Page 1 of 16
Padmapriya Shirali is part of the Community Math Centre based in Sahyadri
School (Pune) and Rishi Valley (AP), where she has worked since 1983, teaching a
variety of subjects – mathematics, computer applications, geography, economics,
environmental studies and Telugu. For the past few years she has been involved in
teacher outreach work. At present she is working with the SCERT (AP) on curricular
reform and primary level math textbooks. In the 1990s, she worked closely with the
late Shri P K Srinivasan, famed mathematics educator from Chennai. She was part
of the team that created the multigrade elementary learning programme of the
Rishi Valley Rural Centre, known as 'School in a Box'. Padmapriya may be contacted
at padmapriya.shirali@gmail.com
Padmapriya Shirali
A PRACTICAL
TEA
SUBTRACTION
CHING
At Right Angles | Vol. 2, No. 3, November 2013
Page 2 of 16
Most assessments conducted across the country indicate that the first stumbling block for many
children is the subtraction operation, followed by division. On looking more closely we see that
the difficulties often arise in subtraction contexts involving double digit or larger numbers. This
difficulty is largely caused by three factors: (i) improper understanding of place values (ii) lack of
understanding of the rationale behind the formal subtraction procedure, (iii) not seeing the
connection between addition facts and subtraction facts.
This article follows the sequence of place values and addition operations and is closely linked to
the ideas introduced in the preceding articles of this series. I proceed on the assumption that the
reader is acquainted with the earlier ideas and activities talked about.
When do we first introduce children to subtraction? We use the concept of subtraction to
introduce ‘zero’ by removing one object after another: say 10 balls onwards till we reach zero
balls. In my childhood it was taught as a nursery rhyme: “Ten green bottles hanging on the wall,
if 1 green bottle were to accidentally fall, 9 green bottles hanging on the wall, etc”.
Let children show 10 initially with their fingers transition points (60, 59; 50, 49; etc). Teachers can
and say “10 are open”. Close one finger, say “9 use the number chart to make children observe
open”, then close another, say “8 open” and so these points.
on, all the way down to “1 open”; then close all Reciting numbers backwards is of value at various
and say “zero fingers”. Make sure that there is a points in Classes 1, 2, 3, 4; it reinforces the child's
correspondence between what they say and understanding of the way numbers are sequenced
what they show. Some children have a tendency and their place values. It helps the child to handle
to count mechanically and not see the numbers in a flexible manner which is a prerequisite
correspondence. This naturally leads to for doing mental arithmetic.
inaccuracy in counting and improper
One can choose the right challenge from the
development of the number sense.
extensions given for different age groups
The ability to recite numbers backwards from 10 (classes 2 to 4)
to 1 comes a little after mastering forward
Extension 1: Counting backwards from 10 to 0 or
counting. The challenge can be raised to reciting
20 to 0 in steps of 2. numbers from 20 to 1, or 50 to 30, or 83 to 65,
etc. Extension 2: Counting backwards from 100 to 0
in steps of 10. If the child has difficulty in reciting backwards
one can allow the child to use a number line or Extension 3: Counting backwards from 100 to 0
number chart or tens and units material as an in steps of 5.
aid. Providing some visual support is necessary till
Extension 4: Counting backwards from 100 to 0
the child internalises the pattern and observes
in steps of 20. the transition points. Teachers can draw the
number line 1 to 20 on the floor and have Extension 5: Counting backwards from 300 to 0
children walk back from 10 to 1 in steps of 1 and in steps of 25.
2, saying the numbers aloud. Extension 6: Counting backwards from 600 to 0
While conducting this activity a teacher will in steps of 75. (Much more challenging.)
surely notice that the stumbling blocks are the
§
§
§
§
§
§
ACTIVITY
ONE
Counting Backwards
From 10 to 1 in Steps of 1
TEACHING SUBTRACTION
At Right Angles | Vol. 2, No. 3, November 2013 Vol. 2, No. 3, November 2013 | At Right Angles
Page 3 of 16
Most assessments conducted across the country indicate that the first stumbling block for many
children is the subtraction operation, followed by division. On looking more closely we see that
the difficulties often arise in subtraction contexts involving double digit or larger numbers. This
difficulty is largely caused by three factors: (i) improper understanding of place values (ii) lack of
understanding of the rationale behind the formal subtraction procedure, (iii) not seeing the
connection between addition facts and subtraction facts.
This article follows the sequence of place values and addition operations and is closely linked to
the ideas introduced in the preceding articles of this series. I proceed on the assumption that the
reader is acquainted with the earlier ideas and activities talked about.
When do we first introduce children to subtraction? We use the concept of subtraction to
introduce ‘zero’ by removing one object after another: say 10 balls onwards till we reach zero
balls. In my childhood it was taught as a nursery rhyme: “Ten green bottles hanging on the wall,
if 1 green bottle were to accidentally fall, 9 green bottles hanging on the wall, etc”.
Let children show 10 initially with their fingers transition points (60, 59; 50, 49; etc). Teachers can
and say “10 are open”. Close one finger, say “9 use the number chart to make children observe
open”, then close another, say “8 open” and so these points.
on, all the way down to “1 open”; then close all Reciting numbers backwards is of value at various
and say “zero fingers”. Make sure that there is a points in Classes 1, 2, 3, 4; it reinforces the child's
correspondence between what they say and understanding of the way numbers are sequenced
what they show. Some children have a tendency and their place values. It helps the child to handle
to count mechanically and not see the numbers in a flexible manner which is a prerequisite
correspondence. This naturally leads to for doing mental arithmetic.
inaccuracy in counting and improper
One can choose the right challenge from the
development of the number sense.
extensions given for different age groups
The ability to recite numbers backwards from 10 (classes 2 to 4)
to 1 comes a little after mastering forward
Extension 1: Counting backwards from 10 to 0 or
counting. The challenge can be raised to reciting
20 to 0 in steps of 2. numbers from 20 to 1, or 50 to 30, or 83 to 65,
etc. Extension 2: Counting backwards from 100 to 0
in steps of 10. If the child has difficulty in reciting backwards
one can allow the child to use a number line or Extension 3: Counting backwards from 100 to 0
number chart or tens and units material as an in steps of 5.
aid. Providing some visual support is necessary till
Extension 4: Counting backwards from 100 to 0
the child internalises the pattern and observes
in steps of 20. the transition points. Teachers can draw the
number line 1 to 20 on the floor and have Extension 5: Counting backwards from 300 to 0
children walk back from 10 to 1 in steps of 1 and in steps of 25.
2, saying the numbers aloud. Extension 6: Counting backwards from 600 to 0
While conducting this activity a teacher will in steps of 75. (Much more challenging.)
surely notice that the stumbling blocks are the
§
§
§
§
§
§
ACTIVITY
ONE
Counting Backwards
From 10 to 1 in Steps of 1
TEACHING SUBTRACTION
At Right Angles | Vol. 2, No. 3, November 2013 Vol. 2, No. 3, November 2013 | At Right Angles