According to the understanding of the many, the game could not be fair enough since it brings the results at some points which are not genuine as per the expectation of the participant since the die is just through and gives some random outcome which may not favor the needs of the participant prompting for repeat of the process in order to get the correct value.

Normally, the theoretical value of the player winning the game will depend on the number of games played at ago. But it is believed to be ½ as the value for one winning the game. This because of the fact that the total probability being 1. From the experiment outcome, the probability of one player winning depends majorly on the results obtained by the player in the game. For the Claire, she will be able to get 41/60 as the experimental value of the game while that of the other colleague Sharon will be 19/60. This normally depends on the results obtained from their respective tallies of the experiment.

For the fair sample space of the game, a grid can be used instead and this could be fair to both parties involved in the game. This grid will enable them to come up with a fair way of getting the outcome of the game for any single throw.

For a fair game, it would be in order to take the turn taking technique in which we interchange the mode of the throwing of the die to get the value for recording, and this will eliminate the element of doubt to some points in the play. Since the die has six faces, and the outcome depends on the number shown after the through, the grid will solve the menace of getting the correct answer by the participants in the game.

The investigation could have been extended by using another extra die to make them three. This will make the tallying procedure to take some time and give at least some accurate values in the table. Using two dice would not have been so accurate to some extent compared to using three dice. Still a grid could have been drawn to show how the tallying could have been somehow simply since each die could have been dealt with solely and result obtained and recorded.

For the investigation involving the human body parts of 6 group members, it can be deduced that for the human bodies, the part that almost gives a ratio of 1:1 is the base of the hand to the tip of the longest finger. This shows that they are somehow proportional to each other in terms of sizes. It is believed that some parts of the human body do have some kind of similarity especially the arm which has already given the required comparison.

For Barbie and Ken, there results for the same height is somehow different and does not give the exact value as required by the data.

This could have attributed to the way they carried out the measurement and the mode of recording. If she could have been proportion to her height which is 30cm, then she would have been about 3cm. The foot length of each and every person in the group would have taken at least tenth of the height measurement. Like the case of the Barbie, her foot length just took the approximated the length which almost tenth to that of her height.

For the creepy critters, the data that was obtained is as shown below

These values shows the theoretical values of the results obtained in the experiment and at some points can be proved to be correct depending with the values in the experiment. This values once plotted against each other will give a graph which is somehow similar in nature for the two different creepers critters as carried out by the two students.

Reference

Gardiner, A. (1987). Discovering mathematics: The art of investigation. Oxford [Oxfordshire: Clarendon Press.

Niss, M. (1993). Investigations into assessment in mathematics education. Dordrecht: Kluwer Academic.

Schmidt, W. H. (1997). Many visions, many aims. Dordrecht: Kluwer.

Lundy, D. C. (2002). Lunar landing and return: A simplified physics and mathematics investigation : the Apollo 11 saga.

Le, V.-N. (2006). Improving mathematics and science education: A longitudinal investigation of the relationship between reform-oriented instruction and student achievement. Santa Monica, CA: RAND.