Teacher Notes
It IS as easy as pi, FUNShops
Pirate Passcodes (3-4)
LOGISTICS
Class grade/age: 3-4th grade
Class size: 20 students
Instructional Time: 110 minutes
Location: Science Lab or Classroom
Safety: use plastic knives with caution; stamping paint can be messy so
use carefully and wear gloves.
BACKGROUND
Pi is an irrational number (a number that cannot be expressed as a ratio/fraction; after
division, its decimal places go on and on forever without any recognizable or repeating
pattern). As a ratio of a circle’s circumference to diameter, pi as a number is constant
(always the same) regardless of the size of a particular circle (Wilson, 2000).
Given its infinite and pattern-less nature, it can be quite redundant and laborious to
write down the never-ending digits of pi during calculations; rather, we use the symbol
π to represent the value of pi. When measuring circular objects, a particular pattern
can be observed in that a circle’s circumference (or distance all the way around) is
always a little more than 3 times its width (or diameter).
Pi is often approximated as 3.14 for simplicity’s sake during calculations, but some
organizations use a value of pi with a certain number of digits past the decimal place.
For example, NASA uses 16 digits after the decimal place. According to the piday.org,
only 39 digits past the decimal are needed in order to accurately calculate the
spherical volume of the entire universe. Why would we need to use a certain number
of digits when performing pi-related calculations? It turns out, the more decimal places
used in a given calculation involving pi, the more accurate the calculation becomes
(Lamb, 2012). Since pi is infinite & lacks a pattern it can be a fun challenge to
memorize as many digits as possible and/or to obtain more and more digits through
various computation methods.
Pi can be applied to anything related to circles or spheres. Pi is used to calculate
simple things such as figuring out the height of a container of spheres or a container
for spherical candies to calculations involving tornados, wire insulation, or even wheels
and tires. Some of the more complex applications include global navigation, jet flight
paths, and NASA rocket launches.
SUMMARY OF ACTIVITIES
INQUIRY NOTE: The goal of this lesson is not to lecture about pi then apply relevant
calculations. Instead, it is designed to progressively introduce students to a FUN
storyline within the context of geometry and circles, in general. This provides students
with opportunities to question, experience, and discover rather than to be told. The
teacher’s role is facilitator; asking the right questions will help students to develop their
own ideas, thereby giving them ownership of their knowledge.
In this two-part lesson, students will be presented with a scenario: We are all pirates
that have found an ancient treasure worth millions of dollars! We have been trying for
Illinois Math and Science Academy, Statewide Student Initiatives
Written 10/9/15 by Christine Moskalik and Carmela Jones
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It IS as easy as pi, FUNShops
YEARS to get into the treasure chest, but it is indestructible and it’s locked up by some
type of passcode!! We need to figure out the passcode to get to the treasure inside! A
clue is delivered via telegram stating “The passcode is hidden in every circle.” In order
to try to figure out what the passcode is, they need to begin to learn more about circles.
In part one, students will make a human-circle and identify ways to measure it while
learning relevant terminology. They will then apply some of these new words and
concepts as they dissect a Styrofoam sphere. Clues from a fellow pirate are delivered
via telegram during the lesson; these clues may help students identify and test
possible passcode candidates.
In part two, students will begin to expose the relationship of pi (ratio of circumference
to diameter) by building upon the sphere dissection and identifying some possible
passcodes along the way. Eventually students will uncover the correct passcode (the
value of pi out to 20 digits) and make a secret circular cipher (a secret code to hide
written information) so they never forget the passcode and they can keep it secret from
any other treasure-hunters.
STANDARDS – Common Core Mathematics
CCSS-3-5.OA. Operations and Algebraic Thinking.
CCSS-MP.4. Model with mathematics.
CCSS-MP.5. Use appropriate tools strategically.
OBJECTIVES
The students will …
1. recognize that pi is a symbol that represents a real number.
2. dissect a Styrofoam sphere to expose various characteristics of a circle.
3. discover the relationship of the diameter and the circumference of a circle.
4. create a cipher to represent a value of pi with 25 digits in the decimal.
