Using number games: developing number sense

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Sharp Tutor Tue, Jan 11, 2022 04:36 PM UTC

In school mathematics, this element of playing and having fun with numbers often gets missed out on. This unit aims to address this by giving ideas for identifying and using number games as activities that offer rich learning opportunities to help your students develop their sense of numbers.

1. Elementary Mathematics
Using number games: developing
number sense
Teacher Education
through School-based
Support in India
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2. TESS-India (Teacher Education through School-based Support) aims to improve the classroom practices of
elementary and secondary teachers in India through the provision of Open Educational Resources (OERs) to
support teachers in developing student-centred, participatory approaches. The TESS-India OERs provide
teachers with a companion to the school textbook. They offer activities for teachers to try out in their
classrooms with their students, together with case studies showing how other teachers have taught the
topic and linked resources to support teachers in developing their lesson plans and subject knowledge.
TESS-India OERs have been collaboratively written by Indian and international authors to address Indian
curriculum and contexts and are available for online and print use (http://www.tess-india.edu.in/). The OERs
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adapt and localise the OERs further to meet local needs and contexts.
TESS-India is led by The Open University UK and funded by UK aid from the UK government.
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3. Using number games: developing number sense
What this unit is about
‘Number sense’ is a term that is often used but is quite hard to define. In general, it refers to a student’s
ability to work with numbers flexibly and fluidly. Number sense involves giving meaning to numbers – that
is, knowing about how they relate to each other and their relative magnitudes. It is also about the effect of
mathematical operations on numbers, such as whether multiplication of a given number by another would
make the number bigger or smaller. Having a sense of number is vital for the understanding of numerical
aspects of the world.
Learning and improving your sense of number is a lifelong activity that starts with children. In school it
requires exploring and playing with numbers, and being encouraged to think about patterns and
relationships between numbers. In school mathematics this element of playing and having fun with numbers
often gets missed out. This unit aims to address this by giving ideas for identifying and using number games
as activities that offer rich learning opportunities to help your students develop their sense of numbers.
What you can learn in this unit
• Some ideas to develop and strengthen your students’ sense of number.
• How to use number games as a teaching strategy to stimulate engagement, participation and
mathematical reasoning.
This unit links to teaching requirements of the NCF (2005) and NCFTE (2009) and will help you to meet
those requirements, outlined in Resource 1.
1 Using games for developing number sense
Pause for thought
Think back to when you were a child. Did you learn anything about numbers outside of school?
For example, you might have learned to count prior to attending school, or you might have
come to know about money, age or sharing things equally from your life outside of school.
How did such learning happen?
Playing games is something children do from an early age. It is generally accepted that playing games
stimulates the development of social interaction, logical and strategic thinking, sometimes
competitiveness, or at other times teamwork and togetherness.
Games can give a sense of suspense, joy, frustration and fun. Research literature has shown that using
games in teaching mathematics leads to an improved attitude towards mathematics, enhanced motivation
and support for the development of children’s problem solving abilities (Ernest, 1986; Sullivan et al., 2009;
Bragg, 2012). It is argued that the mathematical discussions that happen while playing mathematical games
leads to the development of mathematical understanding (Skemp, 1993).
This unit gives examples of some tried and tested number games to help develop the number sense of
students. It will also discuss how to spot good number games and learn to identify the learning
opportunities the games can offer for students.
The first activity is an example of a game that helps to develop the understanding of number relationships. It
uses a mathematical tool the students are already familiar with: the ‘hundred square’. Many such games are
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4. Using number games: developing number sense
freely available in books and on the internet. The activities in this unit come from NRICH, a free mathematical
resources website that is part of the University of Cambridge’s (UK) Millennium Mathematics Project.
Before attempting to use the activities in this unit with your students, it would be a good idea to complete all,
or at least part, of the activities yourself. It would be even better if you could try them out with a colleague as
that will help you when you reflect on the experience. Trying them for yourself will mean you get insights into
a learner’s experiences which can, in turn, influence your teaching and your experiences as a teacher.
Activity 1: What do you need?
For this activity, students work in pairs or small groups. You can use Resource 2, ‘Managing groupwork’, to
help you prepare for the activity.
Give students a printout or copy of a hundred square (Figure 1), or make them use one they already have in
their books. Make sure they can all see the hundred square. It is also important not to tell them how to go
about doing this task but to let them discover it for themselves so they have to think about strategies.
