This book was written for an assignment in my teacher education
program. The mathematics is on 3 of the 4 types of Fair-Division
from the Fair - Division unit of a Discrete mathematics course.
The three types used are Divider - Chooser, Lone Chooser, and
Lone Divider.

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Look!!! My Mom bought
me a cake!

I know it's for me
because today is my birthday.
In our family, we get a whole
cake to eat by ourselves on our
birthday!!! Plus this is my favorite cake
ever because it costs $24 and 24 is my
favorite number!

I could eat the cake
under a tree

Or by the sea...

I could eat the cake
on a boat

Or maybe I'll eat it
with a goat!

Jorge, will you grab a
knife so we can cut the
cake?

What did Dad just say?
I thought it was mine...

I know what to do!
Dad says he likes
strawberry three times
more than chocolate

So if Dad would only pay $6 for
all of the chocolate, he would
pay $18 for all of the
strawberry!

MATH NOTE:
6 x 3 = 18
AND
$6 + $18 = $24
which is the cost
of the cake

$18

Since the strawberry is worth
$18 to Dad, if it is split into
three parts, then each piece
is worth $6

MATH NOTE: $18 divided
by 3 is $6

So if I cut the cake like
this, both slices would make
Dad happy! They would each
be worth $12 to him.

$12

MATH NOTE:
$6 (from 1/3 of the strawberry)
plus $6 (from all of the chocolate)
is $12

MATH NOTE:
$6 (from 1/3 of the strawberry)
plus $6 (from 1/3 of the strawberry)
is $12

But I would choose the piece
with the most chocolate because I
like chocolate a whole lot!!!

Mine

I like chocolate two times more than
strawberry. I would only pay $8 for
the strawberry, but I would pay $16
for the chocolate!

$16

MATH NOTE:
$8 + $16 = $24
which is the cost
of the cake.

$16 (all of the chocolate) +
$8/3 (1/3 of the strawberry) =
$16+8/3 = $48/3 + $8/3 = $56/3

$8/3 (from 1/3 of the strawberry) +
$8/3 (from 1/3 of the strawberry)
= $16/3

MATH NOTE:
If the strawberry is worth
$8, dividing it into 3 parts
makes each part worth $8/3

So I think the piece I'm getting
is worth $56/3 which is a whole
lot more than $16/3

Jorge when you cut, don't forget
that your sister doesn't eat
strawberry

WHAT!!!! Now I have to share
with Sammy too??!?!?! IT WAS
SUPPOSED TO BE MY CAKE!

I know what to do!
I'll cut the cake in half

One half I'll cut into three pieces
so that Dad is happy with every piece.
The other half I'll cut into three pieces
so that I am happy with every piece.
Then Sammy will choose her favorite
piece from each half and we'll all
have two pieces!

My half

Dad's half

Remember, I think half the
chocolate is worth $8 and half the
strawberry is worth $4...

And Dad thinks half of the
chocolate is worth $3 and
half of the strawberry is worth $9

MATH NOTE: 4 x 2 = 8
(Jorge, like chocolate twice as much)
AND
3 x 3=9
(Dad likes strawberry 3 times as much)

So if I cut my half like this
I would be equally happy
with all three of the pieces

And Dad's half would
need to be cut like this
so that he is happy with
all three pieces.

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Look!!! My Mom bought
me a cake!

I could eat the cake
under a tree

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"My Cake!"

sdcsafire

Jorge plans to eat his birthday cake but ends up having to share it with his family. He uses math to divide the cake fairly, but is initially upset about sharing.

(35 pages)

Privacy level: PUBLIC

153 reads 8 fans

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