Use Place Value, Known and Derived Facts to Multiply and Divide Mentally 5 - Reasoning

The concept of using place value, known, and derived facts to multiply and divide mentally is an essential skill in mathematics that enables students to solve problems quickly and efficiently without the need for written calculations. This skill is particularly useful when dealing with division (÷), as it allows students to break down complex problems into simpler steps by utilising their understanding of numbers and their relationships. By recognising patterns, applying their knowledge of multiplication tables, and using techniques such as halving or doubling, students can mentally manipulate numbers to find the answers to division questions.

Reasoning plays a crucial role in this process, as it requires students to explain and justify their methods and answers. For instance, when dividing a number by 5, a student might recognise that multiplying by 2 and then dividing by 10 (since 5 x 2 = 10) is an effective strategy. This demonstrates an application of derived facts (using known multiplication facts to derive a division fact) and an understanding of place value (shifting digits one place to the right when dividing by 10). Such mental strategies are not only a demonstration of numerical fluency but also encourage logical thinking and a deeper comprehension of how numbers work.