Quandaries and Queries

my name is ken and i'm asking this question for my nephew who is a sixth grade student.

dorothy was going to see the wizard of oz...she stopped at the bakery and bought a box of cookies.

she met the scarecrow and gave him half the cookies. she ate half of the remaining cookies and threw one half cookie away.

she met the tin man and gave him half the cookies. she ate half the remaining cookies and threw one half cookie away.

she met the lion. she gave him half of her cookies. she ate half the remaining cookies and threw the LAST half cookie away.

how many cookies did dorothy leave the bakery with?

Hi Ken,

I tell my students that this is a "working backwards" problem. You start at the end and work backwards. I find it helpful to construct a table.

Number of cookies What was done with them
Gave half the cookies to the scarecrow
Gave half the cookies to the tin man
Gave half the cookies to the lion
Ate half the cookies and threw away the LAST half a cookie.

Now you can see why it is "working backwards". The one number you know is in the last row. At that time she had 1 cookie. She ate half of it and threw the other half away.

Number of cookies What was done with them
Gave half the cookies to the scarecrow
Gave half the cookies to the tin man
Gave half the cookies to the lion
1 Ate half the cookies and threw away the LAST half a cookie.

Now you can complete the next-to-the-last row. She gave the lion half the cookies ansd was left with 1, so she must have had 2 cookies at that time.

Number of cookies What was done with them
Gave half the cookies to the scarecrow
Gave half the cookies to the tin man
2 Gave half the cookies to the lion
1 Ate half the cookies and threw away the LAST half a cookie.

Now the row before that. Before she threw away half a cookie she had 2 and a half cookies. This was after she ate half the cookies. Thus she must have had 5 cookies.

Number of cookies What was done with them
Gave half the cookies to the scarecrow
Gave half the cookies to the tin man