A bag of marbles
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Age
5 to 7
Challenge level
Problem
Image
Suppose that in a bag of marbles,
all the ones that -
are rough to
feel, have a blue colour on them;
sparkle when
rolling, have a red colour on them;
are cold to
touch, have a white colour on them;
are dark inside,
have a green colour on them.
What can you say about each of the marbles A -
J?
Image
Imagine you are making marbles. What colours must be put on marbles that -
sparkle when rolling but are dark
inside?
are cold to touch and feel
rough?
are cold, but sparkle when
rolling?
What colour(s) could be on a marble that -
is cold?
sparkles when rolling?
What colours would you find on a cold, sparkly, dark and rough marble?
Getting Started
You could print off this sheet which has pictures of the marbles on. If you cut them out, you could move them around and group them as you work on the problem.
Is there only one marble that sparkles when rolling and is dark inside?
How do you know?
Student Solutions
We were particularly pleased with the kinds of answers and explanations that came with these solutions.We had many sent in and here are just two as a sample. First from Daniel at Englefield Green Infants School:
A. rough to feel and sparkley when rolling
B. rough to feel and dark inside
C. dark inside and sparkle when rolling
D dark inside and cold
E. cold, dark and rough
F. cold, sparkle when rolling, rough
G. rough, sparkle when rolling, dark inside
H. cold, rough
I. sparkle when rolling
J. sparkle when rolling, cold, dark inside.
On marbles that
sparkle when rolling but are dark inside - red and green
are cold to touch and feel rough - white and blue
are cold, but sparkle when rolling - white, red.
What colour(s) could be on a marble that
is cold - white
sparkles when rolling - red
The colour you would find on a cold, sparkly, dark and rough marble -
blue, green, red and white.
The second one is from Rebecca at Montsaye Community College:
Marbles -
A- would be rough to feel and Sparkles when it rolls
B- would be rough to feel and Dark inside
C- would Sparkle when it rolls and Dark on the inside
D- would be Dark on the inside and cold to touch
E- would be Cold to touch, Rough to feel and and Dark on the inside
F- would be Cold to touch, Rough to feeland Sparkle when it rolls
G- would Sparkle when it rolls, be Rough to feel and Dark on the inside
H- would be cold to touch and Rough to feel
I- would Sparkle when it rolls and be cold to touch
J- would Sparkle when it rolls, be cold to touch and dark on the inside
If I was making the Marbles-
If the Marble would Sparkle when it rolls and be dark on the inside I
would put Red and Green on it.
If the Marble would be cold to touch and Rough to feel I would put White
and Blue on it.
If the marble would be cold to touch and Sparkle when it rolls I would put
White and red on it.
If a Marble was cold it could be-
Just white,
White and Blue,
White and Green,
White and Red,
White and Blue and Red,
White and Blue and Green,
White and Red and Blue and Green.
If a Marble Sparkled when it rolled it could be-
Red.
Red and Blue,
Red and Green,
Red and White,
Red and Blue and White,
Red and Blue and Green,
Red and White and Green,
Red and White and Green and Blue.
If a Marble was cold, sparkly, dark and rough it would be-
White and Red and Green and Blue.
Other solutions came from;
Kristy at Singapore International SchoolVarious un-named
pupils from Buckingham College Preparatory School
Talia and Alex at
Red Hill Field School
Saskia and Amrita
at Jebal School
Rhea at Mason
Middle School
Alaa at Gateway
School
Lauren at
Danesfield School
A girl called
Charlie at Culford Preparatory School
Sarah at Seabrook
High School
Sofia at Glenarm
College
Samantha at
Kaleen School
Libby, Patrick,
Peter and Olivia at Danes Hill School
Marianne and
Aramide at Clapham Manor School
Samantha at Driftwood Middle
and last but not least, Meghan and Kia
Samantha at Driftwood Middle
and last but not least, Meghan and Kia
Well done everyone!
Teachers' Resources
A Bag of Marbles
Image
Suppose that in a bag of marbles, all the ones that -
are rough to feel, have a blue colour on them;
sparkle when rolling, have a red colour on them;
are cold to touch, have a white colour on them;
are dark inside, have a green colour on them.
What can you say about each of the marbles A - J?
Image
Imagine you are making marbles. What colours must be put on marbles that -
sparkle when rolling but are dark inside?
are cold to touch and feel rough?
are cold, but sparkle when rolling?
What colour(s) could be on a marble that -
is cold?
sparkles when rolling?
What colours would you find on a cold, sparkly, dark and rough marble?
Why do this problem?
This problem builds on simple sorting skills and gives children the experience of using logical reasoning.
Possible approach
It would be helpful if pupils had a sheet of marbles to cut out so that they could physically move or group them. (You might find it useful to print off this sheet which depicts four sets of the marbles.) In addition, some children might benefit from having coloured
pens to use so that they can record different marbles easily.
The first part of the problem, describing each marble, could be done as a whole group so that everyone become more familiar with the different attributes. You could then ask pairs of pupils to work on the second and third parts of the problem, emphasising that you will be interested in how they arrived at their solutions. You may like to draw attention to efficient ways of approaching the
problem that you see, or to clear ways of recording their solutions. It might be appropriate to stop them briefly after five minutes or so, once they have had a chance to look at the first question in the third part "What colour(s) could be on a marble that is cold?". The idea here is for the children to appreciate that there is not just one right answer - there are in fact several possibilities.
You could challenge the class to find all the possible marbles which fit the criteria, perhaps by having a section of a display board devoted to collecting examples over the week to come.
Key questions
How do you know that the marbles you've chosen are correct?
What other colours could be on a marble which is cold/sparkles when rolling?Possible extension
Children could be challenged to look at how marbles could be coloured if they have exactly two attributes, or three attributes or all attributes, and to record the number of possibilties each time. Do they have a system for making sure they don't leave out any possibilities each time?
Possible support
Having circles of paper cut out to represent marbles, and coloured pens to mark each with, may help children access this problem.