Choose an appropriate representation

Detailed Explanation: Choose an appropriate representation

A good representation makes the important information easy to see. First ask:

1. What is the situation about?
2. What do I need to find or compare?
3. Which representation shows that information most clearly?

Common choices include:

• Table: organizes exact values.
• Number line: shows order, distance, or change.
• Diagram: shows parts, shapes, or relationships.
• Graph: shows comparisons, patterns, or change.
• Equation or expression: shows a rule or calculation.
• Words: explains the situation in context.

Example

Four students recorded how many books they read last month:

The question is: Which student read the most books, and how do the numbers compare?

Step 1: Identify the purpose.

We need to compare different students’ numbers. A representation that makes heights or amounts easy to compare would be helpful.

Step 2: Choose a representation.

A bar graph is appropriate because each student is a category, and the length or height of each bar shows the number of books.

Step 3: Label the graph.

• The horizontal axis lists the students.
• The vertical axis shows the number of books.
• The scale should count by $1$, from $0$ to $5$.

A simple version is:

Books
  5 |    █
  4 |    █     █
  3 |    █     █     █
  2 | █  █     █     █
  1 | █  █     █     █
  0 +--------------------
      Ana Ben  Cam Diya

Step 4: Read the representation.

Ben’s bar reaches $5$, which is higher than the others. Therefore, Ben read the most books.

The bar graph also makes comparisons easy:

• Ben read $3$ more books than Ana: $(5-2=3)$.
• Diya read $1$ more book than Cam: $(4-3=1)$.

A table would show the exact values, but the bar graph is the better choice here because the main purpose is to compare the students. Always check the labels and scale so you do not confuse the graph’s markings with the actual data.