Essay NMBR140: Introduction to Mathematical Thinking – APA Referencing Format – Mathematics Assignment Help

Assignment Task:

1. Investigation Each of you has been given a picture of a three-dimensional shape (a polyhedron, if you like names). Each of the shapes is from a collection of particular shapes, your job is to investigate your shape and the collection of shapes. 

There are two parts to complete. (NMBR140)

(a) You must produce a video presentation with narration (no longer than 5 minutes) containing your solution to parts (i) and (ii) below. (And also make sure you read the hints about the video that we provide at the end of this question.) 

(b) You must provide a written solution to part (iii). 

The questions you need to answer are given below. 

(i) What is the name of your shape? 

This shape is one of a collection of shapes, what is the name of that collection, and how many shapes are in that collection? You should also discuss the history of this collection of shapes. Why the name of the collection? Why were people interested in them? And so on. 

(ii) Have any of the shapes in the collection you found been used in applications in the real world? Do any of these shapes appear in nature? Describe a couple of the applications, and some places were they appear in nature.

2. Playing with numbers. Bianca is looking after a sick relative and must measure exactly 2mL of medicine. After a long search Bianca only finds two measuring cups, one holds 13mL and the other 36mL. No other measurements are shown on the cups. In fact, these two cups and the medicine bottle are the only containers that the medicine can be put into. And you can’t mark the cups in any way. But, most importantly, you can’t just judge how much is or is not in a cup, you have to be exact with your measurement of the medicine. 

(a) Using just these two cups (and the medicine bottle) how can Bianca measure 1, 2 or 3mL? Here you should play around with the cups and measurements, stopping when you get to one of those amounts. As you’ll see in the example below, carefully explaining what you have done is tricky but important. 

(b) Can Bianca use these to measure exactly 2mL? If you have already answered this, then use these cups to measure exactly 3mL. 

(c) Can Bianca use these two measuring cups to measure 1mL? Again, you might have the answer already. If you have, then fill in the gap by making sure you can find all of 1, 2 and 3mL. 

(d) Extension question: Describe a way of getting any possible measurement using these two cups? Or explain why some measures are impossible to get. 

The answers here can be quite complicated. For example, if Bianca only had cups holding 3mL and 7mL then one solution for getting 2mL is 

(i) Fill the 7mL cup 

(ii) Fill the 3mL cup from the full 7mL cup leaving 4mL in that cup 

(iii) Empty the 3mL cup back into the medicine bottle 

(iv) Fill the 3mL cup from the 7mL cup leaving 1mL [for part (a) you would stop here] 

(v) Empty the 3mL cup back into the medicine bottle 

(vi) Pour the 1mL into the 3mL cup leaving the 7mL cup empty 

(vii) Fill the 7mL cup again 

(viii) The 3mL cup has 1mL in it at the moment, now fill that cup with 2mL from the full 7mL cup leaving the big cup holding 5mL 

(ix) Empty the 3mL cup back into the medicine bottle 

(x) Fill the 3mL cup from the full 7mL cup leaving 2mL in the big cup