Materials:
 Yarn, sphere (1/4 large skein, any color)
 Scissors, safety, 5 (1/group of four)
 Pre-scored Styrofoam spheres, 1” and 2” – 10/size (each pair gets 1” and 2”)
 Q-tips, 20 (1/student)
 small cups, plastic, 3-4 oz. – 10 (1/pair)
 paint, tempera, 1 bottle
 paper towels, 1 roll
 washable marker, Crayola, fine tip – 20 (1/student)
 plastic knives, sturdy, any color – 20 (1/student)
 paper plates, any type/size – 25 ( 1/student plus 1/group for trash)
 ink, stamping refill, 2oz. bottle any color
 Styrofoam bowl, 12 oz. – 20 (2/pair – one for act 3, one for act 4)
 gloves, small, non-latex – 20 (1/student)
 calculators, 10 (1/pair)
 pencils, sharpened, with erasers – 10 (1/pair)
 Rulers, 12”, plastic – 10 (1/pair)
Illinois Math and Science Academy, Statewide Student Initiatives
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It IS as easy as pi, FUNShops
Advanced Prep Materials:
Floor circles
 Blue painters/masking tape
 Measuring tape
 Scissors
Styrofoam spheres – pre-score:
 2” – 35 (1/student plus 5 extras to cut in halves and quarters)
 1” – 35 (1/student plus 5 extras to cut in halves and quarters)
 Foam cutter
 Card stock
 Copy paper
 Pencil
 Pointed forceps
Telegrams (optional):
 Ribbon/string/yarn
 Copy paper – tan/light brown
 Pi telegram doc
 Alternative: voice-recording of pirate reading telegrams
Handouts/printables:
 Student page doc (pg. 1-5)
 8.5 x 14, white, plain paper – 10 (for booklet, pg. 1-4)
 8.5 x 11, white, cardstock – 10 (for data collection page, pg. 5)
 Color wheel doc
 8.5 x 11, white, Cardstock – 5 (for color wheel reference card)
 Pi riddles doc (for teacher)
 8.5 x 11 white copy paper – 1 (for printing riddles)
Ciphers







lanyard string, any color, 24” – 20
scissors
Metal lanyard hook – 20
Plastic zipper-style bag, quart-sized – 1
Quart-sized zipper bags
Beads pony beads (nine solid colors, 600 (25/student); clear, 20 (1/student)
disposable bowl, Styrofoam, 12 oz. (1/group)
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It IS as easy as pi, FUNShops
ADVANCED PREPARATION INSTRUCTIONS:
1) Floor circles: Place tape on the middle of the floor (in the shape of a small “x”) to
represent the middle of the circle. Use the measuring tape to go about five feet
from the “x” in each of the four cardinal directions (N, S, E, W) and place a separate
small piece of tape on the floor each time. This will give students some idea of
where to stand in order to create the human-circle.
2) Styrofoam Spheres: Make a tiny cardstock “sphere-stand” for the Styrofoam
spheres so they don’t roll around while you are scoring them. Use a 1” and 1.25”
strip of cardstock to wrap around the small and large Styrofoam sphere,
respectively; secure with scotch tape; you will place the spheres in these holders
while you cut into them with the foam cutter (see pics, below). Draw a straight line
down the middle of a sheet of copy paper and add one line on each side, about ½
the size of the sphere, representing the total width of the sphere (this is so you
know where to place the sphere so you score as close to the middle of the sphere
as possible. Pre-score each Styrofoam sphere (10, one/pair for both large and
small spheres) using a heated wire foam cutter to mark the cutting location for the
students when they do the sphere dissection.
Cut the five extra spheres in half, and then cut a few of those halves into quarters;
that way if the student’s cuts are uneven, you will have some extras (that are sized
more accurately and are smoother) to share with them. Stab the spheres with
pointed forceps to hold them while using wire foam cutter to cut all the way through
the foam.
3) Telegrams: print telegram file on light brown paper and cut each clue out as a strip.
Roll each clue into the shape of a cylinder and tie it up with a piece of
string/ribbon/yarn. Alternatively have someone dress up like a pirate appear and
announce the clue (speaking like a pirate would)! Another option is to record
someone (who speaks like a pirate particularly well) reading the telegrams to make
an audio clip to play during the lesson.
