Grabbing my daughter's book....Jenn in NC wrote:DS is finishing up 5b today and can't figure out how to solve problem #20 in review 3, pg 104 (last page of the book.) I'll just type it out:
For some reason I am stumped in trying to explain this to ds. I can see intuitively that the answer is $20... b/c that would bring David to $110 and Peter to $220. But I am sure there must be a more proper way to come to this answer. Help, anyone?
- David and Peter had $90 and $200 respectively. They were each given an equal amount of money. Then Peter had 2x as much as David. How much did each boy receive?
This is what my oldest did. I'm sure there are other ways.
first she call 90 one bar
David = ___
Peter = ___ + ____ + 20
now, they each get same amount of money (how to draw that on here. I know. I'll use a ?. She actually drew a box.)
David now has + 90
Peter now has + 90 + 90 + 20
ok. What Peter has is 2 groups of David, right?
Well, she has a good enough understanding to go to this:
? + 90 + ? +90 = ? +90 +90+20
2 groups of David = 1 group of Peter
Then she crossed out equal things on each side leaving
? = 20
edit to clarify: in reality she didn't write 90, she wrote it with bars, I just got lazy typing. So when I say she crossed out equal things, she crossed out bars and ? (boxes).
but.... as you'll see below in my edit... it is easier than what she did.
if we double Peter's new amount it is the same as DAvid's new amount
make a mirror image of Peter's amount
double Peter + _________ + _________ +
David + ________ + ________ + 20
they have in common one and 2 _________
that leaves is the same as 20
I don't know if that makes sense on the screen. But for her, the trick was to start off thinking of Peter's money in terms of how it related to groups of David's money plus extra.