# Jugs to Measure – more or less

Challenge On Boarding – measuring is comparing

We compare things all the time.  From when we were very young, we look out for some things which are bigger or smaller.  We are interested in how much bigger we are now than a month ago.

What do we measure?

What do you think the most important measurements are for us nowadays?  Here are some of the things we can measure.  What units do we use to measure these things? Do a quick survey to find out which one your friends feel is the most important to measure.

Things we need to measure

• Height
• Speed
• Wealth (or debt)
• Weight
• Energy used
• Popularity
• Skill (say in football or music)

On Boarding Challenge

How would you compare two people’s skill in a sport, art or school subject?

Challenge On Boarding – Measuring means Multiples

Metric Measures

Traditional measures were easy to do but not very accurate.  Anyone can measure using a number of strides but they won’t be the same as another person’s stride and might not even be very similar from stride to stride for you.

The scientific revolution (also known as the enlightenment or renaissance) brought not only the need for precision but the metric measurement system that could allow that precision.

Metric measures start with a metre and the rest of the measures (litres and even grams) are based on that.

Multiple measures

Once we have standardised measures, we can use multiples of exactly the same measure.

Money is a great example of this.  It starts with a penny.  We have other coins that are a multiple of a penny (2 pennies, 5 pennies etc.).  This means we can measure any multiple of a penny using coins and make any amount without having say a 7p coin.

On Boarding Challenge

How many different ways can you make 7p using coins?

Challenge On Boarding – Difference between measures

Change or difference in measures

9 out of 10 times, when you go to the shop to buy something using cash, you will get change.  Even though it is possible to make any sum of money (that is a multiple of 1p at least), it is still almost impossible (or at least very inconvenient) to shop without using the concept of change.

The idea of change is that of using the difference in value (say between a £1 coin and a bag of crisps).

We can use this idea in our jugs challenge.  We can, for example, measure out 2 litres using the 2 jugs (even though it’s not a multiple of 3 or 5)

Multiples of 3 and 5

Work out the multiples of 3 and 5

On Boarding Challenge

Explain how you could actually measure out 2 litres using the 3 and 5 litre jugs.

Download or share all of these challenges with this pdf and let us know how you got on with it by tweeting using #momentofmaths and start to see Every moment is a #momentofmaths.

If you would be interested in joining an online maths club session that explores this or other Maths Explorers’ challenges, our online programme are now live. There are a few places remaining. Find out more at https://online.roots2grow.org/