This also keeps up the suspense.
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
Figure 1 A hundred square.
Part 1: Deciding on what you need to know
Write the following on the blackboard:
Eight clues
1. The number is greater than 9.
2. The number is not a multiple of 10.
3. The number is a multiple of 7.
4. The number is odd.
5. The number is not a multiple of 11.
6. The number is less than 200.
7. Its ones digit is larger than its tens digit.
8. Its tens digit is odd.
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5. Using number games: developing number sense
Tell the students the following:
I have got a number in my mind that is on the hundred square but I am not going to tell you
what it is. However, you can ask me four of the eight clues that are written on the
blackboard and I will answer with yes or no.
There is something else I need to tell you: four of the given clues are true but do nothing to
help in finding the number. Four of the clues are necessary for finding it.
Can you find out, in your group, the four clues that help and the four clues that do not help in
finding the number I am thinking of? What is it that you need to know to find a chosen
number from your hundred square?
Part 2: What is the number?
This part is to test the students’ conjectures about what they found out in part 1 of the activity.
• Say to the students: ‘I am thinking of a number – in your groups, decide on four clues to ask me to
find out what number I am thinking of.’
• After a few minutes ask one group for their clues and try them out. Whether they work or not, ask
for the reason they chose those four clues. Ask if a group has a different set of clues and try those
out. Stop when the clues work and discover your chosen number.
• Repeat this for several different numbers, or ask a student to take over your role and think of a
number.
• Follow this with a discussion of which four clues are not needed to find the number, and why this is.
What makes the best clues, and why?
(Source: adapted from NRICH, http://nrich.maths.org/5950.)
Video: Using local resources
http://tinyurl.com/video-usinglocalresources
Case Study 1: Mrs Bhatia reflects on using Activity 1
This is the account of a teacher who tried Activity 1 with her elementary students
I do agree that games are fun activities to do but I am always a bit sceptical when it is claimed they can
offer rich opportunities for learning mathematics. I found it hard to believe that these number games
could supplement the learning that happens in the normal traditional teaching I do in my classroom, when I
explain mathematical ideas clearly to my students. But I decided to give it a go because I do find that even
my younger students seem bored at times when doing mathematics, and that saddens me and makes me
feel I have to try something else.
My class is large – about 80 students. Although they are supposed to be only from Classes III and IV, the
attainment between the students varies a lot: some of the students seem to still struggle with early-year
concepts of numbers, others are happy and able to do the work of higher classes. Finding activities that all
of them can do and that challenge them all is very hard.
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6. Using number games: developing number sense
As I do not have access to resources such as a photocopier or large sheets of paper or scales for all
students, in preparation for this activity I asked the students to draw a hundred square on the inside cover
of their exercise books for homework. Most of the students had already done this, but some had not. I did
not want to spend any time in the lesson letting those students draw one there and then so I made sure
that when the students went into groups of four or five they were sat right next to someone who had done
the homework so they could both look at the same hundred square. To move them into groups I simply
asked the odd rows of students to turn around and work with the students sitting opposite them.
I was very uncomfortable with not giving the students precise instructions on how to go about finding out
which clues were necessary or not, or to discuss this with the whole class first. I was really worried they
would not know what to do. But I thought I would try and see if the activity would work and presented the
task in the way it was described.
I decided that if the students still did not know how to proceed after four minutes, I would tell them. It did
not take them that long. To make sure they were on-task I walked through the classroom and listened in on
their discussions. I asked some of the groups ‘How will you find out?’ Their answers varied in the choice of
numbers they would try the clues with, and their rationale for why to pick those. I noticed that
neighbouring groups would listen to their replies as well, sometimes changing their approaches. In that
way they all learned from each other without having to stop the whole class to discuss this.
I really liked the buzz in the class – there was excitement and engagement. The students were smiling a lot
and developing their mathematical arguments to discuss, agree and disagree with each other. Everyone
seemed to have a point to make and seemed to be included in the work of the groups.
After a while I told them they had three more minutes to decide on the clues, and that they had to make
sure that everyone in their group knew and understood what the agreed clues were. I asked that because I
wanted to make sure that all students in the group, whatever their attainment, would learn from this game.
For this reason I also did not ask the ‘smartest’ student of the group the questions in the second part of the
activity.
