JELLY BEANS
USEFUL RESOURCES
KEY CONCEPTS
★ Number and operations
★ Fractions and division
★ Logical reasoning
Pencils and paper
STEP 1: THE PROBLEM
How many jelly beans are in
the jar?
Key questions
•
•
•
•
•
What are you asked to find out?
What colours are the jelly beans?
How many red jelly beans are there?
Can you start with the first clue? Why?
What colours can you work with first?
STEP 2: REFLECTION
Angelʼs solution method using
a chart
Key questions (based on student solutions)
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•
•
•
•
How does knowing how many red ones help you
to get started?
What order did you use the clues in and why?
Which are the tricky parts? Why?
After finding that there are 120 blue jelly beans,
what did you do to find out how many black and
green there are?
Which strategy do you like most? Why?
STEP 3: THE CHALLENGE
New clues and a different number of
jelly beans. How many jelly beans now?
Key questions
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•
•
•
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View & Do: Problem Solving 3 © 2011 Blake Education
How does Angel solve the problem?
How does James solve his problem? Would his
solution work? Why?
Would it be very efficient?
Will you use the same strategy or a different one
for this challenge? Why?
JELLY BEANS
THE PROBLEM
Jelly bean jar clues:
For every orange jelly bean in the jar there are 4 blue ones
For every yellow jelly bean in the jar there are 5 blue ones
For every red jelly bean in the jar there are 6 green ones
There is the same number of blue jelly beans as green ones
There are 20 red jelly beans in the jar
★ How many jelly beans in the jar and how many of each colour?
CUT HERE
JELLY BEANS
THE CHALLENGE
There are now:
For every red jelly bean in the jar there are 3 green ones
For every blue jelly bean in the jar there are 4 yellow ones
For every red jelly bean in the jar there are 5 orange ones
There are 20 red and blue jelly beans altogether
There is a gross of jelly beans altogether
★ How many are there of each colour?
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PROBLEM SOLUTIONS
JELLY BEANS
Typical solutions for this problem are:
Solution 1: Clues are followed in the correct order, but finding instead of dividing to find out
how many yellow jelly beans means a multiplication is carried out. The follow-on from this
results in a very large number of jelly beans to put in the jar. A very large jar would be needed
and alarm bells should have rung.
Solution 2: Clues have been used in the correct order and a correct answer has been found
unfortunately though there is no clear pathway for back tracking or double checking the answer.
Solution 3: In this example the colours are listed in the best order and each step is worked
out and much of the sequence and thinking is visible. The working out makes it quite easy to
backtrack to check the answers to each part.
TICK AND FLICK RUBRIC
Use this rubric as the basis for your assessment of the student’s work on this problem.
Item
A
B
C
D
E
identified and
sequenced
the clues
effectively
independently
identified and
sequenced the
clues correctly
independently,
but with fixups, sequenced
the clues
correctly
used the two
obvious clues
independently
and when
prompted,
sorted the best
sequence for
the remaining
clues
found the first
clue and when
scaffolded,
sequenced the
remaining clues
correctly
when
scaffolded,
found the first
and second
clues in the
sequence and
with assistance,
was able to
follow the
remaining clues
computation
strategies.
independently
used efficient
mental
computation
strategies
including the
multiplicative
ones
independently
used fairly
efficient
computation
strategies
including the
multiplicative
ones
used efficient
strategies
the two
easiest clues,
but needed
prompts for the
more complex
ones parts
used a
calculator for
the first two
clues, but
then needed
assistance with
the remaining
clues parts
used a
calculator
for all
computations
attempted
solution
approach and
checking
sophisticated
systematic,
effective
representation
used and
answers
checked
without
prompting
clear and
systematic
representation
and when
prompted,
back tracked
to check the
solution
insufficient
representation
for back
tracking and
checking to
be carried out
effectively
when
scaffolded,
parts of the
representation
could be
explained
and matched
against the
problem
representation
not recorded
and answers
unchecked
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View & Do: Problem Solving 3 © 2011 Blake Education
JELLY BEANS
Solution 1
red = 20
green = 6 x 20 = 120
blue = green = 120
1 yellow = 5 blue = 600
orange = 5 x blue
5 x 600 = 3000
= 3920 lollies
Solution 2
orange = 30
yellow = 14
red = 20
blue = 120
green = 120
434
Solution 3
red = 20
green = 6 x red = 120
240
green = blue = 120
yellow = blue ÷ 5 = 120 ÷ 5 = 24
blue = green
orange = blue ÷ 4 = 120 ÷ 4 = 30
240 + 50 = 24
290
314 jelly beans altogether
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