• Written by Danilo C. Caysido
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Mathematics Investigation is one of the major concerns of the K to 12 Mathematics Program. Through this activity, the students learn to become observant, very careful in analyzing data and expose to systematic way of putting or writing observations in a formal manner.

Engaging in Mathematics Investigation, first, the students are exposed to new opportunities to find solution to unfamiliar situations; second, they tried to put emphasis to those aspects of the discipline least susceptible to replacement by technology, third, they are provided with opportunity and expectation for sustained exploration of a situation, fourth, they are also provided the chance to learn more about Mathematics, and finally, teachers are provided with different source of motivation.


There are several stages in an investigation. First is preliminary Skirmishing or collecting all ideas in relation to the situation or problem to be investigated. Second is Gestating or selecting the nearest possible solution needed. Third is Exploring Systematically or a step by step application or use of the selected strategy or strategies. Fourth is Making Conjectures or guesswork based on presumption or insufficient evidence. Fifth is Testing Conjectures or continuous testing of different strategies gathered.  Sixth is Explaining or Justifying which refers to elaborating how things happened. Seventh is Reorganizing or systematic arrangement of ideas to be easily understood by the readers. Eighth is Elaborating or expounding the ideas by presenting more examples to support the principle obtained and Lastly is Summarizing or collecting all informations being organized. This last step can be presented in a general rule or formula which explains the whole work under investigation.

Several questions may be asked when writing a formal report on Investigation:
1. What is the problem?
2. What systematic approach can I use to produce a pattern in this problem?
3. What is the pattern?
4. How is the pattern can be applied?
5. Is there a rule?
6. Can I write a description or formula of this rule?
7. Can I prove this rule?
8. Can I apply this rule to other situations?
9. Are there other rules?

Two points to be considered in writing a report on Investigation
1. You are attempted to convince  the reader beyond any doubt, that you are correct in every detail, and have considered all situations; and
2. You try to pre-empt any question on the part of the reader and answer them within the report.

Investigation on Pattern Recognition

Determine the number of angles formed given n rays.

A.     If a ray is drawn, no angle is formed.
    If two rays are drawn, connecting the endpoints, one angle will be formed.
    If three rays are drawn, there are 3 angles to be seen as illustrated below.

B.   How many angles will be formed if 4 rays are drawn? 5 rays? 6 rays?

C.   What is the pattern? Applying the pattern discovered, give the number of angles formed with 7, 8, and 9 rays.

D. Draw the angles.

E. How much is the no. of angles increased when the number of rays is increased by 1?    (Hint: Get the first differences in y.)




                                                                            3                      For three rays, there are 3 angles                                                     1                                      formed namely; angle 1, angle 2 and                                                   2                                              angle 3.

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