Round Numbers up to 1 Million 9 - Reasoning

In an exercise exploring the concept of rounding numbers up to 1 million, students are prompted to engage in a reasoning task involving number and place value. The task requires students to write down two six-digit numbers, in this case, 351,012 and 451,006, and then add them together. Once combined, the sum of 802,018 is obtained. The next step is to round this total to the nearest 100,000, which results in 800,000. However, the exercise doesn't end there; students are also asked to round each of the original six-digit numbers to the nearest 100,000 before adding them, which gives 400,000 for 351,012 and 500,000 for 451,006, resulting in a total of 900,000 when combined.

The activity reveals an interesting observation: the sum of the rounded numbers does not match the rounded sum of the original numbers. This discrepancy highlights the impact of the rounding process on the final result. Students learn that rounding numbers before adding can lead to a different total than adding first and then rounding. This exercise not only reinforces the students' understanding of place value and rounding but also encourages them to think critically about the order of operations and its effects on their calculations. It's an important lesson in precision and the implications of rounding in mathematical problems.