wintersuntime
  • wintersuntime
Can someone be nice enough to help me please with this worksheet -> http://crsearch.fcps.edu/crsearch/retrieveresourcefile.cfm?hxresid=R001EED
Mathematics
schrodinger
  • schrodinger
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wintersuntime
  • wintersuntime
It's the one of building staircases
dan815
  • dan815
what are you confused about?
wintersuntime
  • wintersuntime
about how to get 100

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dan815
  • dan815
what do you mean
dan815
  • dan815
could you please ask your question clearly about what is confusing you
wintersuntime
  • wintersuntime
what is the total numbers of cubes how many steps I need in 100
dan815
  • dan815
ah okay like this
dan815
  • dan815
|dw:1438307419721:dw|
dan815
  • dan815
|dw:1438307470634:dw|
dan815
  • dan815
you see how the number of cubes needed is increasing for each step
wintersuntime
  • wintersuntime
yes but I need to find out the total number of cubes
wintersuntime
  • wintersuntime
for 100
dan815
  • dan815
right look at this pattern
dan815
  • dan815
for 1 step its 1 for 2 its 1+2 for 3 its 1+2+3 for 100 its 1+2+3+4....+99+100
dan815
  • dan815
you have to see what the sums upto
dan815
  • dan815
there is a trick to find out what that sums upto
dan815
  • dan815
|dw:1438307608134:dw|
dan815
  • dan815
if you add the first and last together the 2nd and 2nd last the 3rd and 3rd last they all give u the same number
dan815
  • dan815
how many of those additions will there be if u add this way
dan815
  • dan815
there is another way to look at it
dan815
  • dan815
lets take a simpler example
dan815
  • dan815
1+2+3+4+5 = ?
dan815
  • dan815
what you can do is rewrite another replica of it backwards 1+2+3+4+5=? 5+4+3+2+1=? --------------- 6+6+6+6+6= 5*6 --------------- we added 2 sums we only want to find out 1+2+3+4+5 so we divide 5*6 by 2= 5*6/2= 30/2=15 so 1+2+3+4+5=15
dan815
  • dan815
we can use this same trick for this 1+2+3+4+5+6.....99+100
dan815
  • dan815
can you figure that out
dan815
  • dan815
http://prntscr.com/7z2m2l
wintersuntime
  • wintersuntime
so for 100 its 99
wintersuntime
  • wintersuntime
dan815
  • dan815
so for 1 to 100
dan815
  • dan815
lets do a smaller example how about 1 to 10
dan815
  • dan815
1+2+3+4+5+6+7+8+9+10=? remember the trick from before?
dan815
  • dan815
lets add this set back to itself
dan815
  • dan815
1+2+3+4+5+6+7+8+9+10=? 10+9+8+7+6+5+4+3+2+1 =? now add each column ------------------------------ 11+11+11+11...+11 =? how many 11s will there be?

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