jellybean maths activities - · pdf filefrank maths problems my estimate of how many...

JENNIFER MOYLE

2010

Jellybean Maths Activities

Using Rod Clement’s Counting on Frank for inspiration

© J E N N I F E R M O Y L E , 2 0 1 0

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

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: Explain what method you used to estimate how many jellybeans were in the jar:

The actual amount of jellybeans in the jar is: Describe the way you calculated how many jellybeans were actually in the jar:

The total number of

people that the

jellybeans will be

shared between:

Draw how the jellybeans can be divided…

Write a number sentence using

the + operation only


the x and / or + operations only


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.

2

3

4

5

6

7

8

9

10

11

12

13

© Jennifer Moyle, 2010

Frank Maths Problems… An Example…

My estimate of how many jellybeans are in the jar: Explain what method you used to estimate how many jellybeans were in the jar:

The actual amount of jellybeans in the jar is: 37 Describe the way you calculated how many jellybeans were actually in the jar:

The total number of

people that the

jellybeans will be

shared between:





the and / or + operations only




jellybeans each of the people will

get, and what will happen to the

left overs if there are any.

2 ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺

☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺

☺

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

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.

Discuss with the people around you why the following is not the correct way of dividing the 37 lollies between two people…

☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺

☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺

☺


Frank Maths Problems…

My estimate of how many jellybeans are in the jar: 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.

The actual amount of jellybeans in the jar is:

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.

The total number of

people that the

jellybeans will be

shared between:





the X and / or + operations only




jellybeans each of the people

will get, and what will happen to

the left overs if there are any.

Mo

del

led

Ex

erci

ses

wit

h

the

teac

her

2 people

☺1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111

☺1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111

1 remainder

60 + 60 + 1 = 121

(60 x 2) + 1 = 121

121 ÷ 2 = 60 r 1

or

121 ÷ 2 = 60 ½

or

121 ÷ 2 = 60.5

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.

3

people

□□□□ □ = 10

□□□□ ◦ = 1

□□□□

◦ remainder

40 + 40 + + 1 = 121

(40 x ) + 1 = 121

÷ 3 = 40 r 1

or

121 ÷ 3 = 403

1

or

121 ÷ 3 = 40.3


evenly between 3 people they would

all get jellybeans. There


be fed to the dog.

Stu

den

ts s

olv

e pro

ble

ms

usi

ng t

he

Tea

m –

Pair

– S

olo

Str

uct

ure

.

4

people

30 + 30 + 30 + 30 + 1 =

121

(30 x ) + = 121

÷ 4 = 30 r 1

or

121 ÷ 4 = 4

1

or

121 ÷ 4 = .


evenly between people they

would all get 30 jellybeans. There


be fed to the dog.

5

people

remainder

+ + + +

+ = 121

( x 5) + = 121

121 ÷ = 24 r1

or

÷ 5 = 121 1

or

121 ÷ 5 = .


evenly between people they

would all get jellybeans.

There would be left over

which could be fed to the dog.

Stu

den

ts s

olv

e pro

ble

ms

usi

ng t

he

Tea

m –

Pair

– S

olo

Str

uct

ure

. 6

people

( 20 x 6) + 1 = 121

121

90


Stu

den

ts s

olv

e pro

ble

ms

usi

ng t

he

Tea

m –

Pair

– S

olo

Str

uct

ure

. 7 people

121 ÷ 7 = 17 r 2

or

121 ÷ 7 = 1217

2

or

121 ÷ 7 = 17. 29

S

tuden

ts s

olv

e pro

ble

ms

usi

ng t

he

Tea

m –

Pair

– S

olo

Str

uct

ure

.

8 people

15 + 15 + 15 + 15 + 15

+ 15 + 15 + 15 + 1 =

121

9 people

( 13 x 9) + 4 = 121

10 people

121 ÷ 10 = 12 r 1

or

121 ÷ 10 = 12 10

1

or

121 ÷ 10 = 12.1

Group Members: A = ____________ B = _______________ C = ________________ D = ________________


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)

Curriculum Framework Core

Values

LEARNING EXPERIENCE:

Mathematics: Counting on Frank Chance and Data

Writing: Mathematics Journal and Report

PREPARATION

AND

RESOURCES:

ASSESSMENT AND

RECORDING: 1.1 1.2 1.3 1.4 1.5 1.6 1.7

2.1 2.2 2.3 2.4 2.5

3.1 3.2 3.3 3.4 3.5 3.6 3.7

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:

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

book

12 prepared jars of

jellybeans

12 x M & Ms

Jellybean survey

table

Maths PowerPoint

12 x feely bags

48 x Jellybean

survey results

To what extent where the students

working toward being able to:

a) Estimate the number of jellybeans

in a jar to ≥ 20 and M & Ms to ≥

20

Student worksample – checklist

b) Identify the possibility of the jellybean colours being evenly

distributed in the jar


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.


