Year 4: Roman numerals
Focused learning objectives
Starter: Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens and units/ones)
Main: Read Roman numerals to 100 (I to C) and know that, over time, the numeral system changed to include the concept of zero and place value
Be familiar with the letters that the Romans used to represent numbers
Understand the rules the Romans used to write numbers 1–100
Understand some of the differences between the number system we use today and the system the Romans used
numeral, number, place value, place holder, digit, one-digit number, two-digit number, three-digit number, four-digit number
Individual whiteboards and pens for the children
Large sheets of sugar paper split into a ten by two grid as shown in Figure 9.1 (these will combine in the plenary to make one big hundred square containing Roman numerals).
Ten by two grid
A large 1–100 square (so children can compare and contrast Roman numerals with our number system)
Write the following three numbers on the board:
4205 4025 4052
Make sure the children can read each number and then ask them to discuss in pairs which number is the odd one out and why. Encourage them to find reasons why each number could be the odd one out and to be ready to justify their reasoning.
Take feedback, making sure that comments made about the place value of the digits in the number are discussed. The following questions can help to elicit specific information if it is not part of the initial feedback:
Now move on to further questions, such as:
Now put the following digits on the board:
and ask the children to record on their individual whiteboards numbers such as:
Summarise that we have been using our knowledge and understanding of place value to carry out this activity. We know that the value of a digit depends on where it is positioned and by moving digits around we can change numbers. We have been able to create different numbers using the same digits.
For children who are not confident with four-digit numbers, ask them to engage in similar activities but with three-digit numbers.
Explain that, although the number system we use today has been used for a long time, in the past the way we recorded numbers looked very different. Tell the children that during the lesson they are going to explore the system the Romans used to record numbers and at the end of the lesson you would like them to think about what is the same and what is different about the Roman system compared with the system we use today.
Show the children the symbols the Romans used for 1 (I), 5 (V), 10 (X), 50 (L) and 100 (C). Now show them the following numbers written in Roman numerals and ask them to work in pairs to try and work out what numbers they might represent:
Take some responses, asking the children to justify their suggestions, but at this stage don’t discount suggestions that don’t follow the ‘rules’ the Romans devised. Explain that all number systems have been created over time and that to avoid confusion we all need to follow the same rules. The Roman system created numbers by adding together the value of the numerals and recorded these using the fewest numerals possible; therefore XVI would be 10 + 5 + 1 =16. They nearly always recorded the biggest numerals they needed on the left and the smallest on the right. In pairs ask them to have a go at writing the following numbers using Roman numerals:
Share their solutions and discuss any differences of opinion.
Now write the following on the board:
With their partner ask them to discuss what is the same and what is different about each pair of numbers and what different numbers each set of numerals could represent. Take feedback and let the children share their ideas.
Now explain the next rule the Romans used. To prevent very long numbers, one smaller numeral could be used to the left of a larger numeral to show that this number was subtracted from the total – therefore instead of writing 4 as IIII you could write it as IV (5 – 1) and instead of writing 9 as VIIII you could write IX (10 – 1). Look back at the set of numbers on the board and clarify what numbers are represented by each set of numerals.
Ask the children to work in pairs to think how they would use this system to record:
Explain that as a class they are going to record all of the numbers from 1 to 100 as Roman numerals. Split the class into groups so that different groups are responsible for writing different numbers, e.g. 1-20, 21-40, 41-60, 61-80 and 81-100. In pairs the children need to agree how to record these numbers. They then compare their answers with another pair and where there is a difference of opinion they justify their reasoning. When the group has agreed their numbers they need to record their agreed numerals on the big piece of sugar paper.
Give children the Roman numerals from 1 to 20 on pieces of card and the children could work in pairs to sort these into the correct order before copying them on to the large piece of sugar paper.
Challenge the children to write Roman numerals in response to questions such as:
Start at 4 and count on in tens. Record this number pattern using Roman numerals. What patterns can you see in the way the numbers are recorded?
Record the following on the board and ask the children to discuss in pairs what is wrong with each of these and then to correct your mistakes:
IIIIII, IIIX, VIX, XXXXX, XXXXXIIIIIIIII
Now collect the large pieces of sugar paper and stick them together to make one large hundred square containing Roman numerals. Compare this hundred square to the one we use today. Ask questions such as:
Help the children to recognise that the Romans used an additive system while we use a positional system (our place value system is built around the position/columns in which we place numbers).
Over the next few days challenge the children to find examples of Roman numerals still being used today. Ask them to bring in images of these that can be shared with the class.
This lesson involves regular opportunities for children to discuss their thinking in pairs. Listen to the language they use and their confidence in justifying their reasoning.
Whilst they are working, ask children questions such as these:
- Why have you decided to write the number that way?
- How do you know you’ve recorded it correctly? What rules did you use?
The numbers the children will find most challenging are those that involve the element of subtraction, e.g. 4, 9, 14, 19. Children may forget about this rule or apply the rule incorrectly; for example, they might record 19 as XVIIII or think they can record a number such as 8 as IIX (10 – 2). You might want to record a list of the ‘tricky’ numbers on the board to help remind the children of the numbers they can apply the subtraction rule to.
Look out for children who have a limited understanding of place value. Comparing and contrasting the Roman numerals to our number system may expose some gaps in understanding about how our number system works. Children may not have fully understood the significance of zero and how this is used as a place holder within our number system.
Ways the lesson could be adapted
For classes who find it challenging to work collaboratively the lesson could be structured so that children work in pairs to record as many numbers, using Roman numerals, as they can on a blank hundred square. They could then bring this to the plenary to compare and contrast it with our Hindu–Arabic hundred square.
For children who already have some prior knowledge of Roman numerals you could ask them to convert a number pattern into Roman numerals to explore whether similar patterns exist, e.g. 3, 13, 23, 33, 43, 53, etc. or 9, 18, 27, 36, 45, etc. This would again provide a good forum to compare and contrast the systems and to reinforce the importance of place value within the number system we use today.