The discussion about why the clues were needed or not needed gave the students the opportunity to talk
about their ideas. Sometimes, at the first go, they expressed themselves clumsily, but I then asked them to
‘say that again’, and I was amazed by how quickly most of them managed to express themselves more
fluently the second time round. To make sure that not only the ‘smartest’ students answered I asked any
student whether they agreed with what was said and insisted on them repeating the statement in their
own words if they did. If they did not agree, they had to say why.
Reflecting on your teaching practice
When you do such an exercise with your class, reflect afterwards on what went well and what went less well.
Consider the questions that led to the students being interested and being able to progress, and those you
needed to clarify. Such reflection always helps with finding a ‘script’ that helps you engage the students to
find mathematics interesting and enjoyable. If they do not understand and cannot do something, they are
less likely to become involved. Do this reflective exercise every time you undertake the activities, noting, as
Mrs Bhatia did some of the smaller things that made a difference.
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7. Using number games: developing number sense
Pause for thought
Good questions to trigger reflection are:
• How did it go with your class?
• What questions did you use to probe your students’ understanding? Which questions
were most successful in enabling students to demonstrate their mathematical thinking?
• Did all your students participate?
• Did you feel you had to intervene at any point?
• Did you modify the task in any way? If so, what was your reasoning for doing so?
2 Essential characteristics of good games for
mathematical learning
There are plenty of number games to be found in books and on the internet, but are they all good and
effective for learning mathematics? To help in deciding which games offer good mathematical learning for
use in the classroom it is helpful to first think about the characteristics of good educational games in
general. Gough (1999) identified that a good game needs:
• an element of competitiveness; this can be achieved by having two or more players who take turns
to achieve a ‘winning’ situation of some kind
• an element of choice and decision making about the next move throughout the game
• an element of interaction between the players in that the moves of one player affect the others.
Activity 2 presents some games that help to develop an understanding of number relationships. Many such
games can be found freely in books and on the internet. Activities 1, 2 and 4 of this unit are adapted from
the NRICH mathematical resources website.
Activity 2: Being strategic about numbers
Preparation
This game asks the students to think about place value and is enjoyed by students of all ages. For younger
students the size of the boxes can be reduced.
Several variations to the game set-up and scoring systems are suggested. Once the students understand
the set-up you can also ask them to come up with more variations and scoring systems of their own, as
these will also require mathematical thinking.
For this activity students will need six-, nine- or ten-sided dice (with numbers 1 to 6, 1 to 9 or 1 to 10) or
spinners with ten segments numbered 1 to 10 or 0. You can find templates for spinners in Resource 3
These resources can be used again in Activity 4.
Game 1 below describes how to set up the basic game, and Games 2 to 6 describe variations and
developments from Game 1.
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8. Using number games: developing number sense
Playing the games
Game 1
This game is best played in pairs, or with two pairs playing against each other.
Each player draws a set of four boxes, as shown in Figure 2.
Figure 2 Each player has a set of four boxes.
Instruct the students as follows:
Take turns to roll the dice, read the number and decide which of your four boxes to fill with that
number. Do this four times each until all your boxes are full. Read the four digits as a whole number.
Whoever has the larger four-digit number wins.
Here are two possible scoring systems:
• One point for a win. The first person to reach 10 points wins the game.
• Work out the difference between the two four-digit numbers after each round.
The winner keeps this score. First to 10,000 wins.
Game 2
Whoever makes the smaller four digit number wins.
You’ll probably want to change the scoring system from Game 1.
Game 3
Set a target to aim for. Then the students throw the dice four times each and work out how far each of
them is from the target number. Whoever is the closer to the target number wins.
Here are two possible scoring systems:
• One point for a win. The first person to reach 10 points wins the game.
• Work out the difference between the two four-digit numbers and the target number after each
round. Keep a running total. First to 10,000 loses.
Game 4
This game introduces a decimal point. The decimal point will take up one of the cells so this time the dice
only needs to be thrown three times by each player. Choose a target number. The winner is the one closest
to the target.
Two possible versions:
• Each player decides in advance where they want to put the decimal point before taking turns to
throw the dice.
• Each player throws the dice three times and then decides where to place the digits and the decimal
point.
Again, different scoring systems are possible.