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Written 10/9/15 by Christine Moskalik and Carmela Jones
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It IS as easy as pi, FUNShops
4) Handouts/printables: Print pages 1-4 of the student page on legal sized white copy
paper (8.5 x 14) to make the booklet; each pair gets one booklet to share (10
copies). Print page 5 onto white cardstock for the data collection page; each pair
gets one data collection page to share (10 copies). Print the Pi Riddles on one page
(enough for each teacher).
5) Ciphers: Cut a 24” length of lanyard string and tie it onto the lanyard hook so two
equal lengths are hanging down from the knot near the hook. Place these into the
plastic zipper-style baggie. Bag up the different colored beads into one set/table or
group of four students (5 baggies filled with beads). They will all be working from
the same bowl.
CLASSROOM SET-UP
1) FLOOR CIRCLES (SEE #1 ADV PREP) – make sure there are floor circles in your room; if not,
make them yourself.
2) PAINT/CUPS: Put a small amount of paint in each of the ten small plastic cups before class
starts (1/pair).
3) PAPER TOWELS – moisten a stack of 20-30 paper towels in advance (to be used for hand
wipes); have another stack of 20-30 dry paper towels ready to hand out for activity 2 (they
will wipe off excess paint from spheres before dissection).
4) STAMPING: Place about 10 drops ink/student into a bowl (40 drops shared by the group or
pairs) just before the stamping activity (the ink will dry-out if done too early). NOTE: you
may have to add a few more drops to the bowl as the stamping activity progresses.
5) PASSCODE WEBSITE: ONLY able for use on IMSA campus; have an alternative ‘locked
treasure’ in place for your own purposes. At IMSA, have the treasure/passcode website
pulled up, projected, and ready. Make sure you try out a few passwords along the way
during the lessons. Have your group leaders/assistants remind you to test a possible
(incorrect) password along the way.
NOTE: External People have to make their own website or have some other way to
“lock/unlock” the treasure chest.
ACTIVITIES:
Part 1
Activity 1: Circular Sensations
Activity 2: Sphere Dissection
Part 2
Activity 3: Stamping Circles
Activity 4: Circular Ciphers
Illinois Math and Science Academy, Statewide Student Initiatives
Written 10/9/15 by Christine Moskalik and Carmela Jones
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It IS as easy as pi, FUNShops
Part 1
Goal:
Teacher will
capture student
interest and
gauge prior
knowledge.
Goal:
Students will
kinesthetically
explore some
ways to
measure circles.
Introduction
Estimated Time: 5-10 minutes
1) Welcome students to class by introducing the story line:
 We are all pirates that have found an ancient treasure worth millions of
dollars! We have been trying for DAYS to get into the treasure chest, but it is
indestructible and it’s locked up by some type of passcode!! We need to
figure out the passcode to get to the treasure inside!
 We used a treasure chest website made by an IMSA student who allowed
unlimited attempts but only worked with one passcode: the value of pi,
with 20 decimal places  3.14159265358979323846
i. You will need to provide your own version of a “locked” treasure.
You could do this with a plastic or wooden treasure chest and just
pretend it remains locked until the correct passcode is identified.
ii. NOTE: number of digits for a ‘working’ passcode can be adjusted,
but that will in turn affect how long the cipher is.
2) Ask if anyone in here knows how to figure out a passcode? (allow a few responses).
3) During the discussion have a telegram (dramatically) delivered (or simply pretend
to find a telegram that you plant in advance somewhere in the room); the telegram
contains the following clue, which was uncovered by one of our fellow buccaneers!
 “the passcode is hidden in every circle”
 It’s up to us to figure out the passcode so we can get our hands on that
treasure!!
4) Have the students look around the room and ask them if they can find any
passcodes hidden in circles? (entertain a few responses; if someone suggests “pi”
ask them “what flavor, apple?” and continue the dialogue; the passcode IS pi but
don’t reveal this yet…maybe see if they know some digits of pi and if so, try 3.14 as
a passcode – it won’t work because the passcode has to be >20 digits long in
order to “work”).
