Perform Mental Calculations, Including with Mixed Operations and Large Numbers 2 - Reasoning

In this mental arithmetic exercise, students are tasked with performing division operations on the number 2,432 using different divisors: 64, 32, and 16. Each calculation requires the student to divide 2,432 by these numbers in sequence, which are each factors of two. The first calculation is 2,432 divided by 64. Following this, the second calculation involves dividing the same number, 2,432, by 32, which is half of 64. Lastly, the third calculation requires dividing 2,432 by 16, which is half of 32.

Upon completing these calculations, students are prompted to reflect on the process they used each time and to observe any patterns that emerge. The key observation to be made here is that as the divisor is halved (from 64 to 32, and then from 32 to 16), the quotient doubles. This pattern is consistent with the mathematical principle that when dividing by half of the amount, the answer is doubled. This exercise not only reinforces the students' understanding of division and factors of two but also encourages them to recognise and articulate patterns in numerical operations, enhancing their reasoning skills.