JENNIFER MOYLE
Jellybean Maths
Activities
Using Rod Clement’s Counting on Frank for inspiration
2010
Contents:
1) Frank Maths Problems – Number – Years 2 – 4 (in CL groups)
2) Frank Maths Problems – Number – Years 5 – 7 Team-Pair-Solo CL
activity
3) Counting on Frank DWP for 3 consecutive Chance and Data lessons –
Years 5 – 7
4) Activity Sheets for lesson described in DWP
5) Rubric for Maths Journal Self/Peer/Teacher Assessment
6) Sample Mathematics Checklist for Specific Learning Objectives
7) Jellybean Maths for Year 8 – 10 – Chance and Data and Number
©JENNIFER MOYLE, 2010
Note to Readers:
Many of the lessons that follow rely on a sound working knowledge of how to facilitate cooperative learning
activities which embrace Johnson and Johnson’s five essential elements:
- Face to face interaction
- Social Skills Focus
- Individual Accountability
- Positive Interdependence
- Group Processing / Reflecting
Specific Strategies used also include:
- Numbered Heads
- Think-Pair-Share
- Round Robin
- Team-Pair-Solo (Kagan)
It is important to research cooperative learning theory and practice and understand how and why it works. I
recommend the works of Johnson and Johnson, Barrie Bennett, and Laurie and Spencer Kagan.
Enjoy viewing and experimenting with these lessons – and please feel free to ask any questions you have
about them, or share your experiences and/or student worksamples of them. Please modify as your context
necessitates.
Cheers and good luck
Jennifer 
Frank Maths Problems…
My estimate of how many jellybeans are in the jar:
The actual amount of jellybeans in the jar is:
The total number of
people that the
jellybeans will be
shared between:
2
3
4
5
6
7
8
9
10
11
12
13
© Jennifer Moyle, 2010
Explain what method you used to estimate how many jellybeans were in the jar:
Describe the way you calculated how many jellybeans were actually in the jar:
Write a number sentence using
Draw how the jellybeans can be divided…
the
+ operation only
Write a number sentence using
the
x and / or + operations only
Write a number sentence using
the
÷ operation only
Describe in words how many
jellybeans each of the people will
get, and what will happen to the
left overs if there are any.
Frank Maths Problems… An Example…
My estimate of how many jellybeans are in the jar:
The actual amount of jellybeans in the jar is:
The total number of
people that the
jellybeans will be
shared between:
2
37
Explain what method you used to estimate how many jellybeans were in the jar:
Describe the way you calculated how many jellybeans were actually in the jar:
Write a number sentence using
Draw how the jellybeans can be divided…
the
+ operation only
Write a number sentence using
the
 and / or + operations only
Write a number sentence using
the
÷ operation only
☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺
☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺
18 + 18 + 1 = 37
(2 x 18) + 1 = 37
37 ÷ 2 = 18 with a remainder of
1 jellybean.
☺
or
37 ÷ 2 = 18.5 or 18½
Discuss with the people around you why the following is not the correct way of dividing the 37 lollies between two people…
☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺
☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺
☺
© Jennifer Moyle, 2010
Describe in words how many
jellybeans each of the people will
get, and what will happen to the
left overs if there are any.
If there are 2 people and 37 jellybeans,
each person would get 18 jellybeans
each. There would be one jellybean left
over. This jellybean could be cut into
halves and ½ given to each person, or
they could toss a coin to see who gets
the left over one.
Frank Maths Problems…
My estimate of how many jellybeans are in the jar:
90
The actual amount of jellybeans in the jar is:
Modelled Exercises with the teacher
The total number of
people that the
jellybeans will be
shared between:
121