 Try a few passcode guesses on the website make sure you hit “TRY IT”
button; simply hitting “enter” will not work.
5) Ask them what (else) they know about circles? (gauges prior knowledge)
6) Announce that we’ll be learning more about circles today so we can try to figure out
what the passcode is and unlock the treasure!!!
Activity 1: Circular Sensations
Materials:
 Blue Masking/Painters Tape (on floor)
 Yarn
 Scissors
 Measuring tape
 Student booklet, 10 (1/pair)
 Pencil, sharpened 10, (1/pair)
Estimated Time: 20
Procedures:
1) Have students get up and stand in a circle (there will be taped markings on the
floor to designate where they should stand in order to form a proper circle).
2) Ask the students to identify things we can measure for our circle (they may say the
distance around the circle, the may sat the distance across the circle/from side to
side, they may not say anything, etc.).
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It IS as easy as pi, FUNShops
3) Ask them how can we measure these things? What tool/s should we use? Will a
ruler or tape measure be a good tool? (No). Why or why not? (Have them identify
any limitations for using certain tools – ruler isn’t long enough, tape measure is too
rigid, etc.)
 Eventually you will show them the yarn/scissors and guide them to the idea
of taking measurements with the yarn and then measuring the yarn.
4) Take some of the measurements they suggest; you may need to use probing to
help them identify things they want to measure (i.e. Do you want to know how big
our circle is? What would tell us how big our circle is? How could you determine
that using this yarn?).
 Make note that “HOW BIG” could mean all the way around, OR all the way
across – Do both!
5) Using a sphere of yarn, have one student hold the end of the yarn, and pass the
sphere of yarn all the way around the circle of students you just formed; each
student should gently hold onto the yarn so it forms a circle. The teacher should
NOT be a part of the yarn circle; keep hands free to cut the string and facilitate the
other measures.
 Cut the yarn with the scissors once it reaches the 1st student again. This will
create a rough circumference measure for the circle.
 Have them identify ONE word that is important in describing what we just did
with the yarn (we took it all the way AROUND the circle).
 Set the yarn aside for now – student will want to see how long the yarn is but
make sure you have them remain in a circle for the next step!!
6) Using the yarn and scissors within your circle, create a few diameters with
additional pieces of string. Make sure the students keep holding the yarn so the
diameters cross over each other at the CENTER (or as close to center as possible).
 Have them identify ONE word that is important in describing what we just did
with the yarn (we took it all the way ACROSS the circle).
 Have the students identify where the diameters cross as the “center point” of
a circle.
 Put a student near the middle where the diameters intersect and have the
student announce his/her name. Repeat for a few more students. This will
illustrate to the students that circles are named for their center point AND
that diameters must cross through the center point!
 Give a student in the middle a pair of scissors and ask her/him to cut one
piece of yarn (a diameter) in half (a radius). What one word could be used to
describe what we just did (CUT, or HALF).
 Discuss fractions at this point (half vs. whole a measure across); how many
“pieces” did we get when making the yarn go across, etc.
7) Allow the students to see how long their pieces of yarn are. You may need to go out
in the hallway to show the students how long the yarn is for the measurements they
just created.
 Suggestion: have some students hold the pieces of yarn end-to-end to help
visualize the length.
 If you don’t have time, you can wait to do this until activity 3, step 8.
Transition to next activity: Distribute the student booklet (1/pair) and pencils and have
them begin to complete it as you address the concepts during this transition.
Emphasize the relevant vocabulary words by using some of those key words from steps
5-6 above (AROUND, and ACROSS, HALF, CENTER). Ask them “who remembers the two
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It IS as easy as pi, FUNShops
words we used to describe the different yarn-measurements?” Tell them that the word
“circum” means around. Ask students, when you the word “circumference” can you
identify which yarn-measure represented the “circumference” of our big circle? (yarn all
the way around the circle). Also, the word “dia” means across, so ask students, when
you hear the word “diameter”, which yarn-measure do you think represented the
“diameter” of our big circle? (yarn going across the center of the circle). Lastly, the
word “radius” means ray (ray of sun) or spoke (as in a wheel or bicycle spoke). Ask
them - What do they think this all has to do with our passcode? Any ideas? (they may
suggest the passcode could be those vocab words; have them try it out using the
website/electronic passcode – these wont’ work). We better keep thinking – let’s
explore a smaller version of a circle and see what else we can come up with!