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9. Using number games: developing number sense
Game 5
This game really requires strategic thinking and can be very competitive! Tell your students the following:
Play any of the games above. This time you can choose to keep your number and put it in one of
your cells, or give it to your partner and tell them which cell to put it in. It’s really important to take
turns to start each round if this game is going to be fair.
This variation of the game becomes even more challenging when you play it with more than two people.
Game 6
This is a cooperative game rather than a competitive one – to be played by three or more people.
Tell your students the following:
• Choose any of the games above. Decide in advance which of you will get the closest to the target,
who will be second closest, third, fourth, etc.
• Now work together to decide in whose cells the numbers should be placed, and where.
(Source: adapted from NRICH, http://nrich.maths.org/6605.)
Video: Planning lessons
http://tinyurl.com/video-planninglessons
Case Study 2: Mr Mehta reflects on using Activity 2
From reading through the instructions for this activity I could see some of the learning opportunities it
could offer, but I was not sure to what extent this would be a ‘good’ game. I discussed this with a colleague
and we decided to first try it out ourselves in the staff room. And oh my, is it fun to play! We could hardly
stop, and other teachers had a go as well.
I was a little bit worried about making up teams of younger and older students as I teach mixed-age
groups, so when we first played the game I made students of similar age play in pairs against each other.
We played game 1 and then game 2, each one a couple of times. Since then we have used these and other
games regularly, sometimes at the beginning of the lesson to energise the students (especially good after
lunch), and sometimes at the end of the lesson. It also works well as a reward, telling the students if they
finish their work quickly we can play ‘being number strategists’.
I have used game 6, the ‘cooperative’ version of the game, with mixed-age groups and it is lovely to see how
most of the older students support the younger ones. I initially thought it would help the older ones in their
learning because they would have to help and communicate their mathematical thoughts with the younger
students, and that has indeed been the case. At the same time I realised I made the assumption that the
younger ones would be reluctant to talk with the older students – but that has proved wrong! The younger
students are very happy arguing with the older ones about the mathematics involved.
Because we do not have dice in the school, I made the spinners myself. I made them on cardboard and they
have now been used often, so it was worth the effort. I would like to make one big dice that I can roll and
then all the students would have to work with the same numbers – just as a variation on the game.
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10. Using number games: developing number sense
It was good to read about the characteristics of a ‘good’ game. I had never really thought about it in
detail. From watching the students play I think that much of the excitement and thinking that happens
comes from having ‘an element of choice and decision making about the next move throughout the
game’. And the characteristic of ‘an element of interaction between the players in that the moves of one
player affects the other players’ seems to trigger them into strategic thinking behaviour – thinking
beyond the next step. This strategic thinking really helped them to develop their understanding of place
value because they had to think very carefully about the value of each digit.
Pause for thought
In the case study, Mr Mehta was positive about the interaction between the older and
younger students in his class. What strategies might he have used to support the students’
learning if the younger students had been more reluctant to talk or the older children had
dominated the discussion?
Reflect about how your own lesson(s) went using some of these questions:
• What did you like about these activities?
• What is it about these tasks that make students want to participate and engage?
• What mathematical learning opportunities did these activities offer?
• Is there anything you would like to add or modify?
Make some notes of your thoughts and ideas in response to these questions and discuss
them with the teachers in your school or at a cluster meeting.
3 Identifying the mathematical learning
opportunities of number games
As stated at the beginning of this unit, playing number games can be beneficial for developing good social
interaction, thinking and problem-solving skills, and can provide motivation for learning.
The games used so far in this unit have offered mathematical learning opportunities – that is, the games
helped the students to develop their understanding of specific mathematical concepts and ideas – in this
case, number sense. This means that games are not only fun for the students but are also a valid way to
learn mathematics.
For example, in Activity 2 the mathematical learning opportunities for the students can be described as:
• learning about place value
• learning about the magnitude of numbers
• learning to use mathematical operations efficiently and accurately
• learning to work with numbers flexibly and fluidly.
Learning about these mathematical ideas is of considerable importance in the curriculum and essential for
developing number sense.
The next activity builds on the game in Activity 2. The learning opportunities are extended to working with
different operations, understanding number relationships and the effect of different mathematical
operations on numbers.
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11. Using number games: developing number sense
Activity 3: Grid games
This series of games follows on from the game ‘Being strategic about numbers’ in Activity 2.
Again there are several variations to choose from. These games are best played in pairs, or with two pairs
playing against each other.