Write a number sentence using
Draw how the jellybeans can be divided…
2
☺1111
1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111
people
☺1111
1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111
3
people
the
+ operation only
60 + 60 + 1 = 121
Write a number sentence using
the X and / or
 □□□□
□ = 10
 □□□□
◦= 1
40 + 40 +
+ 1 = 121
(60 x 2) + 1 = 121
(40 x
) + 1 = 121
 □□□□
remainder
30 + 30 + 30 + 30 + 1 = (30 x
121
people
+
people
)+
= 121
+
+
+
+
Students solve problems using the
Team – Pair – Solo Structure.
or
121 ÷ 4 =
or
121 ÷ 4 =
1
4
(
x 5) +
= 121
= 121
= 24 r1
If 121 jellybeans were divided
evenly between 2 people they would
both get 60 jellybeans. There
would be one left over which could
be cut in half and shared.
If 121 jellybeans were divided
evenly between 3 people they would
all get
jellybeans. There
would be one left over which could
be fed to the dog.
If 121 jellybeans were divided
evenly between
people they
would all get 30 jellybeans. There
would be one left over which could
be fed to the dog.
If 121 jellybeans were divided
evenly between
÷ 5 = 121
or
121 ÷ 5 =
( 20 x 6) + 1 = 121
Describe in words how many
jellybeans each of the people
will get, and what will happen to
the left overs if there are any.
.
or
remainder
© Jennifer Moyle, 2010
÷ operation only
121 ÷ 2 = 60 r 1
or
121 ÷ 2 = 60 ½
or
121 ÷ 2 = 60.5
÷ 3 = 40 r 1
or
121 ÷ 3 = 40 13
or
121 ÷ 3 = 40.3
121 ÷
5
people
the
÷ 4 = 30 r 1
4
6
Write a number sentence using
+ operations only
remainder
1
◦
Students solve problems using the
Team – Pair – Solo Structure.
Explain what method you used to estimate how many jellybeans were in the jar:
I counted how a line of jellybeans from the top to the bottom of the jar. That was 10. I counted how many jellybeans
were on the bottom of the jar. That was 9. I multiplied the two together and got 90.
Describe the way you calculated how many jellybeans were actually in the jar:
We put the jellybeans into groups of ten, and sorted the groups into an array. Then we counted the groups by tens and added the 1 jellybean
that was left over. There were 12 groups of 10 jellybeans plus 1, which made 121. Then we put them all back into the middle and repeated
the process. We got 121 twice.
1
would all get
There would be
.
people they
jellybeans.
left over
which could be fed to the dog.
121 ÷ 7 = 17 r 2
Students solve problems using the
Team – Pair – Solo Structure.
7
people
8
people
Students solve problems using the Team – Pair – Solo Structure.
or
121 ÷ 7 = 121 2 7
or
121 ÷ 7 = 17. 29
15 + 15 + 15 + 15 + 15
+ 15 + 15 + 15 + 1 =
121
9
people
10
people
( 13 x 9) + 4 = 121
121 ÷ 10 = 12 r 1
or
121 ÷ 10 = 12 110
or
121 ÷ 10 = 12.1
Group Members: A = ____________ B = _______________ C = ________________ D = ________________
© Jennifer Moyle, 2010
JELLYBEAN MATHEMATICS – DAILYWORK APPROPRIATE FOR YEARS 5 - 7
MATHEMATICS: Understanding Chance and Probability: Describing Probability Numerically as a Fraction, Percentage and Decimal (Lsn 19, Wk 2,
60m)
LEARNING EXPERIENCE:
Curriculum Framework Core
PREPARATION ASSESSMENT AND
Values
AND
RECORDING:
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Mathematics: Counting on Frank Chance and Data
RESOURCES:
2.1
2.2
2.3
2.4
2.5
3.1
3.2
3.3
3.4
3.5
3.6
3.7
Writing:
Mathematics
Journal
and
Report
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.1
5.2
5.3
5.4
CF Overarching Learning
Outcomes:
1
2
3
4
5
6
7
8
9
10
11
12
13
CF Mathematics Learning
Outcomes:
AM1-2 WM3 WM4 WM5 N6a-b N7
N8 M9a-b M10ab M11
CD12 CD13ab CD14 S15abc S16 A17ab A18ab A19
SOS Maths Chance & Data
Outcomes:
CD12
Understand Chance
Levels 2–
5
CD13a&b Collect and Process Data
Levels 2-5
CD14
Summarise & Represent Data Levels 2-5
SOS Maths Number Outcomes:
N8
2–5
Calculate
Levels
CF and SOS English Writing
Outcomes:
E4 & 9
Writing Processes & Strategies Levels 2-5
© Jennifer Moyle, 2010
Introduction 1:

Teacher to read and discuss aspects of Counting on Frank by Rod Clement

Teacher reviews concepts of chance and data including the language of chance, 1:2 chance,
1:6 chance, and numerical ways of describing probability (fractions, percentage and ratio)
Body 1:

Teacher to allocate groups to students (mixed ability groups as per Kagan), discuss group
names (establishing identity), and number from 1 – 4 (Numbered Heads CL strategy)

Teacher to distribute jars of jellybeans, ask students to estimate and record the number of
JBs in the jar.

Teacher to show photo of the full jar alongside remnants from the packet, ask students to
reassess their estimate.

Teacher and students to discuss the possibility of:
- Each group having the same number of jellybeans
- There being an even number of each colour jellybeans

Students count the jellybeans, and classify them. Record results.

Teacher and students create a class table of the results. Discuss distributions of colours,
convert to fractions, percentages and ratios.

Students test the theory of probability by conducting an experiment (jellybeans from jar in
feely bag).

Students record and analyse data.
Conclusion 1:

Share results in a whole class discussion.

Students create a written report of their mathematical investigation in their maths journal,
including designing, conducting, representing and summarising data.

Peers to read and give yellow and green hat (DeBono’s Hats) feedback







Counting on Frank To what extent where the students
working toward being able to:
book
12 prepared jars of
a) Estimate the number of jellybeans
jellybeans
in a jar to ≥ 20 and M & Ms to ≥
12 x M & Ms
20
Jellybean survey
Student worksample – checklist
table
Maths PowerPoint b) Identify the possibility of the
jellybean colours being evenly
12 x feely bags
48 x Jellybean
survey results
distributed in the jar
Student worksample – checklist
c)
Design an experiment to test
probability of individual coloured
jellybeans from a feely bag.
Student worksample – rubric
d)
Accurately record results of
experiment.
Student worksample – rubric
e)
Calculate the probability of getting
any one colour jellybean from the
jar and representing it as a fraction,
decimal, percentage, and ratio.
Student worksample – checklist
Specific Learning Objectives:
At the end of these lessons the students will be
working toward being able to:
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
Estimate the number of jellybeans in a jar to ≥ 20 and
M & Ms to ≥ 20
Identify the possibility of the jellybean colours being
evenly distributed in the jar
Design an experiment to test probability of individual
coloured jellybeans from a feely bag.
Accurately record results of experiment.
Calculate the probability of getting any one colour
jellybean from the jar and representing it as a fraction,
decimal, percentage, and ratio.
Describe their mathematical investigation in their
maths journal in a logical sequence including
designing, conducting, representing and summarising
data.
Include a range of mathematics vocabulary correctly
in writing journal.
Calculate missing information from the jellybean
packet survey.
Make observations of the data from the jellybean
survey.
Conduct an independent group survey of the contents
of a packet of M and Ms and write a report of the
results.
© Jennifer Moyle, 2010
f)
Introduction 2:

Introduce the jellybean packet survey. Discuss what the table shows us, and what
information is missing.
Body 2:

Students to calculate missing information.

Students to create a list of observations in relation to the data.

Students answer questions provided on worksheet.
Conclusion 2:
Teacher and students to review answers and discuss results.
*****************************************
Introduction 3:


Include a range of mathematics
vocabulary correctly in writing
journal.
Maths Journal – anecdotal records
h)
Calculate missing information from
the jellybean packet survey.
Worksample – checklist
Introduce concept of M and Ms packet and the task.
i)
Groups independently follow the same procedure to estimate the number of M & Ms,
count the M and Ms, classify them in colours, calculate probability of each colour being
extracted from a feely bag using the language of chance, fractions, decimals, percentage
and ratio.
j)

Students to evenly distribute M & Ms between them and write a complementary number
sentence.
Conclusion 3:

g)
Review results from Jellybean Experiment.
Body 3:

