# Mathematical Tasks - Math Problem Example

Summary
Working on mathematical tasks involving geometric thinking, as experienced in various tasks, falls under different levels of difficult from learner to learner. For example, there are problems those mere calculations in order to arrive at conclusions, while there are problems that need applications of mathematical concepts and problem solving techniques in order to arrive at a solution…

## Extract of sample "Mathematical Tasks"

Then we have 14 x 4 -= 56cm
Similarly, CD = 15 x 4 = 60 cm
The perimeter of CDE then becomes
60+52+56 = 168cm

Measurement as a mathematical object is also very necessary in this mathematical task where the measurement units are given in centimeters. Mathematical process like connection where mathematic ideas interconnect and build on one another to produce a coherent whole has highly been applied on this task. Mathematical processes like representation is also very important as it helps the learner to organize, record, and communicate mathematical ideas.

Geometric reasoning.
(ii) Chapter 3 is about geometric reasoning. Basing on task 3.3.3 the following mathematical task has been formulated.
B

A C

To construct a circle inside the triangle to touch the side of the triangle which is generally termed as an inscribed circle, then there is a lot of geometry involved (Bates, 1979).

This can be done as follows: -
(a) Bisection of angle BAC and extending the bisecting line to a point, p.
(b) Bisecting the angle ACB and extending the bisector to a point, m.

Where the two bisecting lines meet, say point O, becomes the centre of the circle.
With a pair of compasses, you pin at the meeting point of the two lines and draw a circle that touches the vertices of the triangle ABC. This is what is called an inscribed circle.

This can be shown in fig,1.2 below: -

B

o

A C

Measurement as a mathematical tool is highly used here. The length of the sides of the triangle can be measured as well as the radius of the inscribed circle. Reasoning and proof are mathematical processes that are also applied on this mathematical task. It is only...
A mathematical task like the one below entails many more mathematical objects apart from geometry because algebra can also be involved.
Measurement as a mathematical object is also very necessary in this mathematical task where the measurement units are given in centimeters. Mathematical process like connection where mathematic ideas interconnect and build on one another to produce a coherent whole has highly been applied on this task. Mathematical processes like representation is also very important as it helps the learner to organize, record, and communicate mathematical ideas.
Measurement as a mathematical tool is highly used here. The length of the sides of the triangle can be measured as well as the radius of the inscribed circle. Reasoning and proof are mathematical processes that are also applied on this mathematical task. It is only through concrete reasoning and proofing what you reason by for example bisecting the angles that one comes to see that the circle touches the sides of the triangle but not the vertices.
Use of mathematical tools like a pair of compasses, calculators and rulers has also been highly applied to solve this mathematical task. Mathematics thinking and language is highly exercised and mathematics ideas expressed precisely.
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