For this activity students will again need six-, nine- or ten-sided dice (with numbers 1 to 6, 1 to 9 or 1 to
10), or spinners with ten segments numbered 1 to 10 or 0. You can find templates for spinners in Resource
Instructions for all games
Students take turns to throw the dice (or turn the spinner) and decide which of their cells on the grids to
fill in.
This can be done in one of two ways: either fill in each cell as you throw the dice, or collect all your numbers
and then decide where to place them.
Playing the games
Game 1
Each of the students draws an addition grid like Figure 3.
Figure 3 An addition grid.
Throw the dice nine times each until all the cells are full.
Whoever has the sum closest to 1,000 wins.
There are two possible scoring systems:
• One point for a win. The first person to reach 10 points wins the game.
• Each player keeps a running total of their ‘penalty points’, which is the difference between their
result and 1,000 after each round. First to 5,000 loses.
You can vary the target to make it easier or more difficult, or you can get the class to practise using
negative numbers (above 1,000 positive, below 1,000 negative) and suggest that the team closest to zero
after ten rounds wins.
Game 2
Each of the students draws a subtraction grid like Figure 4.
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12. Using number games: developing number sense
Figure 4 A subtraction grid.
Throw the dice eight times each until all the cells are full.
Whoever has the difference closest to 1,000 wins.
Here are two possible scoring systems:
• One point for a win. The first person to reach 10 points wins the game.
• Each player keeps a running total of their ‘penalty points’, which is the difference between their
result and 1,000 after each round. First to 5,000 loses.
You can vary the target to make it easier or more difficult, perhaps including negative numbers as your
target.
Game 3
Each of the students draws a multiplication grid like Figure 5.
Figure 5 A multiplication grid.
Throw the dice four times each until all the cells are full.
Whoever has the product closest to 1,000 wins.
Here are two possible scoring systems:
• One point for a win. The first person to reach 10 points wins the game.
• Each player keeps a running total of their ‘penalty points’, which is the difference between their
result and 1,000 after each round. First to 5,000 loses.
You can vary the target to make it easier or more difficult.
Game 4
Each of the students draws a multiplication grid like Figure 6.
Figure 6 A multiplication grid.
Throw the dice five times each until all the cells are full.
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13. Using number games: developing number sense
Whoever has the product closest to 10,000 wins.
Here are two possible scoring systems:
• One point for a win. The first person to reach 10 points wins the game.
• Each player keeps a running total of their ‘penalty points’, which is the difference between their
result and 10,000 after each round. First to 10,000 loses.
You can vary the target to make it easier or more difficult.
Game 5
You could introduce a decimal point and play any of the games above. The decimal point could take up one
of the cells, so the dice would only need to be thrown four times by each player. You will need to decide on
an appropriate target.
(Source: adapted from NRICH, http://nrich.maths.org/6606.)
Case Study 3: Mrs Mehta reflects on using Activity 3
I have used these different games now in a number of lessons, and with various classes. What I like about
them are that the students really get engaged with and practise their sums a lot. The competitiveness and
rules of the game make them talk and think strategically. They really think about place value, the
magnitude of numbers and the effect of different mathematical operations on numbers. It works for
younger and older students.
Sometimes I tell the students which game or operation I want them to use, at other times I let them choose
for themselves. Initially, I had thought that the younger or lower-attaining students would stick to what they
felt comfortable with doing. But that has proved not to be the case: sometimes they do stay in their comfort
zone, but often they really push themselves and go for sums which I would personally never have given them.
I also like that it is self-correcting. Of course mistakes in calculations are made, but they check each other
and tell each other when they do not agree. I think playing in pairs against each other helps with that. On the
other hand, sometimes I really do think they have to do it for themselves, so I let them play one against one.
I now use these kinds of number games regularly instead of doing lots of practice. I do think they make the
students think more about what they are doing mathematically. I have not used these number games yet
instead of my normal way of teaching, but I am slowly getting convinced that perhaps I should give that a
go because I have realised that all the students have some knowledge of doing sums – no doubt also a lot
of misconceptions – but perhaps by using games I might find out what these misconceptions are exactly,
and then plan my teaching to address these.
Pause for thought
• How well did it go with your class?
• Did you modify the task in any way like Mrs Mehta did? If so, what was your reasoning
for doing so?
