Friday, 2 November 2012

How do you measure 1/4kg with a 1kg weight?

A follow-on from Fraction-o-rama

Gentle Reader,

You may recall in my previous post about "Fraction-o-rama", I promised to describe some interesting solutions to one of the problems.

The problem was about measuring our 1/4kg of rice using only a 1kg weight and some balance scales.

Now, before I go any further, let me issue the following....


The author of this blog does not condone the use of food
for non-eating purposes. There are enough starving people
in our world that using rice for a maths activity is morally 
questionable. The rice used in this activity has been used for 
many years for maths and is probably not good to eat anymore.
It's use for this purpose pre-dates my current ethical position.

The Task

You may recall, the task in Fraction-o-rama was to measure out 1/4kg of rice. 

Well, using all the measures was too easy, so I removed all but the 1kg weight to see what would happen. I only gave back the 250g weights at the end to check the process.

Here are two solutions:

Solution #1 - The Walker Method

First you measure out 1kg of rice.

Then you divide it in half until the balance is even.

Then you tip out one bucket and divide the remaining bucket in half until it balances.

Then you tip out one bicket and see if the remaining bucket equals the 250g weights just to check.

Solution #2 - The McAllister Method


First you tip out 1kg of rice on the table.

Then you divide it roughly into 4 groups.

Then you get 2 sets of balance scales and put one pile in each bucket. The buckets A1 and A2 were pretty even but buckets B1 and B2 weren't.

You adjust the amount of rice on each bucket until it balances.

Now you know that the A buckets are even with each other and the B buckets are even with each other. You need to test that one of the A buckets is the same as a B bucket.

Oops! A1 is heavier than B1.

So adjust what is in these buckets until they balance.

Finally check that one of them is the same as the 250g weights.

So what?

Well, I was stunned. Not only did some of the kids work out how to divide the kilogram of rice into quarters evenly, they actually demonstrated two different methods.

I was a very happy teacher and I do believe that some valuable learning happened, especially for the expositors of the two methods, Messrs Walker and McAllister.

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