Question 3

Sharing a total number of objects means dividing them into parts for each person.

Step 1 — Understanding the Activity

We need to work in pairs. We will collect 12 items. Then, we will share these items between us. We must find different ways to do this.

Step 2 — Identifying the Total Objects

The total number of objects we have to share is given. Let $N$ be the total number of objects. $N = 12$

$\boxed{N = 12 \text{ objects}}$ We will share these 12 objects between two people.

Step 3 — Exploring Different Ways to Share

Let us say Person 1 gets $x$ objects. Then Person 2 will get the remaining objects. The number of objects Person 2 gets is $12 - x$. We can list all possible whole number values for $x$. The number of objects cannot be negative. So, $x$ must be from 0 to 12. We can find 13 different ways to share the objects.

Step 4 — Observing the Diagrams

The diagrams show some of these sharing methods. The first diagram shows 4 objects and 8 objects. $4 + 8 = 12$ The second diagram shows 6 objects and 6 objects. $6 + 6 = 12$ The third diagram shows 2 objects and 10 objects. $2 + 10 = 12$ These are three examples of sharing 12 objects.

Answer

(i) Person 1 gets 0 objects, Person 2 gets 12 objects. (ii) Person 1 gets 1 object, Person 2 gets 11 objects. (iii) Person 1 gets 2 objects, Person 2 gets 10 objects. (iv) Person 1 gets 3 objects, Person 2 gets 9 objects. (v) Person 1 gets 4 objects, Person 2 gets 8 objects. (vi) Person 1 gets 5 objects, Person 2 gets 7 objects. (vii) Person 1 gets 6 objects, Person 2 gets 6 objects. (viii) Person 1 gets 7 objects, Person 2 gets 5 objects. (ix) Person 1 gets 8 objects, Person 2 gets 4 objects. (x) Person 1 gets 9 objects, Person 2 gets 3 objects. (xi) Person 1 gets 10 objects, Person 2 gets 2 objects. (xii) Person 1 gets 11 objects, Person 2 gets 1 object. (xiii) Person 1 gets 12 objects, Person 2 gets 0 objects.