To understand and use properties of number.
To work systematically to identify prime and non-prime numbers.
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Resources |
Vocabulary |
Prime numbers teachers’ notesheet
Calculators
A4 paper
100 squares (small)
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multiplies, doubles, digits, even, factors, prime numbers, more than, less than, between, square |
Organisation |
Near ability pairs on mixed ability tables
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Whole Class Preparation: (about 5 mins) |
What Introduce a context, such as ‘The monster wants to take some children to eat. It looks down the register and selects children by their register number. It will eat child 5 but not 6, child 29 but not 30’.
List these numbers under two headings on the board
Eaten Not eaten
5 6
29 30
Ask children to suggest roughly four other numbers less than 50 for you to place under one of the two headings. Use the teachers’ prime numbers notesheet to help decide which column to place the numbers in.
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Paired Work: (about 10 mins) |
In pairs, write down any suggestions you have about how the monster decides which children to eat.
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Class Sharing: (about 15 mins) |
Which numbers do you think will decide whether or not a person will be eaten? Record children’s ideas on the board under the heading ‘Good enough to eat’ Suggestions may be: double digits, no curves, multiples of 11, digital roots, odd, not square...
The monster returns and more numbered children are considered and sorted into eaten or not eaten. As the new information is collected, the children discuss and refine descriptions that, typically, are not precise enough.
Help children realise those people labelled with prime numbers will be eaten. A prime number is a number that is only divisible by one or itself.
How do we know if numbers are prime numbers? Accept a variety of explanations.
Is 51 prime? How do you know? Share suggestions for identifying prime numbers, for example, no even numbers except 2; no numbers ending in 5 except 5; no numbers with digits that add to a multiple of 3 except 3. How doyou know t his?
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Paired Work: (about 15 mins) |
Another monster comes. It eats lots more children. Children 25, 13, 7 and 19 are eaten. Children 6 and 12 are safe. The children should work out the fate of 10 to 15 more numbers under 1000. Ask them to explain the reasons for their choiceof number. Record the se explanations on the board.
How could we organise this information? Table, ordering the numbers, missing numbers, number grid.
Children then work in pairs to formulate one or more rules ready for sharing.
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Class Sharing: (about 15 mins) |
Share ideas for rules. Record on the board.
How did you check for the numbers?
Why didn’t you divide by 4? 8? 9? In their everyday language, children should talk about the rules for even numbers or squares not being prime.
When can you stop dividing the number by ever-higher prime numbers to test it? They may realise that they can stop halfway, or even at something near the square root of the next square number bigger than the number.
Reflect on the value of strategies used: starting with vague ideas then refining.
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