Please see the updated version of this story, August 26, 2018, with illustrations by S.D. Monahan
Not Your Average Halloween
By Marsha Landau
“We’re
back!” shouted the plump pumpkin, pushing the bright orange sphere over its
head to reveal Caroline.
“What
a haul!” said the order of fries.
Daniel tore at the Velcro and exploded out of his box.
“I
got the most!” bragged the beautiful butterfly. Tonnica managed to wriggle out of her wings without ever
letting go of her treat bag.
“Mrs.
Pointer gave us raisins again!”
whined Eric as he stepped out of a giant football.
Mr.
Mathis, Caroline’s father, slipped quietly into the front hall behind his
charges, giving Ms. Mathis a “thumbs up.”
“No
tree nuts, no peanuts, no sesame seeds,” he reported. “Only safe treats, thank
goodness!”
“Mmmm...do I smell cocoa?” asked Caroline. “Thanks, Mom!”
“I
thought it seemed pretty cold out, and your costumes didn’t look very warm,”
said Ms. Mathis. She herded the
children into the kitchen and poured four mugs of hot chocolate.
“This
is the best Halloween! Everyone on
the block was home, so we got lots of treats. The only trick we
had was old Dr. Landau, who asked us math problems before she gave us our
treats. I had to answer 9 + 8,”
reported Tonnica.
“Yeah! I had 15 - 7,” said Eric.
“3
x 6 for me,” said Caroline.
Daniel
swallowed a sip of hot chocolate and said, “12 ÷ 4.”
“Well,”
said Ms. Mathis, “you did say ‘Trick or
Treat,’ didn’t you?”
“I’m
ready for some treats,” said Daniel,
turning to his bag.
“I
know I got the most,” Tonnica said
again.
“I
wonder,” said Ms. Mathis. “The hot
chocolate should hold you for awhile.
Before stuffing yourselves full of sweets, how about counting up your
treats. And, by the way, I
promised your parents you’d only have two treats today and take the rest home.”
“I’ve
got an idea,” said Caroline, going to the cupboard. She returned with four plates. “We can count our treats onto the plates so we can see them
and keep our own separate from everyone else’s.”
The
children followed Caroline’s suggestion.
Eric
finished first. He had 19.
Caroline
was next with 21.
Daniel
had 25.
Everyone
watched Tonnica as she finally shook her empty bag and announced, “32!”
“You
always had to be right in front, didn’t you, Tonnica--that’s why you got more,”
said Eric, folding his arms across his chest. “This isn’t fair!”
“That’s
not true!” exclaimed Tonnica. “I got more because I used my sparkliest smile
with whoever opened the door.”
“Well,
I didn’t do much better,” said Caroline, comparing her smaller pile of treats
with the mountain in front of Tonnica.
“How
about sharing?” suggested Daniel.
“What
do you mean?” asked Tonnica, surrounding her plate with her arms.
“I
don’t know,” Daniel admitted.
Eric
moved his chair closer to Tonnica’s.
He was about to attack her collection when Tonnica interrupted him in
mid-pounce.
“Whoa!”
she said. “Slow down! I MIGHT be willing to share if I knew what you meant.
Tell me what you think we should do.”
“I
think we should each get a fair share of ALL the treats we got as a whole
group,” said Eric.
“So
everybody gets the same number of treats,” added Caroline.
“But
I had the MOST. I think I should at least get to keep my favorites and only
have to give up my un-favorites. I could do that,” said Tonnica.
Daniel,
Caroline, and Eric thought that over for a minute, then nodded in agreement.
“Now
what?” asked Eric.
“It
sounds like you have the beginning of a plan,” said Ms. Mathis. “But you better
figure out a way to make fair shares before you touch those treats!”
It
got very quiet.
“Wow,”
said Ms. Mathis, “I can almost hear the wheels turning in your heads!”
~~~~~~~ (good stopping place to allow your child to think about how to solve) ~~~~~~~~~~~~
Suddenly
Eric jumped up. “I’ve got it! Let’s put all our treats together in
one big pile and then take turns taking treats until the pile is gone! That’ll be fair,” he said, nodding his
head in agreement with himself.
“No way!” exclaimed Tonnica, dragging her plate full of
treats even closer to the edge of the table so she could protect it from
invaders. “We all agreed that I could keep my favorites! I don’t like that
plan.”
“Maybe
there’s another way,” said Daniel.
“I have 25 treats and Eric has only 19. If I give him one, I’ll have 24 and he’ll have 20. If I give him two, no, wait--I can give
him three treats and we’ll be even!”
“Oh! Maybe Tonnica and I should be even,
too,” said Caroline. “Tonnica has
32. I have only 21. She has 11 more. If she gives me five, she’ll still have
one more. Well, she does have the most right now. Okay–I guess that’s fair. What do you think, Tonnica?”
Tonnica
was studying her treats, trying to see whether there were five she would be
willing to give up.
“Wait
a second!” said Eric, before Tonnica had a chance to agree. “If we follow this plan, Daniel and I
get 22, Caroline gets 26 and Tonnica gets 27. How is that fair?”
“I
need a pencil and paper,” said Daniel.
“There’s got to be a way to make this work.”
Daniel
got busy writing numbers, crossing them out, then writing new ones.
In
the meantime, Caroline went to the junk drawer and dug around until she found a
huge box of paper clips. With
Tonnica’s help, she counted out piles of clips just like the piles of
treats--19, 21, 25, 32. They moved
clips, counted, moved some more, and counted again.
“We’ve
got it!” the girls said.
At
that very moment, Daniel looked up from his numbers and said, “24, 24, 24, and
25” just as the girls said the same thing!
Everyone
laughed. The problem was
solved.
“That
was fun,” said Tonnica. “It felt
like we were balancing weights on a scale.”
“Except
that you get one extra treat!” said Eric.
“No,”
said Tonnica. “I’m giving the
extra treat to Ms. Mathis.”
“Why,
thank you, Tonnica,” said Ms. Mathis.
“Now that you’ve all agreed on a plan, you can go ahead and move the
treats around. Remember, you can
eat just two.”
And
that’s exactly what they did.
The End
###
Notes to Parents and Teachers Reading this Story with Children:
Notes to Parents and Teachers Reading this Story with Children:
Interrupt the story when Ms. Mathis can almost hear the
wheels turning as the children get to work on their problem.
Talk about “sharing” as one of the meanings of division.
The children in the story are just learning the concept of
division. Eventually they will learn the procedure for finding the average or
mean of N numbers: add them up and
divide by N.
Before learning the procedure, children can invent their own
ways to produce equal shares. In the story, the ideas were:
(1)
Put them all together and deal them out like playing cards. This was Eric’s
plan. It was probably what the girls did with the paper clips. Substituting
paper clips for treats made it possible to act out the solution without
fighting over particular treats.
(2)
Balance the treats pair-wise. This produced only a partial solution in the
story (22, 22, 26, 27), but if someone had thought of extending the process,
the solution could have been found. That is, pair each of the sets of 22 with a
larger set and balance again. For the children in the story, this is a very
concrete way to solve the problem—each child who had to give up treats could
negotiate which treats to give away while retaining “control” of his or her
collection.
(3)
Use paper and pencil. Daniel used numbers and the strategy “guess and check” to
get to the solution.
Eventually, the children will use the algorithm:
19 + 21 + 25 + 32
4
which equals 24 with a remainder of 1.
-->
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