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It began in Devon in 2008, with a conversation describing how the
Maths Team were keen to raise the profile of mathematics
investigations and to go one step further in promoting mathematical
thinking and problem solving in primary classes. Having already
established a thriving network of Lead Teachers and a 'guided
mathematics' project for higher-attaining children across the
county, the team believed that getting involved in trialling NRICH
resources would complement and enhance existing priorities. So, in
November 2008 Liz was invited to Devon to launch 'Enriching
Mathematics' with a group of 25 teachers. The aims of the project
- To raise teachers' awareness of the NRICH website as a source
of 'low threshold, high ceiling' rich mathematical tasks
- To help teachers use rich mathematical tasks to develop using
and applying in the classroom
- To explore the potential of rich mathematical tasks as contexts
in which to assess pupils' progress
- To improve the quality of support offered for teachers on the
NRICH website through trialling of problems and subsequent
We began with a problem
and Liz drew two V-shapes on the flipchart:
Liz invited the teachers
to talk to a neighbour about what they noticed and we shared some
of their observations:
"Each one uses the numbers 1 to
"The total of the numbers in each "V" is
"In the "V" on the left, the three
numbers on the left-hand "arm" (1, 4 and 5) add to 10, so do the
three numbers on the right-hand "arm" (3, 2 and 5)."
Liz picked up on the last
point and explained that she was going to define a "Magic V" as one
where the left "arm" had the same total as the right "arm". She
asked them whether they thought there might be other Magic Vs for
the numbers 1, 2, 3, 4 and 5. Some nodded hesitatingly, some nodded
vigorously, some looked as if they were thinking ... And so the
challenge was set: How many Magic Vs using the numbers 1 to 5 could
they find? How would they know that they had found them all?
This problem is called (unsurprisingly) Magic Vs
published on the NRICH website in November 2008. What we describe
above is outlined in more detail in the teachers'
and it was great to see everyone engrossed in the
challenge, no matter whether they were a Year 1 teacher, a Year 5
teacher or a consultant! If you haven't come across this problem
before, do take a moment to have a go at it before reading on. What
do you notice about Magic Vs? Can you explain any similarities?
The whole-group discussion provided opportunities for us to share
solutions and ways of working. We reflected on the mathematical
'content' knowledge we'd needed (addition, subtraction, number
bonds, odds/evens ...) and the strategies we'd used to solve the
problem (trial and improvement, working systematically, identifying
patterns ...) . Liz commented on what she had noticed as the
teachers worked: they were talking, listening, making conjectures,
working together, testing out theories, explaining, generalising
... . From these discussions, we drew up a list of
characteristics of rich tasks and exchanged ideas about the kind of
classroom 'climate' that encourages children to engage in
mathematics in similar ways.
The teachers agreed to trial some of the investigations and games
on the NRICH website with their children and complete evaluation
forms, reflecting on the lessons as they did so. These feedback
forms were devised using prompts taken from the Devon teachers'
reflective lesson study journal. To encourage more teachers to take
part, Devon generously provided half a day's supply cover per
teacher, up to four teachers per school, Subject Leader briefings
were used to introduce NRICH and each Subject Leader was encouraged
to try out some of the resources with either their whole class or a
group and evaluate them.
Four months later we all met again. Firstly teachers tried out the
investigation from NRICH which at that time had little in the way
of support materials on the site. Collectively they identified ways
in which the format and structure of the resource could be improved
and suggested guidance to inform teachers' notes which would
accompany the activity.
Following this, teachers shared and discussed their experiences of
how NRICH had impacted on teaching and learning in their
classrooms, and they pooled information on ways the website might
further improve the quality of its support to teachers and pupils.