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 Calculate Levels

2–5

CF and SOS English Writing

Outcomes:

E4 & 9 Writing Processes & Strategies Levels 2-5


Specific Learning Objectives: At the end of these lessons the students will be

working toward being able to:

a) Estimate the number of jellybeans in a jar to ≥ 20 and

M & Ms to ≥ 20 b) Identify the possibility of the jellybean colours being

evenly distributed in the jar

c) Design an experiment to test probability of individual coloured jellybeans from a feely bag.

d) Accurately record results of experiment. e) Calculate the probability of getting any one colour

jellybean from the jar and representing it as a fraction,

decimal, percentage, and ratio.

f) Describe their mathematical investigation in their

maths journal in a logical sequence including

designing, conducting, representing and summarising data.

g) Include a range of mathematics vocabulary correctly

in writing journal. h) Calculate missing information from the jellybean

packet survey. i) Make observations of the data from the jellybean

survey.

j) Conduct an independent group survey of the contents

of a packet of M and Ms and write a report of the

results.

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:

Review results from Jellybean Experiment. Introduce concept of M and Ms packet and the task.

Body 3:

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.

Students to evenly distribute M & Ms between them and write a complementary number sentence.

Conclusion 3: Students to share and compare results from a member of another group.

f) 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

g) 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

i) Make observations of the data from

the jellybean survey.

Worksample – Rubric

j) 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?


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

A Terrier at Work

A Frank Effort

Introduction The purpose of the

experiment is not

explained very well, or

not at all.

The purpose of the

experiment is

described.

The purpose of the

experiment is described

extremely well,

including how fair

testing is planned for.

Designing the

Experiment

Describes the design of

the experiment with

very few or no details at

all.


the experiment with

some good details.


the experiment so well

that it could be easily

followed and replicated

by someone else.

Conducting the

Experiment and

Recording the Data

Makes no or very little

attempt to describe how

the experiment was

conducted and the

results recorded.

Partly describes how

the experiment was

conducted, explaining

what the group

members were

responsible for.

Attempts to explain

how group members

ensured the experiment

was conducted fairly

and the results were

recorded accurately.

Describes how the

experiment was

conducted, explaining

what all the group

members were

responsible for.

Explains how group

members ensured the

experiment was

conducted fairly and the

results were recorded

accurately.

Analysing the Results No analysis of results

made.

Some analysis of results

made.

Analyses the results

from the experiment

carefully and

accurately. Makes

suggestions for future

experiments.

Mathematical

Vocabulary

Uses little or no

mathematical words or

phrases.

Uses some


phrases.

Uses a lot of


phrases.

Self/Peer/Teacher Feedback:

Yellow Hat – Positives

Green Hat – New Ideas, Thoughts for Improvement…

Own Signature: ________________________ Peer / Teacher Signature: _______________________


Mathematics Checklist (for specific learning objectives – sample)

Class: Rm 19 Year: 7 Teacher: Ms Moyle

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 Menzies A A Wide variety of mathematical words used. Sarah worked very hard to achieve her goal of including

15 mathematical words in her journal today, and was

meticulous with her spelling.

Kirk Douglas C C Kirk wrote a brief account only with limited mathematical

vocabulary included.

Georgie Burns C C Georgie has adopted the word “guestimated.” Georgie worked cooperatively today.

Roger Rabbit absent absent absent Roger was very quiet today.

Huey McDuck B B

Archimedes Smith B C

Fred Fibonacci A B

Eric Euler D D

Sandy Escher D C Used some maths vocab. Remained reserved throughout the lesson.

Aaron Aristotle A A Aaron used the maths dictionary to try and find new words he

hadn’t used before.

Joseph Pestalozzi C C Used a range of mathematical words. Peer assessed Jessica’s journal very well, giving

constructive, specific feedback.

Jessica Windsor C C Used a wide range of mathematical words copied from her

maths worksheet and charts on wall.

Well written journal including a sound introduction and

discussion of the findings.

Genghis Khan C B

Harry Hannibal B B

Emily Bronte C C

Charlotte Bronte C C

Emily Dickinson B B

Charlie Dickens D E 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 Number

in

Packet

Average Weight

(Show algorithm)

Percentage of the colour found

in packet (Show algorithm)

Magenta Radish 14 28g ÷ 14 = 2g

60

14 x

1

100 =

60

1400 = 23.3%

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

Total number

in the 5

packets

Average Weight

(Show algorithm)

Percentage of the colour found in the 5

packets (Show algorithm)

Magenta 50 100g ÷ 50 = 2g

300

50 x

1

100 =

300

5000 = 16.6%

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

Team Member

1

Team Member

2

Team Member

3

Team Member

4

Average Rating

8. 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 white blue red yellow orange green pink black

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

11. 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 white blue red yellow orange green pink black

1¾ 1.55 ⅓ 2¼ 2¾ - 2.5 - ½ 3⅜ 0.6


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