Describe their mathematical
investigation in their maths journal
in a logical sequence including
designing, conducting, representing
and summarising data.
Student journal – peer assessment and
rubric
Students to share and compare results from a member of another group.
Make observations of the data from
the jellybean survey.
Worksample – Rubric
Conduct an independent group
survey of the contents of a packet
of M and Ms and write a report of
the results.
Student report – Rubric
Jellybeans Maths
Name: ___________________________ Date: ________________
Start Time ____:____
Finish Time ____:____
1. Estimate how many jellybeans are in your group jar:
2. Describe what chance you think there is in there being an equal distribution of the colours in the
jar...
3. Re-estimate how many jellybeans there are in the jar:
4.
5. Explain why your estimate has changed or stayed the same.
6. Empty the jar and record (write or draw or both) how many jellybeans of each
colour there are, and how many there are in total.
7. How close was your second estimate of how many jellybeans were in the jar? (Describe the
difference in numbers)
8. Were the jellybean colours equally distributed?
9. Why do you think this was so?
10. Compare your data with the other groups in the class. Describe what you notice. Are you surprised
by the results? How could that have happened?
© Jennifer Moyle, 2010
Designing your own experiment...
Jellybeans Maths learning journal
In your journal please describe the maths investigation carefully. Include:





Introduction: Describe the purpose of the experiment and how you designed it so that it could be
fairly tested.
Paragraph 2: Describe what happened when you conducted the experiment (give details).
Paragraph 3: Describe how you recorded the data and comment on any early patterns that you saw
emerging.
Paragraph 4: Analyse the data recorded, explaining what the experiment proved or disproved.
Conclusion: Discuss any issues or concerns there were with the experiment and suggest possible
follow-up experiments.
* Please remember to use as much mathematical vocabulary as you can!
** Also remember to consult the assessment rubric so that you know exactly what is expected of you 
Jellybean Maths Journal Self / Peer/ Teacher Assessment
Name: ___________________________________
Nibbling Away
Introduction
Designing the
Experiment
Conducting the
Experiment and
Recording the Data
Analysing the Results
Mathematical
Vocabulary
Yellow Hat – Positives
The purpose of the
experiment is not
explained very well, or
not at all.
A Terrier at Work
A Frank Effort
The purpose of the
experiment is
described.
The purpose of the
experiment is described
extremely well,
including how fair
testing is planned for.
Describes the design of Describes the design of Describes the design of
the experiment with
the experiment with
the experiment so well
very few or no details at some good details.
that it could be easily
all.
followed and replicated
by someone else.
Makes no or very little
Partly describes how
Describes how the
attempt to describe how the experiment was
experiment was
the experiment was
conducted, explaining
conducted, explaining
conducted and the
what the group
what all the group
results recorded.
members were
members were
responsible for.
responsible for.
Attempts to explain
Explains how group
how group members
members ensured the
ensured the experiment experiment was
was conducted fairly
conducted fairly and the
and the results were
results were recorded
recorded accurately.
accurately.
No analysis of results
Some analysis of results Analyses the results
made.
made.
from the experiment
carefully and
accurately. Makes
suggestions for future
experiments.
Uses little or no
Uses some
Uses a lot of
mathematical words or mathematical words or mathematical words or
phrases.
phrases.
phrases.
Self/Peer/Teacher Feedback:
Green Hat – New Ideas, Thoughts for Improvement…
Own Signature: ________________________ Peer / Teacher Signature: _______________________
© Jennifer Moyle, 2010
Mathematics Checklist (for specific learning objectives – sample)
Class: Rm 19
Teacher: Ms Moyle 
Year: 7
Counting on Frank Activities
9th September, 2010
Number
a) Estimate the
number of
jellybeans in a jar
to ≥ 20
Number
e) Calculate the
probability of getting
any one colour
jellybean from the jar
and representing it as
a fraction, decimal,
percentage, and ratio.
Appreciating Mathematics
g) Include a range of mathematics vocabulary correctly in
writing journal.
Comments/Observations
Sarah worked very hard to achieve her goal of including
15 mathematical words in her journal today, and was
meticulous with her spelling.
Sarah Menzies
A
A
Wide variety of mathematical words used.
Kirk Douglas
C
C
Georgie Burns
Roger Rabbit
Huey McDuck
Archimedes Smith
Fred Fibonacci
Eric Euler
Sandy Escher
Aaron Aristotle
C
absent
B
B
A
D
D
A
C
absent
B
C
B
D
C
A
Kirk wrote a brief account only with limited mathematical
vocabulary included.
Georgie has adopted the word “guestimated.”