Using the prompts on the feedback forms, teachers were invited to
comment on four aspects in particular:
Engagement, challenge and
Awe and wonder!
children not usually seen as 'maths stars' to shine
improving relationships, respect for others' processes and
- Suggestions for teachers'
Blog or bribe for
Video clips from
More recognition of
published solutions 'e-certificate'
- General improvements to NRICH
Attractive interface for
children needed (as a separate section) so interactive ones do not
have solutions for children
Search alphabetically and
by problem title (this facility is in fact already available but it
clearly needs to be easier to find!)
- Ways in which children
They became willing to
take a risk
developed enquiry, they were curious!
Problems with legs...
Lead Teachers took
responsibility for the afternoon, giving stimulating presentations
about how NRICH had been used in their own class (or school). They
talked about examples of problems they'd used and highlighted
changes in the ways the children worked and ways that they
themselves as teachers had developed. Here, and in the follow-up article
we share some of their examples and comments in the hope that you
will be inspired to try the same activities with your own
Katie and Barbara both teach the youngest children in Rydon and
Woodlands Park Primary schools and each felt it important that they
should not miss out on mathematical problem solving. Katie
explained that she wanted to bring the problems alive for her
pupils and so adapted some of the resources she found on NRICH. She
combined the ideas in Spiders and Flies and Hubble Bubble to create
a problem about 'Wilma the Witch' who was making a potion which
contained exactly 10 legs. Katie left it up to the children
themselves to choose whatever equipment they wanted to use and she
allowed the children to develop their own recording methods.
There were 22 legs creeping across the
web. How many flies? How many spiders?
(Thank you to Lachlan, age 5, for the
Winifred Wytsh bought a box each
- jelly babies.
- milk jelly bears.
- yellow jelly bees.
- and jelly belly beans.
Each box contained 20 jellies.
Winifred wanted to make a jolly jelly feast that had 32 legs. How
many different ways could Winifred make her jelly
Barbara described how she has become "immersed in NRICH" and has
been devising problems which have similar elements to those on the
website. In particular, she talked about her link with a school in
South Africa which inspired a problem based on different ways of
arranging hopscotch. Children took up this task in independent
learning time and many made hopscotch arrangements out of 'Duplo'.
They were encouraged to notice which were the same and which
different, and to record what they had done, which led to counting
in ones and twos, identifying and continuing patterns. Some
children extended the hopscotch to include more numbers, some drew
hopscotch grids on the playground and some programmed the BBot to
cover their grids.
Barbara used the NRICH
Noah saw 12 legs walk by into the Ark.
How many creatures did he see?
This photo captures the
display of children's work:
Anna from St Andrew's Primary School told us about working with a
group of Year 2 higher-attaining children on the Two-digit Targets
, adapted from a BEAM Maths of the Month activity.
You have a set of the digits from 0 -
Can you arrange these digits in the
five boxes below to make two-digit numbers as close to the targets
as possible? You may use each digit once only
Anna wanted something that would generate talk and require the
children to apply their knowledge. To begin with, they had a go at
the challenge cooperatively in pairs. Then they played it as a game
with one child against the other. However, in this game situation,
each wanted to play strategically and so they stopped talking! Anna
moved on to Four-digit
You have two sets of the digits from 0
The idea is to arrange these digits in
the five boxes to make four-digit numbers as close to the target
number as possible. You may use each digit once only
This time she encouraged one pair to play against the other pair
and in this way, they talked to their partner about what to do as
they planned their strategy. The children were happy to change
their minds and move the numbers around to get as close to the
targets as possible. Having digit cards to manipulate gave them
this freedom, whereas usually they would have been very keen to get
the 'right' answer. Anna felt that the problem deepened their
understanding of place value.
Anna concluded that the problem/s provided great opportunities for
mathematical talk and produced high levels of engagement. The
children became more familiar with large numbers and were able to
transfer their knowledge of number properties (e.g. odd/even,
multiples) to these larger numbers.
the follow-up article you can read more about the project and
learn how Jayne, Amy and Justine embedded creative mathematical
activities in their classrooms.
This article first appeared in Primary
Mathematics, a journal published by The Mathematical Association