Goal:
Students will apply
the circle-related
vocabulary words
(circumference,
diameter, radius,
center point) from
the prior activity
while they dissect
a Styrofoam
sphere.
Activity 2: Sphere Dissection
Estimated Time: 20 min
Materials:
 Tempura Paint, any color
 Small condiment cups/paper cups
 Q-tips, small
 Styrofoam spheres, 2”, pre-scored – 20 (1/student)
 Styrofoam spheres, 2”, halved and quartered – 10 (20 quarters, 10 halves)
 washable marker, Crayola, fine tip – 20 (1/student)
 plastic knives, sturdy, any color – 20 (1/student)
 paper plates, any type/size – 25 ( 1/student plus 1/group for trash)
 Student booklet, 10 (1/pair)
 Student Data Collection page (cardstock), 10 (1/pair)
 Ruler, 12”
 Paper towels
 Pencil, sharpened, with eraser – 20 (1/student)
Procedures:
1) So, now that the students know some basic circle terminology (circumference,
diameter, radius, and center point) they will dissect a Styrofoam sphere to get a
closer look the various parts of a circle.
 Ask, students if they ever thought they would get to do a dissection in a math
“class”?
 Announce – before we dissect, we have a few steps to do first.
2) Distribute the materials – everything BUT the plastic knife (pre-scored Styrofoam
sphere, paint, marker, paper plate, paper towel, data collection page).
3) Tell students to grab a sphere (big or small, it doesn’t matter) and make some
observations about their sphere (round, white, sparkly, there’s a “cut” in the
sphere, etc.).
4) Have them hold the sphere in one hand and have them trace an imaginary path
(using a finger on the other hand) all the way around their sphere (maybe do this
where the ‘groove’ is/where it is scored);
 See if they can name the part of the circle they just “drew” with their finger
(circumference) and relate that to the vocabulary/big group-circle activity
from earlier (MEASURE AROUND).
5) Students will work in pairs for the rest of the activity.
6) First, have students use a Q-tip to place a “small mountain” of paint somewhere on
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Written 10/9/15 by Christine Moskalik and Carmela Jones
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It IS as easy as pi, FUNShops
the groove (pre-scored mark) on a Styrofoam sphere (there are two sizes – small
and large – it doesn’t matter which one they do first but they should take turns;
one student in the pair can roll the large sphere and the other can roll the small
sphere).
 Not too much – it will take too long to dry
 Not too little – there needs to be some paint that comes off initially and then
at the end of their roll.
 Place used Q-tip on the plate for “trash” when finished.
7) They will carefully roll their sphere along the line on their data collection page so
their glob of paint touches the paper twice.
 Ask them what is represented by the space between these two paint-globs
(circumference). There is a place in their student booklet for them to write
that down.
 Allow these paint markings to dry on the paper (you will return to these during
the next activity).
 Wipe off any excess paint from the sphere with a paper towel.
 Have students use pre-moistened paper towels to quickly clean any paint off
their hands
8) Repeat steps 6-7 for the other sphere; the other student in the pair should do this
step.
9) Have students get ready to dissect the larger of the two spheres. After addressing
safety and general procedures, hand out a plastic knife to each student.
10) Students should:
 use the knife to carefully cut the spheres in half (each student will cut a large
sphere; they will do this again in the next activity with the smaller sphere);
they should keep the sphere on the paper plate and on their desk/table and
hold it carefully with their fingers. Encourage them to use caution while
cutting with the knife and have them try to keep both halves even and flat.
DO NOT “HACK-INTO” the spheres!!
o SUGGESTION: Model to show them how to get an even cut -- have
them pull the knife down in one direction, rotate the sphere a little,
and repeat until they cut completely through the sphere.
o Talk about fractions and relate to what was just done (we divided
ONE sphere into TWO halves, = ½).
