answer: 900 Solution: Round 462 to the nearest hundred. The tens digit is 6, which is 5 or more, so round up. 462 rounds to 500.
   Full step-by-step solution

   Step 1: Round 462 to the nearest hundred. The tens digit is 6, which is 5 or more, so round up. 462 rounds to 500. Step 2: Round 358 to the nearest hundred. The tens digit is 5, which is 5 or more, so round up. 358 rounds to 400. Step 3: Add the rounded numbers: 500 + 400 = 900. The estimated total amount raised is about 900 dollars.

5. Noah is organizing a school fundraiser. He sold 287 tickets for the morning show and 415 tickets for the evening show. About how many tickets did Noah sell in total? Round each number to the nearest hundred before estimating the sum. Answer: 700 Solution: Round 287 to the nearest hundred. Since 287 is closer to 300 than to 200, we round up to 300. Round 415 to the nearest hundred.
   Full step-by-step solution

   Step 1: Round 287 to the nearest hundred. Since 287 is closer to 300 than to 200, we round up to 300. Step 2: Round 415 to the nearest hundred. Since 415 is closer to 400 than to 500, we round down to 400. Step 3: Add the rounded numbers: 300 + 400 = 700. Noah sold about 700 tickets in total.

6. Liam is collecting baseball cards. He has 287 cards in his main collection and 156 cards in his special edition collection. About how many baseball cards does Liam have in total? Round to the nearest hundred. Answer: 400 Solution: Identify the numbers to add. Liam has 287 cards in his main collection and 156 cards in his special edition collection. So we need to find: 287 + 156.
   Full step-by-step solution

   Step 1: Identify the numbers to add. Liam has 287 cards in his main collection and 156 cards in his special edition collection. So we need to find: 287 + 156. Step 2: Add the two numbers. 287 + 156 = 443. So the exact total is 443 cards. Step 3: Round 443 to the nearest hundred. To round to the nearest hundred, look at the tens digit. The tens digit in 443 is 4. If the tens digit is 4 or less, we round down. If it is 5 or more, we round up. Here, the tens digit is 4, so we round down. Step 4: Rounding down means 443 becomes 400. 443 is between 400 and 500. Since 443 is closer to 400 than to 500, the nearest hundred is 400. Final Answer: 400

7. Liam is collecting baseball cards. He has 127 cards in his main collection and his friend Noah gives him 48 more cards. About how many baseball cards does Liam have now? Answer: 175 Solution: Liam starts with 127 baseball cards. Then he gets 48 more cards from Noah. We need to find the total number of cards he has now.
   Full step-by-step solution

   Step 1: Understand the problem. Liam starts with 127 baseball cards. Then he gets 48 more cards from Noah. We need to find the total number of cards he has now. Step 2: Write the addition expression. Total cards = starting cards + cards received Total cards = 127 + 48 Step 3: Add the numbers. First, add the ones place: 7 + 8 = 15. Write down 5 in the ones place, and carry over 1 to the tens place. Step 4: Add the tens place. In the tens place, we have 2 (from 127) + 4 (from 48) + 1 (carried over) = 7. So the tens place is 7. Step 5: Add the hundreds place. 127 has 1 in the hundreds place, and 48 has 0 in the hundreds place, so the hundreds place is 1. Step 6: Combine the digits. Hundreds: 1, Tens: 7, Ones: 5 → 175 Step 7: State the final answer. Liam now has 175 baseball cards.