NMBR140: Introduction to Mathematical Thinking – Investigative Project – 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. Your shape is shown below. 

There are two parts to complete. 

(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. 

Shape A Shape B 

One of these will be in the collection of shapes you found in part (i) while the other will not. Why isn’t the other shape in that collection? 

Your explanation should be at a level that anyone could check that the two shapes are different. That is, you can’t just quote some odd phrase as your reason. You need to be able to convince someone that they are in fact different. 

In your answer, you will need to explain how to decide if a polyhedron is in the collection. 

Hints for the video: Based on past videos from students we would offer a few pieces of advice. 

(1) You should target your video at the level of explaining the problem to someone who doesn’t know the topic. Imagine you’re trying to explain it to a good year 6 class. 

(2) Don’t just copy information from a website or book. If you can’t explain what something means, you shouldn’t put it in the video. 

(3) Avoid a purely ‘talking head’ video. That is, the video should not (just) be you talking to the camera. Your image doesn’t need to appear in the video at all, you can appear but you don’t have to. 

(4) If you have to hand-hold a phone or camera to take the video, please rest it on something while you are recording. If your marker is sea-sick, then they may not be concentrating on your video! (These are not the only ways to make the video, there are other options.) 

(5) The referencing requirement applies to the content of the video. Some have a single reference list with the written part of the task, others have references in both places. Both approaches are acceptable. 

(6) And, above all, even though you may not like it, you should watch your final video from start to finish before you submit it. And in enough time to fix any major problems. (Most embarrassing: have you spelled your own name correctly?) 

(iii) What is the difference between these two shapes? We’ve given you two views of each. 

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 30mL. 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 

You now have your 2mL. You should try playing around with smaller numbers first, then try to solve this problem with your given cup sizes. Cups with sizes 3 and 7 have been used here, you might play with those, or something like 4 and 9, or whatever pair takes your fancy. 

Note: You have to find the exact amount in one go. You can’t, work out how to obtain 1mL, and then just repeat that 3 times to say you’ve got 3mL. You have to end up with exactly 1, 2 or 3mL in one of the cups at the end.