Lesson 10 — Activity 3: Look Back and Verify
Completion requirements
Lesson 10 — Activity 3: Look Back and Verify
Getting Ready
Step 4:Look Back and Verify
When you have found the answer to the math problem and written a concluding statement, you're still not done!
It's now the time to check your answer for reasonableness and to verify for correctness. In this activity, you will look more closely at strategies to do this: estimating and using the opposite operation.
Reasonableness and Estimation
You have done quite a lot of estimating for reasonableness already in this course. You know that you can estimate when an exact answer isn't needed and you can estimate to help you judge whether your answer is reasonable.
Here's an example of when a young man was figuring out his earnings for a week of after-school work.
Sean kept a record of his earnings for 5 days. They were as follows:
Day | Hours Worked | Amount Earned |
1 | 2 | $12.00 |
2 | 3 | $18.00 |
3 | 3.5 | $21.00 |
4 | 2 | $12.00 |
5 | 5 | $30.00 |
Sean calculated his earnings and was quite happy when he got a sum of $393.00. However, he checked for reasonableness and realized that he must have made an error in his calculations. In the past, his pay cheques for a week’s work have never been over $100.00.
He looked back at the number of hours worked and estimated that he had worked about 15 hours. At $6.00 an hour, he should have received about $90.00. Sean rechecked his first calculations. He had placed a decimal in the wrong place: $30.00 had become $300.00.
He recalculated and got a sum of $93.00. Although Sean would have been happy with the extra money, he was also happy that he rechecked, because he may have spent money that he did not have.
Sean calculated his earnings and was quite happy when he got a sum of $393.00. However, he checked for reasonableness and realized that he must have made an error in his calculations. In the past, his pay cheques for a week’s work have never been over $100.00.
He looked back at the number of hours worked and estimated that he had worked about 15 hours. At $6.00 an hour, he should have received about $90.00. Sean rechecked his first calculations. He had placed a decimal in the wrong place: $30.00 had become $300.00.
He recalculated and got a sum of $93.00. Although Sean would have been happy with the extra money, he was also happy that he rechecked, because he may have spent money that he did not have.
He looked back at the number of hours worked and estimated that he had worked about 15 hours. At $6.00 an hour, he should have received about $90.00. Sean rechecked his first calculations. He had placed a decimal in the wrong place: $30.00 had become $300.00.
He recalculated and got a sum of $93.00. Although Sean would have been happy with the extra money, he was also happy that he rechecked, because he may have spent money that he did not have.
Opposite Operation
A way to check for the accuracy of your answer is to perform the opposite operation.
This chart shows the opposite operation for each math operation:
Here are mores examples using the opposite operation:
