Canned-Food Drive Estimates
During a canned-food drive, Ms. Ortiz’s class collects 187 cans and Mr. Patel’s class collects 246 cans. The school goal is 450 cans. Before adding, Ms. Ortiz asks students to estimate the total to the nearest ten and to the nearest hundred. One student says, “The answer is about 400, so we did not meet the goal.” Another says, “The answer is about 440, so we almost met it.” The principal wants the exact total and an explanation of which estimate is more useful for deciding whether the goal was met. Students must also explain why the two estimates are different, show the rounding in each case, and whether either estimate changes the final conclusion about meeting the 450-can goal.
1. Estimate 187 + 246 to the nearest ten and to the nearest hundred. Show the rounded numbers.
Read the worked answer
Nearest ten: 187 rounds to 190 because 187 is closer to 190 than to 180; 246 rounds to 250 because 246 is closer to 250 than to 240. The estimate is 190 + 250 = 440. Nearest hundred: 187 rounds to 200, and 246 rounds to 200 because 246 is less than 250, the halfway point. The estimate is 200 + 200 = 400.
2. Find the exact total. Did the classes meet the 450-can goal? How do the estimates compare with the exact total?
Read the worked answer
187 + 246 = 433 cans exactly. Since 433 < 450, the classes did not meet the 450-can goal. The nearest-ten estimate, 440, is close to 433 because it is only 7 cans too high. The nearest-hundred estimate, 400, is farther away because both numbers were rounded to 200. Both estimates are below 450, so both suggest the goal was not met.
3. Which estimate is more useful for deciding whether the goal was met, and why? Does rounding to hundreds change the conclusion?
Read the worked answer
The nearest-ten estimate, 440, is more useful for a close decision because it is closer to the exact total of 433. It still shows the total is below 450, but it also shows the classes came close. Rounding to hundreds gives 400, which is rougher but still below 450. Neither estimate changes the yes-or-no conclusion: the classes did not meet the goal. However, the exact total is needed to know they are 450 − 433 = 17 cans short.