Tree Diagrams

Learning Goals:

By the end of this lesson, students will:

• be able to list outcomes for a two or three-step chance experiment , with and without replacement, using tree diagrams
• calculate probabilities of two and three-step chance experiments, with or without replacement
• Be able to draw and interpret a tree diagram
• Be able to use computer-assisted programs like Geogebra to evaluate tree diagrams

Syllabus Outcomes:

• List all outcomes for two-step chance experiments, with and without replacement, using tree diagrams or arrays; assign probabilities to outcomes and determine probabilities for events(ACMSP225)
• record outcomes of two-step chance experiments, with and without replacement, using organised lists, tables and tree diagrams
• record outcomes of three-step chance experiments, with and without replacement, using organised lists, tables and tree diagrams

Syllabus Working Mathematically Indicators:

• compare results between an experiment undertaken with replacement and then without replacement (Reasoning)
• explain the effect of knowing the result of the first step on the probability of events in two-step chance experiments, with and without replacement (Communicating, Reasoning)
• use knowledge of complementary-events to assist in calculating probabilities of events in multi-step chance experiments (Problem Solving)

Prior Learning:

• Independent and dependent events
• Calculating probabilities of two to three step chance experiments
• With or without replacement
• P(A and B) = P(A) x P(B)
• P(A and B) = P(A) x P(B after A)

Teaching Strategies:

• Group Work
• Technology use
• Open-ended creation of diagrams

Lesson Sequence

Activity 1 (ICT):

Students will have access to a probability and tree diagram simulator from GeoGebra that lets them visualise how probability is calculated using tree diagrams and consolidate their learning from lesson 6. Students are then to use GeoGebra to recreate their tree diagram they made last lesson into the tools provided by GeoGebra. Some questions teachers can asks students is What are the limitations of making a tree diagram? Does using GeoGebra make drawing tree diagrams easier? If not, why is that?

Activity sourced from: https://www.geogebra.org/m/EEwVfExN

Activity 2:

The majority of the lesson is dedicated to students learning how to use GeoGebra to evaluate different events and calculate probabilities in relation to the certain event. If students have completed activity 1 early, students can attempt extension work that finalises what they have learnt throughout the past few lessons

Worksheet sourced from: https://www.mathsgenie.co.uk/resources/92_tree-diagrams.pdf

Homework:

Using GeoGebra or any other computer-assisted program, students are to design their own tree diagrams using different set of manipulatives. Creating follow questions based on the tree diagrams they have created. Students will showcase their tree diagram to their peers and have them attempt the questions they have created.

Lesson Evaluation Questions

• Were students engaged with the ICT activity?
• Were student able to gain a strong understanding from the ICT?
• Was teaching through ICT more effective for students in comparison to lesson 6?