 Have them rub the halves together to “smooth them out” on your count of
FIVE.
 cut one of the halves in half, making a onequarter section of the sphere (we divided a
½ sphere into two pieces, which equals ¼
of the whole sphere).
 use the quarter-piece of the sphere and a
marker to draw 3-4 equally-long lines on
the flat side of one half-sphere.
o See if they can identify and name
the center point (where all
diameter lines intersect).
11) Encourage the students to verbally describe
what they did to draw the lines on the sphere
(went across the inside of the circle) and relate
that to the big group-circle from earlier.
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 If you haven’t tested out any vocab-related passcodes yet, now would be a
good time to try! Ask them which passcodes we should try out?
12) Have students identify examples of items that resemble the markings they just
made on the sphere with the marker (bicycle spokes, wagon wheels, basketball,
snowflake, Boston Bruins symbol, pizza, pie chart, orange, etc. – all things that are
circular!!) and use them during the transition.
Transition to next activity: Have another telegram delivered with the 2nd clue Before you
read the clue, discuss the definition of radius (means “ray” or “spoke”) and relate that
to any item the identified at the end of the prior activity (such as wagon wheel/bicycle
wheel). Use the riddles to help reinforce all of these new vocabulary words. Tie in these
activities with the story-line such as “So, if these vocab words don’t work for our
passcode, what are some other ideas you have?” See what the students say before
you open the telegram and read the clue: “the passcode is a number” (they may
suggest that we take measurements between the two paint markings for both
Styrofoam sphere circumferences; they will measure in the next activity after the paint
is dry).
Take a 5-10 minute break (do the transition before the break if there is time, otherwise
have the break and then open the next part of the lesson with concepts rom the
transition (above)).
Part 2
Goal:
Students will
explore the
relationship of C/d;
specifically that “a
little more than 3”
diameters from a
particular circle can
“fit” within that
circle’s
circumference (in
4th activity they will
learn this is the
concept of pi).
Activity 3: Stamping Circles
Estimated Time: 20 min
Materials:
 Styrofoam spheres, 1” & 2”, dissected – 20 (1 student)
 Plastic knife
 Paper plate
 Paper towels, dry
 Paper towels, moistened
 Disposable bowl, Styrofoam, 12 oz.
 Gloves, 20 (one/student – only for ‘stamping hand’)
 Ink, stamping refill, 2oz. any color
 Student booklet
 Student Data Collection Page (cardstock)
 Ruler, 12”, plastic – 10 (1/pair)
 Pencil, sharpened, with eraser
Procedures:
1) Welcome students back to class (after the break) and use any ideas from the
transition above as a starting point for this activity.
2) So, now that the students have dissected the sphere and have begun to learn the
vocab words (circumference, diameter, center point and radius) and tested the
words and circumference values out as possible passcodes, we will explore these
features a little more in order to discover how they are used to obtain the
treasure’s passcode, still a secret (pi).
3) Are the paint markings dry? Have the students measure the distance between
them.
4) How can we measure the diameter of our dissected foam sphere? (ruler). How
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It IS as easy as pi, FUNShops
5)
6)
7)
8)
9)
precise would that be if the sphere and ruler aren’t held perfectly still? What’s a
better way? (transfer it onto paper somehow – using stamping ink).
 They should guess (hypothesize) how many times their half-sphere (the half
they dissected) would fit inside their circumference (between the two dried
paint globs).
 They may want to test this number (their guess) as a passcode! (it shouldn’t
work).
Have them push the flat side of the sphere (the half they dissected) into the bowl
containing the paint/glue mixture and test their hypothesis (see next step).
Have them test their hypothesis by stamping the flat side of the inked larger halfsphere on to the line between the two dried paint globs to see how many ‘sphere
diameters’ they can to fit within their circumference
 Make sure they covered the entire flat surface with the ink in step 5
 After stamping, they should blow air on their data collection page for a few
seconds to help it dry quickly if needed.
 What did you come up with? (three)
 Was it exactly three? (no, there was a little bit more).
