The Activity
Part 1: A Warmup Special ProblemThe Henderson's Gummybears
In general, allow students to work with the problem on their
own or in groups before you give structure or hints. Provide hints
to select groups or individuals as needed to allow each individual
student to be challenged and/or supported to a degree appropriate
for them. Hints: make a chart that demonstrates how many bears
she has left each day use a model to act it out; to visualize.
Refer to your problem solving resources (flow chart) As students
pursue various strategies of their own design, gently lead each
student or group to make a table as shown below. Students will
need to be equipped with this table when they do the next activity,
"How Old Are These Fossils?"
day of week 
start. 
Sun. 
Mon. 
Tues. 
Wed. 
Thurs. 
Fri. 
Sat. 
Sun. 
day number 
0

1

2

3

4

5

6

7

8

number of gummybears 
128

64

32

16

8

4

2

1

0

Students may ask what to do when there is only 1 gummybear. You
can agree that when that happens, she gives the whole bear away.
You might consider asking students what would happen if bears
could be cut in half. Would she ever run out? (Only if she did
it forever; the limit as the number of days approaches infinity
equals 0). Another version of this problem would be to have students
stand a specified distance from the wall and to walk have the
distance to the wall on your commands. This could be done on another
day to provide added support of the essential concept that needs
to be established: Halving a quantity in successive stages.
Part 2: Discussion: Carbon 14 and the dating of fossils
Before doing "How Old Are These Fossils?" the concept of Carbon
14 dating needs to be introduced to the students, either in a
science class or as a brief discussion during math. In the gummybear
problem, half the quantity was removed each day. This could have
been arranged where half the quantity was removed each week, each
year, or each decade. The term half life is referred to the amount
of time it takes for a quantity to diminish by half. The half
life of gummybears was 1 day. Many other substances in nature
decay or evaporate naturally with the same halving process as
the gummybears. One of these substances is Carbon 14, a compound
present in all living things. The half life of Carbon 14 is 5730
years. Expressed simply, if a scientist knows how much Carbon
14 is in an animal when it is alive, and can measure how much
is in its fossil, then based on the half life of Carbon 14 the
amount of time that has passed since its death can be determined.
This process of dating will be simulated with popcorn by students
in class.
Part 3: Classroom Simulation: How Old Are These Fossils?
Divide the students into about 1012 groups of 2 and/or 3. Designate
half of the groups as "scientists" and the other half as "fossils."
The fossils are equipped with a cup of 128 pieces of popcorn.
For the first 510 minutes of the activity the scientists must
be separated from the fossils; either by leaving the classroom
or going behind a partition. On your cue, each fossil will remove
half of the corn in the cup each minute. Start each fossil at
a different time over a 6 minute period with hand signals so that
the scientists don't catch on, then stop. Allow the scientists
then to circulate among the fossils and gather data and determine
how many minutes each one was "decaying." If time allows, the
rolls can be reversed, and the process repeated. To determine
the age of each fossil group students will need to refer to the
table created in the gummybear problem. Don't volunteer this strategy.
Give the students the opportunity to make this connection on their
own.
Part 4: The Followup Problems
These problems increase in difficulty. Without substantial support
from you, they would be too difficult for most students to figure
out on their own. Even with support they are beyond the abilities
of most students in the lower grades.
1) Ans: answers will vary A hint: Ask students:
a) How many times did each fossil group lose half of its corn?
b) For Carbon 14, how many years pass each time half of the amount
of Carbon 14 is lost?
c) If the corn is Carbon 14, multiply 5730 by the number of times
the group divided its corn, or by the number of minutes old.
Problems 24 require two steps:
a) Determine how many half lives there are in each given number
of years. Each number needs to be divided by 5730, or how many
5730s are there in each number. Rather than dividing, suggest
to students that they multiply 5730 by various integers, 1,2,
etc. until they get the desired number.
b) Now the problem is identical to the gummybear problem. Divide
80 by 2, divide the quotient by 2, and so forth. Repeat this by
the number half lives.
2) Ans: 40 gm
3) Ans: 20 gm
4) Ans: 5 gm
5) Ans: 17,190 years. This problem is an actual dating
problem. First determine how many "halvings" (half lives) of 24
are required to obtain 3. Then multiply this number by the half
life period of 5730 years.
6) Ans: 28,650 years. This is identical in process to problem
5. It takes 5 "halvings" (half lives) of 24 to get .375. So 5(5730)=28,650.
Student Handouts
Gummybear warmup:
Problem of the Day
The Henderson's Gummybears
(C14 Warmup Problem)
The Hendersons have a very big family. At the beginning of summer
vacation, Ms. Henderson decided to give the children a package
of 128 gummy bear candies. She didn't want to give them away all
on one day, so on the first day she gave them half of the bears.
On the next day she gave them half of what she had left that day.
She continued giving them half of what she had each day until
they were all gone. Answer the questions below and show all your
work
1) If Ms. Henderson started giving the bears to the kids on Sunday,
how many bears would she have on Thursday? Explain in words what
helped you find the answer:
2) How many days will pass until all of the bears are gone?
Explain in words what helped you find the answer:
How Old Is That Fossil Data Sheet:
NAME:_______________
PARTNER:_____________
How Old Are These Fossils?
Data Sheet and Questions
Each group started with 128 kernels of corn. The corn represents
Carbon 14. In today's experiment, each minute they throw away
half of their corn, just like the way Ms. Henderson was giving
away gummybears. Visit three fossil groups, count the amount of
corn left in their cup and determine how many minutes they were
throwing way corn.
I AM A (CIRCLE ONE)
Paleontologist
Fossil
DATA
Fossil Measured (Name of
Student Group) 
Number of Pieces of Corn Present 
Calculations 
Minutes of Decay 
1)




2)




3)




PROBLEMS:
1) The halflife of Carbon 14 is 5730 years. This means that
it takes 5730 years for half of the Carbon 14 to go away. Pretend
the corn in today's experiment was Carbon 14. Calculate how many
years old each of the fossils in today's experiment would be.
A sample of wood contains 80 gm of Carbon 14.
2) How much of the Carbon 14 would be left after 5730 years?
3) How much would be left after 11,460 years?
4) How much would be left after 22,920 years?
5) An animal carcass had 24 grams of Carbon 14 when it was live
and 3 grams present when its fossilized remains were discovered.
How old is the fossil?
6) How old would the same fossil be if there was .375 gm of Carbon
14 present when it was discovered?
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