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I always launch my first ever maths lesson of the year by looking at ancient number systems.
Firstly, I display the picture above (from NRich) and generate a conversation - what could it be? Does it remind you of anything? (e.g. tally charts). Get the children to discuss their ideas in small groups and then feedback to the class.
I then gather the ideas and generally children link it to counting and numbers. We talk about it perhaps being evidence of Stone Age counting and that it was found in a cave in Spain and could be up to 25,000 years old (in history you could plot this on the Stone Age timeline).
I then ask children to invent their own counting system using symbols. To start with I do this as a class-led activity and we talk about the numbers that would be useful to have a key for - e.g. 1, 5, 10, 20, 50 and 100.
Children then come up with ideas of symbols in small ability groups. They usually have highly creative ideas but here's one of my own more boring examples (!) :
I tend not to show them an example prior to them thinking of ideas though because sometimes that can limit their creativity. Instead we 'critique' their ideas and say what's effective and why. The children can then come up with their own key independently using the good ideas or you may wish to work with a group to develop their thinking.
Once children have established their counting system, I differentiate simply in the following way:
- less able - represent 16 in as many ways as possible using your system. Try and use a systematic approach. (You could then extend by saying 'what about 18? Are there more or less ways? etc)
- middle - same as less able but with bigger numbers, e.g. represent 26 in as many ways as possible...
- higher - do you think odd or even numbers can be represented in more ways? Why? Represent 27 and 28 in as many ways as possible. Which is the most efficient way? Explain why. Are there any other numbers you would like to include in your key? Yes/no/explain
You could then get children to represent bigger numbers in the most efficient way - e.g. 165, 365 and even into thousands.
I find that this gives you a fantastic idea of what children already know about place value and also counting in 5s and 10s.
Another extension is to get children to write numbers using their key and getting a friend to work out what numbers they have written.
These ideas could continue over a couple of days as you can continue to deepen their thinking and work with any children who need more support.
(Below is an example of very simple differentiation that can be developed as you go along)
This is a really simple and effective starter I created for the following day:
I then love having a discussion about the following:
- Why are numbers important?
- When were they invented?
- What did we use before numbers?
- What ancient number systems do children know about already?
Sometimes this leads into a mind-bending conversation about infinity and Googolplex (but depends on the class!) haha
I find this book below useful during these kinds of discussions:
I then spend a lesson looking at the Egyptian number system.
I tend to get the children to draw the place value system (up to 1,000 or 10,000 for Year 4) and then we do similar activities to above - for example, getting children to represent differentiated numbers. To keep it simple, I split my board in 3 and have 'blue' numbers which are easier, e.g. 17, 24, 36; 'green' numbers which are in the middle, e.g. 76, 89, 94 and 'red numbers' which are harder e.g. 254, 653, 786...
Children can choose their level of challenge and you can really see who gets partitioning and place value and who needs more support. You may put the less able children in one group and do a led version of the activity where you are modelling it. I tend to get the children to write the numbers in columns underneath each other to make it clearer.
See this page for more info on the Egyptian number system!
This then leads in nicely to Roman numerals. I start this lesson by getting the children to come up with rhymes and pictures to remember the order. My class last year came up with:
See this page for more on this!
I then teach and model the rules of reading and writing numerals. The children make some numbers in Roman numerals using lolly sticks which is one of the activities in the White Rose.
Then we talk about the Arabic system and why this was invented. It's good to compare it to the other number systems and look at the benefits. We then look at the importance of base 10 and place value columns. Discuss - How does this make life easier?
I then like linking concrete resources to the place value system and we talk about how 1,10,100 and 1000 are represented in/on:
- Dienes
- Rekenrek
- Numicon
- Place value counters
Another activity I like to do early on is get children to represent 10, 100 and 1000 in as many ways as possible. This can be as simple as getting a large piece of sugar paper with the number 1000 written in the middle on each table and getting children to illustrate, draw and write their ideas. They tend to make links to their previous learning on ancient number systems and use the Egyptian system and Roman numerals to represent the number. It tends to be a really fun and interesting lesson. One of my children amazed me last year when they wrote L multiplied by XX and they also wrote L twenty times and DD.
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