 Then, have them measure the diameter of the stamp with a ruler and record
the value.
Have them do the same test procedure with the smaller half-sphere:
 Test their hypothesis by stamping the small half-sphere on the line between
the two paint globs to see how many ‘small sphere diameters’ they can to fit
within their smaller sphere’s circumference.
 After stamping, they should blow air on their data collection page for a few
seconds to help it dry quickly if needed.
 They should discover that again, it was “three and little bit more”
 Then, have them measure the diameter of the stamp with a ruler and record
the value.
Revisit the big yarn pieces from before (if there is time):
 Let’s test the yarn and see if the same pattern appears?
Ask, what are some conclusions you can make from these activities? (accept
various responses; guide them to the point below).
 Conclusion: no matter how big or small our circle is, it seems like the same
relationship between circumference and diameter is present!!
 Ask: what might this mean for our passcode?
Transition to next activity: So, it looks like every time there is a circle, we can fit at most
three full diameters inside our circumference – but there is always a little bit left over.
Is that a pattern? Let’s call our circumference C and our diameter d (Write this up on
the board). If we want to know how many diameters we can fit into a circumference,
what kind of math problem is that? (division). Here is how we can represent that as a
math problem: C/d. This looks like a fraction - when we have fractions, all we are doing
is division! Let’s practice with some simple problems using a calculator (have another
telegram delivered during fraction/division discussion):
 1/2; where did we see that problem today? Cutting the whole sphere into two
halves = 0.5
 20/5; how many times does “five go into 20”? four
 How many times did your diameter “go into” your circumference? Three, but
then there was always a little bit more
 Now, try the division with our circumference & diameter measurements….
Illinois Math and Science Academy, Statewide Student Initiatives
Written 10/9/15 by Christine Moskalik and Carmela Jones
11
It IS as easy as pi, FUNShops
Goal:
Students will
create a passcode
cipher that
represents 22
digits of pi; this
will help them to
visualize the
constant and
pattern less nature
of pi.
Activity 4: Circular Cipher
Estimated Time: 20 min
Materials:
 Lanyard string tied onto lanyard hook
 Pony beads (10 diff solid colors)
 Pony beads, clear
 Color wheel/cipher decoder
 Cup, plastic/any style, 9oz – 20 (1/student for holding beads)
Procedures:
1) Start with the telegram message: “the number for your passcode has more than 20
characters.”
 Review what “digits” and “characters” are if needed.
2) Relate the simple division you covered at the end of the last activity back to the
circles with which we have been working. Ask the students “Can we try to do
division using the measurements for our circumference and diameter?
3) Have the students follow the instructions on their student page which involves
using a calculator to divide the measurements for “C” by their measurements for
“d” - they’ll find “three and a little more” (may not be exactly pi due to error in
measurements) every time.
4) Review their answers.
5) Ask, does it seem that there is a pattern? (yes, every time we get three and a little
more, just like in the stamping activity).
6) Reveal that the relationship between C and d is a real thing!! It’s pi - and it’s the
same for every circle no matter how big or small the circle is! (if no one suggests we
try the value of pi for our
passcode, guide them to that
conclusion).
 This reveals the nature
of pi as CONSTANT – so
it makes sense that “pi
is hidden in every circle”
(our first telegram clue).
 This also reveals the
nature of pi as being a
NUMBER (our second
telegram clue)
 Ask them what they
think about the third
clue/telegram? How
does that clue fit into
what we are doing (allow
a few responses and
move on).
7) Show an image/website with
the value of pi (figure 2,
above) or write pi and its
symbol on the board.
 Try a few versions of pi
as the passcode (only using a few digits though) and pose the question, if we
are pretty sure pi is our passcode how come it isn’t working? (we don’t know
Illinois Math and Science Academy, Statewide Student Initiatives
Written 10/9/15 by Christine Moskalik and Carmela Jones
12
It IS as easy as pi, FUNShops
how long our passcode is; WAIT, didn’t we get a clue with this information? 
yes, our third clue!)
 Test the value of pi out to 22 digits (total, including decimal, see below) as
the passcode. SUCCESS!
