Lesson Plan Sample Space

Lesson Planning Sheet Title: Sample Space Diagrams Learning Objectives: By the end of the lesson: All students should be able able to list in a systematic and logical manner all the permutations of two events. Most students should be able to list in a systematic systematic and logical manner all the permutations of two events in a Sample Space Diagram. Some students should be able to use a Sample Space Diagram to calculate probabilities of two or more combined events. Key words: words: Logical, Systematic, Permutations, Sample Space Diagram, Probability, Event, Exhaustive  

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Learning Activities

Resources:

Starter/Introduction The problem on the first slide is intended to encourage the students to reach a solution using a logical and systematic approach. approach. To this end the problem should be posed as the students enter the class room so they are able to begin making sense of it with their peers through informal discussions. Once settled, highlight the need for a logical and and systematic approach. Students should be encouraged to doodle and refine their thoughts either on a miniwhiteboard or in their books. books. Once completed have students students come to the board and model their approach. Emphasise the need for a clear logical method of working through t he problem.

Mini-Whiteboards

Development The questions on the second slide are intended to extend the idea using a a logical and systematic approach. Explain how we can exhaust exhaust all the different colour of shorts for a given shirt colour. To be systematic systematic we could could do this alphabetically. alphabetically. Once the shorts have have been exhausted the same method could be used for shirts  –  this is systematic. systematic. Once the list has been created and all the combinations exhausted challenge the students are to consider a pair that is not in the list. Working through the probability questions questions based on this list will then add value value for presenting the combinations in this way. Discuss with the students when a list may not be the most s uitable way of recording the different permutations. Use the third slide to address address this point since the number of combinations is best represented using using a two way table. It may be worthwhile having the students decide whether they would prefer to use a list or a sample space diagram in this instance. However, the problem on the final final slide does make make this point clear. Plenary The plenary is intended to highlight the need for Sample Space Diagrams through providing a larger combination of events. Students could be challenged to create their own Sample Sample Space Diagram by hiding the one displayed. displayed. Allow the students to use mini-whiteboards for  their Sample Space Diagram as this will help them calculate the probabilities by crossing out not related events. Have the students present present their solutions to the teacher one probability probability question at a time. Differentiation More able: Students could consider three or more combinations of events using a list. Challenge the students to draw a Sample Space Diagram for three combinations. Less Able Students may need to practise using lists for one lesson then move on to Sample Space Diagrams in the next. Keeping the number of possible permutations low for two events will enable simpler lists to be draw.  

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