1 Using games for developing number sense

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.

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.