Question

jacob wants to draw a pictogram to show that there are 22 boys and 16 girls in a class.

which of these options would be the best key to use? write a sentence to explain your answer.

option a:
key
blue circle = 1

option b:
key
blue circle = 3

option c:
key
blue circle = 4

Explanation:

🆕 New Concept Discovered: Pictogram Scales and Keys
Representing data using symbols and fractional parts.

Step 1: Analyze the data values

The two numbers we need to represent in the pictogram are:

• Boys: \( 22 \)
• Girls: \( 16 \)

We want to find a key value that allows us to represent both numbers easily using whole symbols or simple fractions of a symbol (like a half-circle).

Step 2: Evaluate Option A (Key = 1)

If \( 1 \) symbol represents \( 1 \) student:

• Boys: \( 22 \) symbols
• Girls: \( 16 \) symbols

While this uses whole numbers, drawing \( 22 \) and \( 16 \) individual symbols is inefficient and takes up too much space for a clear pictogram.

Step 3: Evaluate Option B (Key = 3)

If \( 1 \) symbol represents \( 3 \) students:

• Boys: \( \frac{22}{3} = 7 \frac{1}{3} \) symbols
• Girls: \( \frac{16}{3} = 5 \frac{1}{3} \) symbols

Drawing exactly \( \frac{1}{3} \) of a circle is difficult to do accurately and hard for a reader to interpret.

Step 4: Evaluate Option C (Key = 2) / Alternative Analysis

Let's look at the options provided in the image:

• Option A: Key = 1
• Option B: Key = 3
• Option C: Key = 4

If \( 1 \) symbol represents \( 4 \) students (Option C):

• Boys: \( \frac{22}{4} = 5.5 \) symbols (which is \( 5 \) whole circles and \( 1 \) half-circle)
• Girls: \( \frac{16}{4} = 4 \) symbols (which is exactly \( 4 \) whole circles)

Since a half-circle (\( 0.5 \) of a symbol) is very easy to draw and recognize, Option C is the most practical and efficient key among the choices.

Option C is the best choice because \( 16 \) is perfectly divisible by \( 4 \) (giving exactly \( 4 \) symbols), and \( 22 \) can be easily represented using \( 5.5 \) symbols (where the \( 0.5 \) is represented by a simple half-circle).

Answer:

Option C is the best key to use.