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**Fluency and Understanding**

The importance of knowing their basic number facts is key to the further development in the mathematical skills for any child. By the end of Year 2 we expect the boys to know the first 100 addition facts and the first 100 subtraction facts. We should have also had an opportunity to experiment and develop some conceptual understanding of multiplication and division. By the end of Year 4, we expect a student to know all of their addition and subtraction facts and the 100 multiplication facts, as well as the 90 division facts. This makes a grand total of 390 facts to be learned by the end of Year 4. We expect recall to be able to be attained by a student in 2-3 seconds to know these facts. We call that instant recall.

The importance of fluency on the understanding and application of mathematics is essential. If a student does not know the basic facts, when they go on to applying these facts to other mathematical problems or questions, they will struggle. For example, the basic fact of 8 + 7 = 15, 8 and 7 are a near double. You may double 8 and take 1 away to get 15, double 7 to get 14 and add 1 to make 15. We need the boys to know these facts instantly. If you go onto apply this fact to other sums like;

18 add 7,

18 add 17,

28 add 7,

58 add 7,

80 add 70;

The application of that basic factor of 8 add 7 becomes essential. Without that understanding of what the sum of those numbers is, a student will not be able to apply this to different mathematical questions.

We work hard to develop this understanding in the boys. It allows them to apply and work in a range of different areas in mathematics. The knowledge of basic skills is key to their initial development, and a key benchmark we try to have these boys achieve in their journey through the College.

**Mr John Stewart**

**Head of Junior School**