Rationale
The student's estimate of 452 + 5017 would be 5470.
The student appears to be rounding each number to the nearest ten or hundred before adding them together.
A) 5430
This choice is incorrect because the student is not rounding down to the nearest ten or hundred. In the student's estimations, numbers are either rounded up or down to the closest ten or hundred. For example, in the estimation 151 + 319 = 470, 151 is rounded up to 200 and 319 is rounded down to 300. Therefore, for 452 + 5017, 452 would be rounded up to 500 and 5017 would be rounded down to 5000, summing up to 5500, not 5430.
C) 5500
This choice is incorrect because the student is not rounding both numbers up to the nearest hundred. The student's method seems to round to the closest ten or hundred rather than always rounding up. For instance, in the estimation 974 + 1022 = 1990, 974 is rounded up to 1000 and 1022 is rounded down to 1000. Following this pattern, 452 would be rounded up to 500, and 5017 would be rounded down to 5000, which sums up to 5500.
D) 5400
This choice is incorrect because it implies the student rounded down both numbers, which contradicts the student's method. For instance, in the estimation 151 + 319 = 470, 151 is rounded up to 200 and 319 is rounded down to 300. Therefore, for 452 + 5017, 452 would be rounded up to 500 and 5017 would be rounded down to 5000, resulting in a sum of 5500, not 5400.
Conclusion
The student's estimation method involves rounding each number to the nearest ten or hundred before adding them together. Following this method, the student would round 452 to 500 and 5017 to 5000, resulting in an estimated sum of 5470 for 452 + 5017. The other choices do not align with the student's demonstrated estimation method and are therefore incorrect.
