Pass it On!

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Purpose

This is a level 3 statistics activity from the Figure It Out theme series.

Achievement Objectives
S3-3: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.
Student Activity

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Specific Learning Outcomes

find all possible outcomes using a tree diagram

Required Resource Materials

FIO, Levels 3-4, Theme: Sport, Pass it On! page 5

Activity

In this activity, students find all the possible outcomes of an event. They will need to be able to do this for other statistics work, when they work out the probability of a chosen event occurring.
For example, to find out the chances of getting two heads when two coins are tossed (H = heads and T = tails):
i. Find out all the possible outcomes: HH, HT, TH, TT.
ii. Work out the chances of getting HH: 1 in 4 or 25%.
The students could use a tree diagram to find all the possible two-pass options available.
For example, for question 1b:

tree diagram.
The tree diagram also makes it easy to see how the number of two-pass combinations decreases with a no-pass-back rule. For question 1c, one option (Alana) is removed from each arm of the diagram, leaving only six possibilities.
After the students have drawn several tree diagrams, they may notice a pattern in the numbers and use this to find a more efficient way to calculate the number of combinations of passes. For example, for question 3b, there are six players. The tree diagram is:

tree diagram.
The number of possible first passes is one less than the number of players (6 – 1 = 5). The number of possible two-pass combinations is the number of first passes (5) times one less than the number of first passes (5 – 1 = 4): 5 x 4 = 20.
Applying this method to question 4c:
There are nine players. The number of possible first passes will be eight (9 – 1 = 8). The number of two-pass combinations is 8 x 7 = 56.

Answers to Activity

1. a. 3 possible passes (to Lance, Courtney, or Manu)
b. 9, as shown by this tree diagram:

tree diagram.
c. If you can’t pass the ball back, there are only six possible second passes:

tree diagram.
2. a. 27 ways:

tree diagram.
b. There would only be 12 ways:

tree diagram.
3. a. 5
b. 20
4. a. 6
b. 42
c. 56

Attachments
PassItOn.pdf312.78 KB
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Level Three