Addressing Number Sense Challenges

Warm Up Activity (To improve mental ability):

The students were asked to count the number 15 in descending order one after another; that is, if a student says 15, next will say 14 and so on. All the students also joined him in counting.

Similarly, they counted till 20 in the ascending order. This was to gain students’ attention at the beginning of the class.

Main Activity

The class began with multiple representations of the numbers using fingers. For instance, students would represent number 8 in different ways: that is, 5 in one hand, 3 in another hand, or 4 in both the hands, and so on.

Initially, students had difficulty in understanding the concept. But gradually, with this way of representation, they began to grasp better. As we gave many examples and gave them practice with using different numbers, they were able to understand better. At the end of the activity, students concluded that single number can be represented in many ways and any which way they had wanted. To make their understanding even deeper the same activity was followed for various other numbers.

For instance, for number ‘7’, students will represent as either 5+2 or 4+3, using fingers and so on.

Follow-up Activity: In this activity, I would count my ten fingers 1 to 5 in one hand and 10 to 6 on the other hand and add them as 5+6 and tell the students that I have 11 fingers. Some students were surprised at this. However, a few of them realized that I was counting backwards (10 to 6) on one hand and forward on the other and recognized this as wrong.

This activity was used to strengthen students’ understanding of the concept.

Dienes Blocks: Dienes Blocks consists of different units of place value put together to represent a number.

Students were explained the place values of these shapes and how they are aggregative in nature (that is, how all these shapes can be used collectively to represent three/two digit numbers).

At first, students were asked to get into bench-wise teams. Then, students were asked to show how to represent the number 14 using Dienes blocks. Most of the teams used one ‘ten’ and four ‘ones’. Whereas, one group chose to represent ‘14’ using fourteen ‘one’ blocks.

At the end of the class, one student was called and asked to represent 55. The student was unable to do it in the stipulated time, which was count of 10. This warranted that the concept needed further clarity amongst certain students.

Next, students were given the number ‘35’ to be organized using Dienes blocks. Though group 1’s initial count was just 34, later the students corrected it when it was pointed out.

Which team is the winner?

The other students were of the opinion that group 1 is wrong. One student asked whether there could be values more than 10s in the ones. When we checked group 1’s blocks, it was found that they had run out of tens blocks and they had only unit blocks to keep. Students in groups discussed if this was right or wrong.

At this moment, teacher started evaluating each groups’ blocks beginning with group 4 and he drew the block arrangement of each group on the board. Groups 4, 3 and 2 had the same answer and it was clarified very well by using the blocks and later converting it to numbers. But group 1 was also right. The teacher demonstrated this by translating the block to the count of 35. Other groups counted and verified the number.

After Dienes Block session, we further made the students count the numbers in ascending order. Most of the students were able to play the number game except for one student. The students had problems with the number ‘40’ as they seem to have confused it with ‘14’ when counting. To check student’s understanding, he was asked to count numbers from 47 to 53. This time, he was able to count correctly. The students were also able to count numbers till 100 in the group. They were fast as well as loud.

However, students slowed down when they were asked to count alone. Even students who were fast in counting in groups, tend to think and stammer when the previous number had been told by someone else and not themselves.

During this process, it was noticed while counting that one student skipped number ‘14’. So he was asked to start counting from 1 to 20. It was understood that the problem, was with ‘teen’ numbers. They were misunderstanding them to be numbers ending with ‘ty’. The boy also had a special case issue with the number ‘15’ which he kept pronouncing as ‘five-teen’. But he was completely comfortable while counting numbers between 31-39, but cannot tell 40.

Even though the children were facing problems, the activity enabled them to identify the numbers properly and also helped them in recognizing the numbers. We addressed this problem by asking them to repeat the naming of numbers after us, after we clearly pronounced it for them.