Grade 5c students were ask to pick whether they prefer football or netball. In grade 5c there are 48 students.

Question

22 said they liked both.
12 students like football but not netball.
Half of the remaining students like netball and not football.

Create a Venn diagram showing the result.

1. How many students like netball but not football?
2. How many students like neither netball or football?
From the question above make a question that you can give a tier 3 student, performing above grade average

Answer 1

To solve the problem and create the Venn diagram, let's break it down step by step.

1. Determine the total number of students who like football:

   • Let \( F \) = students who like football.
   • Students who like both football and netball = 22.
   • Students who like football but not netball = 12.

   Therefore, the total number of students who like football is: \[ F = 12 \text{ (Football only)} + 22 \text{ (Both)} = 34. \]

2. Determine the total number of students who like netball:

   • Let \( N \) = students who like netball.
   • Students who like netball and not football = Half of the remaining students.

   First, we need to find the remaining students after accounting for those who like football: \[ \text{Total students} - \text{Students who like football} = 48 - 34 = 14. \] Of these 14 students, half like netball and not football: \[ \text{Students who like netball but not football} = \frac{14}{2} = 7. \]

3. Students who like only netball:

   • Therefore, the number of students who like netball (N) is: \[ N = 7 \text{ (Netball only)} + 22 \text{ (Both)} = 29. \]

4. Finding students who like neither sport:

   • To find the number of students who like neither football nor netball: \[ \text{Students who like neither} = \text{Total students} - (\text{Students who like football} + \text{Students who like netball - Both (not counted twice)}). \] \[ = 48 - (34 + 7) = 48 - 41 = 7. \]

Summary of Results:

1. Students who like netball but not football: 7.
2. Students who like neither netball nor football: 7.

Venn Diagram Representation

• In the left circle (Football):

  • Only Football (12)
  • Both Football and Netball (22)

• In the right circle (Netball):

  • Only Netball (7)
  • Both Football and Netball (22)

• Outside the circles (Neither Sport):

  • Students who like neither (7)

Question for a Tier 3 Student Performing Above Grade Average:

"Consider that a total of 48 students were surveyed about their preferences for football and netball. If 22 students enjoy both sports and there are 12 students who exclusively like football, explain how you would determine how many students prefer only netball and how many do not enjoy either sport. Can you also represent the situation using a Venn diagram? Additionally, if 5 more students join the class and 3 of them state they like only netball, how do the statistics change? Provide a detailed explanation and update the Venn diagram accordingly."