Georgie worked cooperatively today.
absent
Roger was very quiet today.
Used some maths vocab.
Remained reserved throughout the lesson.
Joseph Pestalozzi
C
C
Jessica Windsor
C
C
Genghis Khan
Harry Hannibal
Emily Bronte
Charlotte Bronte
Emily Dickinson
Charlie Dickens
C
B
C
C
B
D
B
B
C
C
B
E
© Jennifer Moyle, 2010
Aaron used the maths dictionary to try and find new words he
hadn’t used before.
Used a range of mathematical words.
Used a wide range of mathematical words copied from her
maths worksheet and charts on wall.
Peer assessed Jessica’s journal very well, giving
constructive, specific feedback.
Well written journal including a sound introduction and
discussion of the findings.
Estimated 12 jbs originally and changed estimate to 20.
(52 away from the total amount of 72 jbs). Worked well
with Emily. Immerse Charlie in classifying and counting
groups of found objects.
and maths, yum!
1.
What colours would you expect to find in a packet of jellybeans?
_______________________________________________________________________________________
2.
In a 190g packet of Allen*s Jellybeans how many jellybeans would you estimate there are? _______
3.
Open and sort your jellybeans, completing the following table:
Colour of
Jellybean
Flavour
Magenta
Radish
Number
in
Packet
14
Average Weight
(Show algorithm)
Percentage of the colour found
in packet (Show algorithm)
28g ÷ 14 = 2g
14
100
1400
x
=
= 23.3%
60
1
60
Totals
Discuss the results of your findings (make brief one sentence statements of fact):
a) ________________________________________________________________________________
b) ________________________________________________________________________________
c) ________________________________________________________________________________
d) ________________________________________________________________________________
e) ________________________________________________________________________________
4.
We are going to collate the results from each of the groups in the following table. Make
predictions for how you think the data will change / stay the same.
Distribution of colours in the pack: __________________________________________________________
Total weight of the jellybeans: ______________________________________________________________
Average weight of the black jellybeans: ______________________________________________________
Colour of
Jellybean
Magenta
Total number
in the 5
packets
50
Average Weight
(Show algorithm)
Percentage of the colour found in the 5
packets (Show algorithm)
100g ÷ 50 = 2g
50
100
5000
x
=
= 16.6%
300
1
300
Totals
5.
Discuss the results of your findings (make brief one sentence statements of fact):
a) ________________________________________________________________________________
b) ________________________________________________________________________________
c) ________________________________________________________________________________
d) ________________________________________________________________________________
e) ________________________________________________________________________________
f) ________________________________________________________________________________
g) ________________________________________________________________________________
6.
Favourite Jellybeans. Complete the tally of our class’s favourite jellybeans…
7.
Blind Taste Testing. Present each colour jellybean to the members of the group, and get them to give
a rating from 1 – 10 on how tasty it is. 1 is gross, 5 is OK, 10 is absolutely top of the wozzer!
Colour of
Jellybean
8.
Team Member
Team Member
Team Member
Team Member
1
2
3
4
Average Rating
Collate this information with the other groups to get the whole class results.
Colour of
Jellybean
Group 1
Group 2
Group 3
Group 4
Group 5
Average Rating
9. Discuss the results of your findings (make brief one sentence statements of fact) and compare with what
people thought their favourite colour jellybean was from the table in question 5:
a) ________________________________________________________________________________
b) ________________________________________________________________________________
c) ________________________________________________________________________________
d) ________________________________________________________________________________
e) ________________________________________________________________________________
11. Whose packet is worth the most?
If each colour jellybean has a different worth, how much is the total packet worth? Show all of your
working out and create an algorithm to prove your answer.
purple
0.1
11.
white
0.2
blue
0.3
red
0.4
yellow
0.5
orange
0.6
green
0.7
pink
0.8
black
0.9
Whose packet is worth the most with the following values?
If each colour jellybean has a different worth, how much is the total packet worth? Show all of your
working out and create an algorithm to prove your answer.
purple
1¾
white
1.55
© Jennifer Moyle, 2010
blue
⅓
red
2¼
yellow
2¾
orange
- 2.5
green
-½
pink
3⅜
black
0.6