• Which aspects of students’ understanding of number relationships and mathematical
operations on numbers did you think these activities were especially effective in
developing?
• What is it in these tasks that make students want to participate and engage?
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14. Using number games: developing number sense
4 Summary
This unit has focused on developing number sense in the elementary classroom by using games that offer
rich mathematical learning opportunities.
In studying this unit you have thought about how using number games as a teaching strategy can stimulate
engagement, participation and mathematical reasoning. You have considered how to adapt activities to
different age groups and levels of attainment by making small changes such as changing the numbers or
using different groupings.
Pause for thought
Identify three opportunities in your lessons when you will use some of the ideas from this
unit.
Resource 1: NCF/NCFTE teaching requirements
This unit links to the following teaching requirements of the NCF (2005) and NCFTE (2009) and will help you
to meet those requirements:
• Learn through activities that allow students to explore the properties of numbers.
• View students as active participants in their own learning encouraging their capacity to construct
knowledge.
• Let students see mathematics as something to talk about, to communicate through, to share one’s
finding, to discuss among them, and to work together on.
• Let students experience success in doing mathematical activities.
Resource 2: Managing groupwork
You can set up routines and rules to manage good groupwork. When you use groupwork regularly, students
will know what you expect and find it enjoyable. Initially it is a good idea to work with your class to identify
the benefits of working together in teams and groups. You should discuss what makes good groupwork
behaviour and possibly generate a list of ‘rules’ that might be displayed; for example, ‘Respect for each
other’, ‘Listening’, ‘Helping each other’, ‘Trying more than one idea’, etc.
It is important to give clear verbal instructions about the groupwork that can also be written on the
blackboard for reference. You need to:
• direct your students to the groups they will work in according to your plan, perhaps designating
areas in the classroom where they will work or giving instructions about moving any furniture or
school bags
• be very clear about the task and write it on the board in short instructions or pictures. Allow your
students to ask questions before you start.
During the lesson, move around to observe and check how the groups are doing. Offer advice where needed
if they are deviating from the task or getting stuck.
At the end of the task, summarise what has been learnt and correct any misunderstandings that you have
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15. Using number games: developing number sense
seen. You may want to hear feedback from each group, or ask just one or two groups who you think have
some good ideas. Keep students’ reporting brief and encourage them to offer feedback on work from other
groups by identifying what has been done well, what was interesting and what might be developed further.
Even if you want to adopt groupwork in your classroom, you may at times find it difficult to organize
because some students:
• are resistant to active learning and do not engage
• are dominant
• do not participate due to poor interpersonal skills or lack of confidence.
To become effective at managing groupwork it is important to reflect on all the above points, in addition to
considering how far the learning outcomes were met and how well your students responded (did they all
benefit?). Consider and carefully plan any adjustments you might make to the group task, resources,
timings or composition of the groups.
Resource 3: Templates for making spinners
Figure R3.1 Template for making spinners
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16. Using number games: developing number sense
Figure R3.2 A larger version of the ten-segment spinner.
Additional resources
• ‘Number sense series: developing early number sense’ by Jenni Way: http://nrich.maths.org/2477
• A newly developed maths portal by the Karnataka government:
http://karnatakaeducation.org.in/KOER/en/index.php/Portal:Mathematics
• National Centre for Excellence in the Teaching of Mathematics: https://www.ncetm.org.uk/
• National STEM Centre: http://www.nationalstemcentre.org.uk/
• National Numeracy: http://www.nationalnumeracy.org.uk/home/index.html
• BBC Bitesize: http://www.bbc.co.uk/bitesize/
• Khan Academy’s math section: https://www.khanacademy.org/math
• NRICH: http://nrich.maths.org/frontpage
• Art of Problem Solving’s resources page:
http://www.artofproblemsolving.com/Resources/index.php
