Narendran V

Metrics, a parameter for any type of measurement, play a major role both in mathematics and in our day-to-day life. While students know that there are different units of measurement, they don’t have an understanding of why we use these terms of measurement. I share here how I tried to help my grade 2 students understand the need to use metrics.

Non-standard measurements
Day 1: The plan was to have an initial discussion with the students about what measurement means and then ask them to measure different objects without using a scale. The idea was to help students realize the need for standard units of measurement. Three students were randomly picked and asked to measure the teacher’s table using three different spans – hand/palm span, finger span, arm span.

Each student first measured the table along the perimeter with their arms and wrote the count on the board. Then they followed the same exercise using their hands and fingers to measure.

Table 1

Type of span	Student 1	Student 2	Student 3
Arm	14	12	17
Hand/palm	27	25	30
Finger	45	41	48

After the three students finished measuring, the class began to discuss the difference in the values that the three students got. “Although all three measured the same table with their arms, why did they get different values?” After debating various reasons for the difference, the students arrived at the fact that the arm lengths of the three students were not the same and hence the difference in values. Happy with this progress, I asked the students, “So what is the solution to this?” One student replied that his arm was the same length as Student 1’s arm. I pointed out that while he may arrive at the same value as Student 1, it wouldn’t be the same for everyone. “How do we ensure that everyone arrives at the same value?”

Learnings from the activity
• Students explored the idea that an object can be measured with any other object as a reference instead of using only a scale.
• Students came to a conclusion as to why the measurement was different for the three students.
• They also arrived at the fact that if we are to get the same measurement value then only one hand should be used to measure.
• They learnt that the position of their arm stretch should be the same to have the correct measurement.

Day 2: Using semi-standard measurements
We began the day by recalling the previous day’s learnings. Then we decided that since it was the difference in the sizes of the arms and hands that lead to the different values, today we will measure the table again using pencils. I divided the students into three groups to carry out the task.

Table 2

Type of span	Group 1	Group 2	Group 3
Pencil	15 pencils	20 pencils	11 pencils

After the exercise, students found that there still was a difference in the values of the measurement of the three groups. So the question again was “Why did the groups arrive at different values?” While it took them a while to arrive at a reason on Day 1, on Day 2, they quickly realized that the difference in values was due to the difference in the sizes of the pencils used by the groups. So again, “How do we all arrive at the same value of measurement?” The students gave the question some thought and said, “We can use the same pencil for every group.” I asked the students to verify this. The three groups chose one pencil and took turns measuring the table. The result of the exercise was the following.

Table 3

Type of span	Group 1	Group 2	Group 3
Pencil	15 pencils	15 pencils	15 pencils

Learnings from the activity
• Students realized that they can use objects like pencils and pens to measure. They were also more comfortable using the pencil than their hands to measure.
• They understood that the measuring object had to be of the same size in order for all to get the same value.
• They also figured out that they get the same value whatever direction they measured the table from.
• They learnt that the unit for the measurement should be based on the object used to measure. For example, if an object is measured using a box, then the value will be “x boxes”.

Day 3: Connecting semi-standard to standard measurement
To reinforce the previous day’s learnings, I once again divided the class into three groups and gave the groups broomsticks of the same length and asked them to measure the teacher’s table. The students first checked to see that the groups received broomsticks of the same length and then set to measure the table. All the groups arrived at the same value (Table 4).

After the exercise, I told the students that standard units of measurement like metre and centimetre were developed so that there was universal agreement on the values measured.

Table 4

Type of Span	Group 1	Group 2	Group 3
Stick	12 sticks	12 sticks	12 sticks

Learnings from the activity
• Students were able to understand and apply the shift from semi-standard to standard measurement (from pencil to a uniform stick).
• Students were able to correlate the stick and the scale they use in class.
• Students explored the proper way of measuring objects with any materials with a defined unit based on the material used as a measuring tool.

Insights in the class

1. Students were able to analyze the errors made when using measuring spans of the hand or arm like marking the start and end point with a chalk.
2. They were able to give assumptions during discussions. Some of them are given below.
   Assumption 1: The difference in the value is because the student’s hand was not placed in a straight line, he/she changed the orientation.
   Assumption 2: Since all the objects used to measure were pencils, the measurement should have been the same but the value differed because the pencils were of different colours, or had an eraser at the back, or were not sharpened well.
3. Students themselves made an order of instruction within the group by giving themselves roles – one to place the object for measurement, one to mark with chalk, and one to count the number of times the object is placed.

Conclusion
Although metric is used in our day-to-day life in most situations and even with a lot of hands-on experience with several tools for measurement, we fail to understand how measurements are done. Even though we use the words metre, grams, and litres every day, we don’t know why or how the terms were developed. When we apply something with complete understanding, we know where and when and how to use it properly. This is why exercises like the one shared above are important.

Note: I would like to thank Mrs.Maheswari K, primary school teacher – Government Primary School KalitheerthalkuppamPet for providing the platform to co teach this idea in her classroom.

References

1. Michele Stephan, Douglas. H. Clements, “Linear and Area Measurement in Prekindergarten to Grade2”, January 2003.
2. Julie Sarama, Douglas. H. Clements, “Length measurement in the early years: teaching and learning with learning trajectories”, 15 January 2021.

The author is an engineer and educator actively involved in teaching language and math at the primary level. He can be reached at narendran.venkataraman@azimpremjifoundation.org.