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102208 Fundamentals for Working Mathematically - Mathematical Investigation Report
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Fundamentals for Working Mathematically Autumn 2020 Mathematical Investigation Report Investigation 1: Yowie Sighting Part 1: Module 2 required students to focus on ratios, measurements, and errors in measurement. We started by forming a group and measuring each group members body parts th...

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  • April 18, 2023
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  • 102208 fundamentals for working mathematically

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102208 Fundamentals for Working Mathematically
Autumn 2020
Mathematical Investigation Report
19689018


Investigation 1: Yowie Sighting

Part 1:

Module 2 required students to focus on ratios, measurements, and errors in measurement. We

started by forming a group and measuring each group members body parts that were listed in

the table with a measuring tape, identifying any patterns, relationships and/or ratios. The

results are as followed;

Student name Heig Arm Should Base of Radi Head Foot Elbow Head
ht span er the us to the lengt to circumferen
width hand to (wris base h should ce
the tip t to of er
of the elbo the
longest w chin
finger joint)

Mahima 148c 148c 38cm 16cm 15cm 18cm 21cm 30cm 27cm
Kumar m m
Ivah Siega 155c 160c 36cm 17cm 16cm 19cm 25cm 32cm 28cm
m m
Aman Reddy 170c 174c 40cm 19cm 23cm 20cm 26cm 32cm 26cm
m m
Akansha 177c 183c 45cm 19cm 27cm 19cm 27cm 33cm 22cm
Sharma m m

After recording the results, we commenced answering the investigation questions with the

first question focusing on the height to arm span ratio. It is believed that a person’s arm span

is usually equal to her height with mathematicians suggesting the arm span to height ratio is

one to one; that means a person’s arm span goes once into their height. By analysing the data

between the 4 group members, 1 member is able to prove this theory with a height and arm

span of 148, arm however, the 3 remaining students measured their arm span to be somewhat
Student 1:
greater than their height.
Height: Arm Span Student 2: Student 3: Student 4:
148:148 Height: Arm Span Height: Arm Span Height: Arm Span
1:1 155:160 170:174 177:183

,As such, while there is a possibility of both measurements to be the same, there is a

higher chance of individuals measuring their arm span to be greater than their height,

therefore, debunking this theory.



Furthermore, the next question required us to identify any other relationships in our

measurements, for instance, the ratios and scale factor through calculation. In order to

find the human ratio, we began by calculating the average human height and foot length

based on the measurements we recorded;



Average Human Height
( 148+155+170+177 ) ÷ 4 ¿ 650 ÷ 4 ¿ 162.5 cm

 the average human height = 162.5cm



Average Human Foot Length
( 21+25+26+27 ) ÷ 4 ¿ 99 ÷ 4 ¿ 24.75 cm

 the average human foot length = 24.75cm


After calculating the average human height to be 162.5cm and our foot length to be

24.75cm, we divided the height by the foot length to determine the human ratio which

will assist us in acquiring Yowie’s height.




Human Ratio
Height: Foot length

162.5: 24.75 6.6 :1

,  the human ratio = 6.6:1, meaning our height comprises of 6.6 multiplied by our foot

length



The calculations assisted us in answering the next question in which we were asked to

find Yowie’s measurements. As we were given the foot length of the Yowie, we were able

to use to human ratio we had calculated in the previous question. However, first we had to

establish the ‘Yowie Ratio’ which would be easy as we were given the foot length.



Yowie Ratio
Height: Foot Length
? : 43 6.6 :1



The human ratio was applied to Yowie, whose foot length is known to be 43cm. Through

this information, we were able to use the ratio to calculate the height of Yowie.



Yowie’s Height
? : 43 6.6 :1 43 x 6.6 ¿ 283.8 cm

 Yowie’s height = 283.8cm

To determine the stride length of Yowie if he were walking, we thought to use a height-

based formula, however, the formulas vary between male and female which may make

our stride length inaccurate as our group is a mix of both genders. As such, we calculated

our stride length by walking 10 steps and measuring the distance from start to finish. In

order to find the average, each group member completed the same process and we

calculated our average stride length.



Average Human Stride Length
The distance each student travelled within 10 steps are as followed:

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