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# National Curriculum - Reasoning and problem solving : Key Stage 2 : Mathematics Content Knowledge

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Key Stage 2
National Curriculum - Reasoning and problem solving
Question 17 of 19

# 5. How confident are you that from the history of mathematics and mathematics in other cultures, you know relevant examples of:

## Example

The use of our standard system of measurement has evolved over time.

The Romans used seeds and beans to measure weights. A foot, divided into 12 inches, measured length. Five feet equalled one pace. 1000 paces measured a Roman mile (close to our mile today). These measures varied widely from place to place.

In the 13th century in England, a royal decree defined weights and measures to make them the same everywhere. The definitions lasted for 600 years.

In the late 18th century in France, a metric system based on a metre and a gram developed and spread. 17 countries signed up to using it in 1875.

Today, only the United States, Liberia and Myanmar have not switched officially to the metric system.

The UK is still not entirely metric. Some of the old measures, called imperial measures, are still allowed, such as miles and pints.

## What this might look like in the classroom

Problem 1
How could you explain to children why standard measures are more reliable than the Roman versions in the example?

One possible solution:
In Roman times a pace was the same as five "feet" − but whose feet? Everyone’s feet were different so the paces must have been approximate measures as one pace would be a different length depending on the feet being used.

Problem 2
We used to use the measure of a cubit which came from Ancient Egyptian times. It was the length of the forearm from elbow to tip of the middle finger. What body measurement was a half−cubit?

Solution:
A hand span– children could check to see if this works!

Problem 3
How many of the following imperial to metric conversion do you know?
Inches to centimetres
Feet to metres
Miles to kilometres
Pounds to kilograms
Ounces to grams
Pints to litres
Gallons to litres

Solution:
These are rounded to the nearest two decimal places:
1in = 2.54cms
1ft = 0.31m
1 mile = 1.61km
1lb = 0.45kg
1oz = 28.35g
1pt = 0.57l
1 gal = 4.55l

What problem solving activities could you make up involving imperial and metric conversions?

## Taking this mathematics further

#### The origin of our measurement system

It is interesting to know where our measurement system originates from. Here are a few facts:
The cubit is one of the earliest known units used by people from ancient civilisations to measure length. The common cubit was the length of the forearm from the elbow to the tip of the middle finger. Half a cubit was measured using a hand span, one sixth of a cubit was the width of the hand and the width of the middle finger was one twenty−fourth of a cubit.
The inch, foot and yard evolved from these units though it is not yet fully understood how. Some people believe these were simple proportions or multiples of the cubit. The Romans and the Greeks inherited the foot from the Egyptians. The Roman foot was divided into 12 unicae which to us became inches. The Roman mile was introduced to Britain during their occupation. Queen Elizabeth 1st changed the original length of the mile to the one we use today.

The grain was the earliest unit of mass and was measured according to the weight of grains of wheat or barley. These were used to measure silver and gold − now called troy ounces.
The pound, stone, quarter, hundredweight and ton were larger units of mass used in Britain. Today only the pound and stone are used. The pound is often used for measuring fruit and vegetables, stones for personal body weight.
The gill started out as an old French wine measure that may have become our gallon. A quart is a quarter of a gallon or two pints.

Investigate body measurements with your children e.g. seven "feet" is around the same as their height, their foot measurement is the same as their forearm from elbow to wrist − what do they discover?

## Making connections

In KS1, children continue their Foundation Stage journey by measuring using non standard units, they then learn why standard units are important and finally move on to measuring to the nearest half and whole metre / kilogram / litre. Using historical information such as measuring length in feet in Roman times and the fact that different people will have had different sized feet will help the children understand why standard units are important. Choosing two or three children to measure items using their feet will help to reinforce this. You could do the same for cubits.

In KS2 children develop their skill in order to measure to the nearest centimetre, 100 g then gram and 100 ml. By Year 6 children should know the basic conversions between metric and imperial measurements for length, weight (mass) and capacity.

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