Numbers in Primary K-5

In the previous chapter, we argued that the pre-primary number curriculum in Math should not go beyond 9 in written form due to the difficulty of understanding the Place Value Concept and the necessity of getting a thorough understanding of Number Sense.

We continue a similar exploration into the curriculum for classes 1 to 5, which normally make up the Primary School.

There are 2 basic purposes for learning numbers in the Primary School. One is to understand the role of numbers in our daily life and the other is to master the basic 4 arithmetic operations. It is on these foundations that the curriculum in the Middle and Higher classes can be understood easily by students.

In their normal daily lives, even adults rarely deal with numbers more than one thousand. Most cannot ‘visualise’ numbers beyond Five Hundred. They may be able to write & operate on numbers of any magnitude, but they may find it difficult to estimate the number of people in an auditorium to the nearest hundred just by sight.

This is one of the reasons there are different units of measurement for the same entity though converting from one to another is very easy in the decimal system. For example, in weight, we have gram, kilogram and a tonne. We can very well say that the weight of a person is 65000gm. But calling it 65 Kgs gives us a comfortable feeling that we can relate to it. We can recall many such examples where we feel comfortable when dealing with smaller numbers.

Most of the life experiences of Primary school children are going to be with numbers less than hundred. We also have to remember that these children are still developmentally in the concrete operations stage and hence would not be able to deal comfortably with large numbers which are just words not comprehensible in daily life.

At the same time, they need to master the 4 basic operations of addition, subtraction, multiplication and division in Primary school.

The algorithms for the 4 operations are standardised and can be fully mastered by just using 3-digit numbers. Operations with bigger number are just an extension of the same idea. Hence for the purposes of mastering the 4 operations, it is enough to teach numbers up to 999.

Keeping these in mind, the Primary Math curriculum need not go beyond 999. If this sounds too radical let us push the limit to 9999.

The concept of place value is one of the most difficult concepts invented by humans. The human civilization took more than 3000 years to feel at ease with it. At younger classes, children can be enabled to understand the meaning of 2 or 3-digit numbers, by using simple manipulatives. Later they understand the implications of the place value system in the addition & subtraction algorithms. At higher classes they use the idea of the decimal place value system to understand systems with other bases. It is then they start understanding that it is not a “natural or God given” system but one invented by humans.

When Place Value System is introduced along with 2-digit numbers in Class 1, children will require at least 2 years of work with Place Value System to thoroughly internalise it, because of the difficult nature of the concept.

Later it would take another 2 years to internalise the algorithms for the 4 operations thoroughly so as to attain fluency.

Hence the following number limits are suggested in the Primary School Math curriculum

With the above limits on numbers taught, children would have enough time to master not only the Place Value Concept but also the algorithms for the 4 operations. Since they would be dealing with numbers which are closer to their life experiences, they would not feel ‘lost’ in the classroom. They would also be able to relate word problems to their life experiences.

In the light of the above, the following topics can be pushed to the higher classes when children would be more experienced and mature to understand them.

Roman Numerals – as this is of no relevance to the basic concepts that need to be mastered. Further this system is used only in very limited situations and that too in the Ordinal sense. The Roman system can be used as a contrast to the Place Value System in the higher classes to gain a deeper understanding of number systems in general.
Clock Arithmetic – this is also of no relevance to basic concepts & competencies. Simple clock arithmetic is a useful skill which children can pick in the classroom itself to keep track of period changes.
International and Indian system of naming numbers – these are beyond the understanding of Primary school students. These can be taken up in Middle School when students would encounter large numbers, requiring this understanding.