• Teachnology: http://www.teach-nology.com/worksheets/math/
• Math Playground’s logic games: http://www.mathplayground.com/logicgames.html
• Maths is Fun: http://www.mathsisfun.com/
• Coolmath4kids.com: http://www.coolmath4kids.com/
• National Council of Educational Research and Training’s textbooks for teaching mathematics and
for teacher training of mathematics: http://www.ncert.nic.in/ncerts/textbook/textbook.htm
• AMT-01 Aspects of Teaching Primary School Mathematics, Block 1 (‘Aspects of Teaching
Mathematics’), Block 2 (‘Numbers (I)’), Block 3 (‘Numbers (II)’), Block 4 (‘Fractions’):
http://www.ignou4ublog.com/2013/06/ignou-amt-01-study-materialbooks.html
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17. Using number games: developing number sense
• LMT-01 Learning Mathematics, Block 1 (‘Approaches to Learning’) Block 2 (‘Encouraging Learning in
the Classroom’), Block 4 (‘On Spatial Learning’), Block 6 (‘Thinking Mathematically’):
http://www.ignou4ublog.com/2013/06/ignou-lmt-01-study-materialbooks.html
• Manual of Mathematics Teaching Aids for Primary Schools, published by NCERT:
http://www.arvindguptatoys.com/arvindgupta/pks-primarymanual.pdf
• Learning Curve and At Right Angles, periodicals about mathematics and its teaching:
http://azimpremjifoundation.org/Foundation_Publications
• Textbooks developed by the Eklavya Foundation with activity-based teaching mathematics at the
primary level: http://www.eklavya.in/pdfs/Catalouge/Eklavya_Catalogue_2012.pdf
• Central Board of Secondary Education’s books and support material (also including List of Hands-on
Activities in Mathematics for Classes III to VIII) – select ‘CBSE publications’, then ‘Books and
support material’: http://cbse.nic.in/welcome.htm
Bragg, L. (2007) ‘Students’ conflicting attitudes towards games as a vehicle for learning mathematics: a
methodological dilemma’, Mathematics Education Research Journal, vol. 19, no. 1, pp. 29–44.
Bragg, L.A. (2012) ‘Testing the effectiveness of mathematical games as a pedagogical tool for children’s
learning’, International Journal of Science and Mathematics Education, vol. 10, no. 6, pp. 1445–67.
Davies, B. (1995) ‘The role of games in mathematics’, Square One, vol. 5, no. 2.
Ernest, P. (1986) ‘Games: a rationale for their use in the teaching of mathematics in school’, Mathematics in
School, vol. 15, no. 1, pp. 2–5.
Gough, J. (1999) ‘Playing mathematical games: When is a game not a game?’, Australian Primary
Mathematics Classroom, vol. 4. no. 2.
National Council for Teacher Education (2009) National Curriculum Framework for Teacher Education
(online). New Delhi: NCTE. Available from: http://www.ncte-india.org/publicnotice/NCFTE_2010.pdf
(accessed 15 March 2014).
National Council of Educational Research and Training (2005) National Curriculum Framework (NCF). New
Delhi: NCERT.
NRICH, http://nrich.maths.org/frontpage (accessed 25 July 2014).
Polya, G. (1962) Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving,
combined edn. New York, NY: Wiley.
Skemp, R. (1993) Structured Activities for Intelligent Learning. Calgary, Canada: EEC.
Sullivan, P., Clarke, D. M. and O’Shea, H. (2009) ‘Students’ opinions about characteristics of their desired
mathematics lessons’ in Sparrow, L., Kissane, B. and Hurst, C. (eds) Shaping the Future of Mathematics
Education: Proceedings of the 33rd annual conference of the Mathematics Education Research Group of
Australasia, pp. 531–9. Fremantle: MERGA.
Except for third party materials and otherwise stated below, this content is made available under a
Creative Commons Attribution-ShareAlike licence (http://creativecommons.org/licenses/by-sa/3.0/). The
material acknowledged below is Proprietary and used under licence for this project, and not subject to the
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18. Using number games: developing number sense
Creative Commons Licence. This means that this material may only be used unadapted within the TESS-
India project and not in any subsequent OER versions. This includes the use of the TESS-India, OU and
UKAID logos.
Grateful acknowledgement is made to the following sources for permission to reproduce the material in
this unit:
Activity 1 and Figure 1: adapted from NRICH, http://nrich.maths.org/5950.
Activity 2 and Figure 2: adapted from NRICH, http://nrich.maths.org/6605.
Activity 3 and Figures 3–6: adapted from NRICH, http://nrich.maths.org/6606.
Every effort has been made to contact copyright owners. If any have been inadvertently overlooked the
publishers will be pleased to make the necessary arrangements at the first opportunity.
Video (including video stills): thanks are extended to the teacher educators, headteachers, teachers and
students across India who worked with The Open University in the productions.
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