Page 292 - Ganit Kaushal

Activities

Activity 1

‘The objective of this activity is to find the sum of two integers.’

Materials Required: Two sheets of coloured chart paper – one red and one green, a pair of scissors, glue, a
white sheet of paper and a geometry box.
1. Cut out 10 small squares of side 1 cm (approx) from the green chart paper. +1

Write +1 on each square to represent the integer +1, as shown in the adjoining picture.
2. Cut out 10 small squares of side 1 cm (approx) from the red chart paper. –1

Write −1 on each square to represent the integer −1, as shown in the adjoining picture.
Performing the Activity

We know that the sum of +1 and its negative (–1) is 0, +1

i.e., one green square and one red square will neutralise each other, and result in 0, as shown in + = 0
the adjoining figure. –1
Case I: When both integers are positive, e.g., +4 and +2.

Take 4 green squares and 2 more green squares. Paste them on a white sheet +1 +1 +1 +1
+1 +1 +1 +1 of paper as shown in the adjoining figure.
+ On counting, we get a total of 6 green squares, which represent +6. +
+1 +1 +1 +1
Thus, (+4) + (+2) = + 6

Case II: When both integers are negative, e.g., –4 and –3.

Take 4 red squares and 3 more red squares. Paste them on a white sheet of –1 –1 –1 –1
paper as shown in the adjoining figure.
+
On counting, we get a total of 7 red squares, which represent −7.
–1 –1 –1
Thus, (−4) + (−3) = −7
Case III: When one of the integers is positive and the other is negative

(a) Suppose we want to find 5 + (−2).
Take 5 green squares and 2 red squares and paste them on a
white sheet of paper as shown in the adjoining figure. +1 +1 +1 +1 +1
We know that one green square and one red square will +
neutralise each other. On counting the remaining ones after –1 –1
neutralising, we have 3 green squares which represent +3, as
shown in the figure above.

Thus, (+5) + (−2) = +3

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