Increasing the number facts - What are they and how do students learn?

In a previous article I explained what the basic number facts and their importance for any student of mathematics. Once students have memorized the basic number facts, they should move to find facts enlarged group.

Number of basic facts: Review

First, a brief overview of basic facts count. These events start with single-digit addition facts (0 0-9 9) and the data reverse subtraction (0-0 to 18-9), more facts multiplicationfrom 0x0 to 10x10 or 12x12 and division facts reverse (11 to 10,010 or 14,412). If we do not expect the students, all of these facts when they are 11 or 12 years old get old, we should allow it difficult to remember the math later prepared and in fact encourage them to use a calculator for any calculation, since not equipped to do in order to draw from memory.

Increased number of facts

Extended facts are those facts that can be easily derived from the number of basic researchI made using the basic principles of value. Extended facts are in all four operations, and to know them or can order extends to quickly find students are not dramatic arithmetic process by providing the tools, the running time of more than mentally. There is no limit to the large number of facts should be understood, and that will be useful, no matter how many or how few students in the position.

Extended facts are derived from a basic numberFact and the application of the rules involved is a multiple of ten (eg 10, 20, 30, etc.) or a power of ten (10, 100, 1000, etc., or 0.1, 0.01, 0.001, etc.). Take as a fundamental fact:

3 +4 = 7

grapple with this basic knowledge that certain number of facts such as these may be extended:

13 +4 = 17
83 +4 = 87
30 +40 = 70
0.03 +0.04 = 0.07

In each of these examples, the basic fact "3 +4 = 7" is used to work for the fact enlarged. Provided that the student understandsValue should follow the facts easily extended. Teachers should place appropriate physical or virtual on-screen material to illustrate these ideas so that they become evident to students: materials such as base ten blocks, bundling sticks, ten frames, or equivalent software models for numbers and operations.

Extended facts to find out the calculation of the workload reduced

Once the teacher takes the value of students extended facts', it is clear thatthe number of examples of calculations for which no written or calculator method is needed greatly. Why should students be expected to use an algorithm written, or to reach a calculator, work for one of the following facts?

280 70 = 350 (increased from 8 +7 = 15)
72-5 = 67 (expanded 12-5 = 7)
50x6 = 300 (increased from 5x6 = 30)
5608 = 70 (increased from 568 = 7)

Students should be encouraged, the best method, the calculation is available, any time to use themto discover, called a response. Sometimes the process has to be written, sometimes a computer is better, at other times, a spreadsheet is a better choice. But if a spiritual method can be used, it is faster and the student is free to reflect on the difficult aspects of solving problems.

future articles of this series will outline strategies for the teaching of facts in issue four operations concentrated.