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

Success criteria

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

Timing

15 minutes

Timing

35 minutes

Timing

10 minutes

Starter/introduction

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:

• What does the 4 represent in each number?
• What does the 2 represent?
• What does the zero represent?
• How do you know which is the biggest number?

Now move on to further questions, such as:

• Using the same four digits, can you make a number between 4 025 and 4 205?
• Can you make a number smaller than 2 000? (e.g. 0 425)

Now put the following digits on the board:
3, 2, 4, 0

and ask the children to record on their individual whiteboards numbers such as:

• the largest four-digit number they can make
• the smallest four-digit number they can make
• a number between 2 030 and 3 000
• two numbers with four hundreds and three units

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.

Simplify

For children who are not confident with four-digit numbers, ask them to engage in similar activities but with three-digit numbers.

Main

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:

• III, VIII, XVI, XXX, XXVII, LI

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:

• 2, 7, 13, 28, 32, 83

Share their solutions and discuss any differences of opinion.

Now write the following on the board:

• IV and VI, IX and XI, XIV and XVI, XIX and XXI

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:

• 14, 19, 24, 29, 34, 39

Take feedback.

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.

Simplify

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.

Extend

Challenge the children to write Roman numerals in response to questions such as:

• How would you record 444 and 999?
• How might you record 1 000? Justify your answer.

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?

Plenary/conclusion

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

Take feedback.

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:

• What patterns can we see in our hundred square? Are there the same patterns in the Roman hundred square?
• How many one-digit numbers are in our hundred square? Why is this different in the Roman hundred square?
• How would the Romans have recorded 0? (They hadn’t developed this symbol! Point out how important 0 is in our number system.)

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.