Comparing Cubes

Two Cubes

Volume = 125 cm3

Volume = 97336 mm3

DIAGRAM NOT TO SCALE

A Mathematics Lesson Starter Of The Day


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Topics: Starter | Roots

  • Transum,
  •  
  • There are a number of concepts involved in this problem. The one most students find quite difficult to understand is converting cubic millimetres to cubic centimetres (or vice versa). Finding the cube root of a number is also challenge to most pupils. This is probably a starter that will require a certain amount of guidance, help and support from the teacher but once the method has been established refresh this page to get the same problem with different numbers.
  • JD, WA
  •  
  • Students don't need to convert cubic mm to cubic cm. They can find the cube root of each and then they are converting mm to cm which is much easier!
    "If there is a better solution find it!" - Thomas Eddison.

    [Transum: Excellent observation JD. Thanks very much for sharing.]

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This starter has scored a mean of 2.6 out of 5 based on 81 votes.


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Answers

Hint: If you don't have a calculator with a cube root function here are the keys
you would need to press to find the cube root of 97336:

97336^(1÷3)

This works because raising a number to the power one third is equivalent to finding the cube root of the number.

Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.



Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...

Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

iPad Air

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent Christmas gift for anyone.

You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...

Click the images above to see all the details of these gift ideas and to buy them online.

Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

Transum.org/go/?Start=August12

Here is the URL which will take them to a self marking quiz about volume.

Transum.org/go/?to=Volume

Student Activity

 


Interesting fact for the Teacher!

There is a simple method to compute the cube roots using a non-scientific calculator, which requires only the multiplication and square root buttons. No memory is required. The following method is used:

This process is continued until the number does not change when the multiplication button is pressed, since the repeated square root gives 1 (this means that the solution has been determined to as many significant digits as the calculator can handle). Then, press the square root button one last time. At this point an approximation of the cube root of the original number will be shown in the display.

A full explanation of why this works can be found onWikipedia, the free online encyclopedia.

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