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Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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Numbers as Shapes

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How Odd

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

How many odd numbers are there between $3$ and $11$?
 
How many odd numbers are there between $4$ and $11$?
 
What do you notice?  Can you explain your observation?
 
Can you find any other pairs of numbers which have this same number of odds between them?
 
Can you find a pair of numbers which have four odd numbers between them? 
 
Can you find another pair of numbers which have four odds between them?  And another pair?
 
How would you find a pair of numbers that have five odds between them?  Six odds?
 
How would you explain to someone else how to find  a pair of numbers that have a certain number of odds between them?