don steward
mathematics teaching 10 ~ 16

Thursday, 23 July 2009

sum 46

place all of the the first ten odd numbers in the little triangles so that the three big triangles all add up to 46

some aspects of this problem can lead to proof: that the central little triangle must be 19 when the big triangle totals are 46; that there are only two (essentially) different solutions, because 17 has to go with either (9 and 1) or (7 and 3)

other totals are possible:  

there are two different solutions with big triangle totals of 34, 38 and 42
the middle numbers for these are 1, 7 and 13 respectively
you can prove that 3 must be a factor of (the middle number minus 1)

a lot of thinking can determine which numbers have to go with which other numbers
it's also good practice at addition, which could be done using cards with dot arrangements for those who might find this helpful

No comments: