What is estimation in the context of word problems?
Estimation is the process of rounding the numbers in a problem to get a rough idea of what the answer should be. It helps you check if your final answer is reasonable.
Estimate the answer: A store sold \(198\) red shirts and \(305\) blue shirts. About how many shirts were sold in total?
Round \(198\) to \(200\) and \(305\) to \(300\). The estimated total is \(200 + 300 = 500\) shirts. The exact answer is \(503\).
What does it mean for an answer to be "reasonable"?
A reasonable answer is one that makes sense in the context of the problem and is close to your estimation. If you estimate \(500\) and your answer is \(5,000\), it's probably not reasonable.
Estimate the answer: You buy \(8\) items that cost \(\$4.95\) each. About how much will you spend?
Round \(\$4.95\) up to \(\$5\). The estimated cost is \(8 \times \$5 = \$40\). The exact cost is \(\$39.60\).
How can you use an inverse operation to check a subtraction problem like \(50 - 20 = 30\)?
Use the inverse operation, which is addition. Check if \(30 + 20 = 50\). Since it does, the answer is correct.
How can you use an inverse operation to check a division problem like \(100 \div 4 = 25\)?
Use the inverse operation, which is multiplication. Check if \(25 \times 4 = 100\). Since it does, the answer is correct.
Your final answer to a multi-step problem is \(42\). Your plan was:
Step 1) \(10 \times 5 = 50\),
Step 2) \(50 - 8 = 42\).
How would you check this work?
Check each step using inverse operations. To check Step 2, calculate \(42 + 8 = 50\). Correct. To check Step 1, calculate \(50 \div 5 = 10\). Correct. The work is accurate.
Problem: You have \(\$100\). You buy \(3\) items for \(\$18\) each. How much is left? First, estimate the answer.
Round \(\$18\) to \(\$20\).
Step 1 (Estimate cost): \(3 \times \$20 = \$60\).
Step 2 (Estimate change): \(\$100 - \$60 = \$40\).
The answer should be around \(\$40\).
You have \(\$100\). You buy \(3\) items for \(\$18\) each. You calculate that you have \(\$46\) left. Is this answer reasonable and how can you check it?
Yes, \(\$46\) is reasonable because it's close to the estimate of \(\$40\). To check: 1) Cost: \(3 \times \$18 = \$54\). 2) Change: \(\$100 - \$54 = \$46\). The calculation is correct.
Why is it important to check your work, even if your answer seems reasonable?
Small calculation errors can lead to an answer that is close but still incorrect. Checking your work step-by-step ensures accuracy and helps you catch mistakes.
