Question 4

Making a pictograph is hard when numbers do not fit the chosen symbol value.

Step 1 — Understanding the problem

Look at the pictographs given. Each happy face symbol stands for a certain number of students. In the first diagram, one symbol means 5 students. In the second diagram, one symbol means 10 students. We want to show 33 students or 27 students. Let us see how many symbols we need for 33 students if one symbol is 5 students.

$33 \div 5$

$= 6 \text{ with a leftover of } 3$

$\boxed{6 \text{ full symbols and } 3 \text{ students left}}$

This means we need 6 full symbols. We also need to show the remaining 3 students. This is $3$ out of $5$ students for one symbol. So, we need to draw $3/5$ of a symbol. Drawing $3/5$ of a happy face is difficult. Now, let us see for 27 students with one symbol meaning 5 students.

$27 \div 5$

$= 5 \text{ with a leftover of } 2$

$\boxed{5 \text{ full symbols and } 2 \text{ students left}}$

We need 5 full symbols. We also need to show the remaining 2 students. This is $2$ out of $5$ students for one symbol. So, we need to draw $2/5$ of a symbol. Drawing $2/5$ of a happy face is also difficult.

Step 2 — Inconsistent Scaling

Let us try if one symbol means 10 students. For 33 students:

$33 \div 10$

$= 3 \text{ with a leftover of } 3$

$\boxed{3 \text{ full symbols and } 3 \text{ students left}}$

We need 3 full symbols. We also need to show $3/10$ of a symbol. For 27 students:

$27 \div 10$

$= 2 \text{ with a leftover of } 7$

$\boxed{2 \text{ full symbols and } 7 \text{ students left}}$

We need 2 full symbols. We also need to show $7/10$ of a symbol. It is very hard to draw $3/10$ or $7/10$ of a happy face. If we draw parts of symbols, it might not look right. Different parts of symbols would make the scale look uneven. This makes the pictograph look messy.

Step 3 — Visual Confusion

Drawing parts of symbols can confuse people. It is hard to guess what $3/5$ or $2/5$ of a symbol means. It is even harder to guess $3/10$ or $7/10$ of a symbol. The pictograph should be easy to understand quickly. Using broken symbols makes it hard to count. It makes the whole picture unclear.

Answer

(i) Difficulty in Representation: It is hard to draw parts of a symbol like $3/5$ or $7/10$ of a happy face. (ii) Inconsistent Scaling: Using broken symbols makes the pictograph look uneven and messy. (iii) Visual Confusion: It becomes difficult for people to quickly understand and count the number of students.