3.14159265358979323846
 NOTE: number of digits for a ‘working’ passcode can be adjusted, but that will
in turn affect how long the cipher is.
 Why would we want a passcode that is 22 digits long? (if someone figures it
out, they probably would have a hard time remembering that many digits of
pi).
8) How can we make sure we don’t ever forget our passcode, but that no else will find
it and steal our treasure? (accept a few answers).
9) Ask if anyone knows what a cipher is? (a way to make a secret code)
 We should make a cipher that represents our passcode so we can always
have access to the goodies in our treasure chest!
 Use the beads, lanyard string and hook to make a pi-cipher out 20 digits
 Each group should have a “stock” of beads (quart-sized zipper bag); students
can get a scoop of beads from this bag in order to make their cipher (this way
they are picking beads from their individual cups, rather than from one stock
source).
10) Ask them to try and identify a pattern in the sequence of numbers (as represented
by the beads). When they cannot, it helps reveal another characteristic of pi (goes
on forever with no pattern).
 This mathematical constant does NOT have a pattern.
 in the ‘grown-up world’ we call this an irrational number.
11) Because it would be hard to write down a number that never actually ends, we use
a symbol to represent the mathematical constant, pi.
WRAP-UP ENTIRE LESSON
Estimated Time: 10 minutes
Procedures:
1) Ask them “Before today’s lesson, had anyone ever heard of pi?” (likely replies may
include apple pie, pi day at school, pi 5K/fun run, reciting many digits of pi, etc.
keep it light and fun while noting/guiding them to the math concepts below)
2) Review what (if anything) they have identified from the question above using
important math concepts. Allow students to explain and/or ask questions about the
relevant concepts such as
 Numbers
 Decimals
 Fractions
 Division
 Shapes/circles
 Symbols?
3) With any remaining time, have students attempt some of the extension ideas
below.
Illinois Math and Science Academy, Statewide Student Initiatives
Written 10/9/15 by Christine Moskalik and Carmela Jones
13
It IS as easy as pi, FUNShops
Assessment:
1) Informal/formative assessments during activities and class discussions
2) Completion of the student pages
3) Completion of the pi cipher
Clean-up:
1) Students should clean up their work areas. Dismiss the class when everything is
cleaned up.
2) Students can take their pi cipher, some pirate coins, and their student pages home.
EXTENSIONS/ADAPTATIONS
1) Have students attempt to memorize as many decimal places of pi as they can in a
certain amount of time and have them compete for who can go the farthest!
2) Make their cipher longer (more than 25 digits) pending available materials.
3) Have students create their own unique cipher decoder by picking different colors to
represent the numbers for the pi digits.
4) Students can measure the circumference of the pirate coins and use pi to
determine the diameter and vice versa.
5) Use symbol cards (obtain in advance if interested) to help students realize pi is a
symbol used to represent an actual number.
REFERENCES:
1. Figure 2, image credit: https://breakingmolds.files.wordpress.com/2014/03/picalculation.gif
2. Lamb, Evelyn. 2012. Scientific American. Blog “How Much Pi do you really need?”
http://blogs.scientificamerican.com/observations/how-much-pi-do-you-need/ Accessed
9.27.15
3. Random History.com. (2009, July 3). 50 interesting facts about pi. In Random Facts.
Retrieved September 9, 2015, from http://facts.randomhistory.com/2009/07/03_pi.html
4. Sylte, A. (2015, March 14). 9 random facts about pi (the irrational number, not the food).
In 9 News. Retrieved September 9, 2015, from
http://www.9news.com/story/life/2015/03/13/pi-day-facts-figures-irrationalnumber/24710313/
5. Tulsa World Website. Article “Pi common in everyday life, not just dessert.” Accessed
September 30, 2015. http://www.tulsaworld.com/business/fyibusiness/pi-common-ineveryday-life-not-just-dessert/article_d1e06850-b460-5ea6-8417-29bed2386234.html
6. Wilson, David. 2000. The History of Pi.
http://www.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html
Accessed 9/27/15.
Illinois Math and Science Academy, Statewide Student Initiatives
Written 10/9/15 by Christine Moskalik and Carmela Jones
14