Conducting Chance Experiments with Spinners – A Mathematics Lesson Plan on Probability

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Summary of Lesson Plan:

In this lesson plan, students use an online digital spinner builder to conduct a chance experiment. They make predications before investigating why their results may be different to their predications. Students also explore how the likeliness of outcomes can be changed as well as different ways of recording and describing probabilities. This experience allows for differentiation in order to help meet the needs of all learning needs within the classroom.

Australian Curriculum Links:

Year 5 Mathematics (Statistics and Probability):

Year 6 Mathematics (Statistics and Probability):

  • Describe probabilities using fractions, decimals and percentages (ACMSP144)
  • Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

Lesson Plan Sequence:

Mathematical Prior Learning:

Students should have previous experience conducting simple chance experiments and identifying and describing the possible outcomes as being likely/unlikely. They have been introduced to concept that the sum of all probabilities of the possible outcomes is equal to 1. They also understand an outcome can be independent of a previous outcome (Bobis et al., 2012).
Students should have knowledge regarding the equivalence of fractions, decimals and percentages and prior experience in
ordering fractions and decimals on a number line from 0 to 1 (BOS NSW, 2012b).

Rationale:

An understanding of chance and probability is crucial for students to become informed citizens who can participate in decision making and be able to predict the outcome of events in a variety of contexts. However before they are introduced to the more complex concept of probability they require a sound understanding of chance. Students also need to explore probability and chance through a variety of contexts and this experience will provide an experimental context. It will also provide a hands experience to explore variation and expectations. The open ended nature of this experience will cater to the diverse learning needs within the classroom as students are able to select how easy/difficult they make their challenges ie. They may only use two variables (colours) to work with in comparison to 6. The choice board format including a range of options also provides choice for the children in what tasks they will complete to demonstrate their knowledge. Conducting the work in pairs will also facilitate collaboration and the sharing of ideas, knowledge and understandings. Lastly, the online digital spinner being used automatically displays a table and will demonstrate the links between chance and data.

Objectives:

For students to:

  • Predict the possible outcomes of the spinner
  • Conduct a chance experiment using the spinner
  • Describe the probability of the spinner outcomes using words, fractions, decimals and percentages
  • Reason why there may be differences between variation and expectation

Lesson:

  • As an introduction and as a whole class students revisit predicting the possible outcomes when throwing a dice using a digital dice on the IWB. The online Spinner Building learning object is introduced on the IWB to demonstrate how it works.
  • In pairs, students then collaborate and negotiate to design and build their own spinner, choosing how many parts they want their spinner divided into and the colours of each part. Together they predict what the outcomes would be if the spinner were to spin 10 times.
  • Students then conduct an experiment and spin the spinner 10 times and record the results.
  • They describe why the results may be the same or different to their predications.
  • Students then complete the Choice Board sheet for their spinner. They are required to explore three tasks in a row (vertically/horizontally/diagonally).
  • Students share their ideas and negotiate and discuss their strategies before recording them in their maths notebooks.

Questioning to extend Working Mathematically focus:

Questions will be asked both directly as students are completing the investigations and indirectly via the choice board (see
Appendix C):

  • Was the spinner more likely to land on one colour? Why? (Reasoning);
  • How did you increase the chances of the spinner landing on ie. Blue? (Reasoning);
  • Why do you think there were differences between your predictions and your results? (Reasoning);
  • Is there another way you could write down the possible outcomes? (Communicating);
  • What influences the sector the spinner lands on? Chance or luck? (Reasoning).

Integration of Technology:

The interactive spinner provides a tool that can be customised to the different learning needs of the students while supporting all students to engage in an experimental investigation. It also enables the accurate construction of a random generator and for large amounts of data to be quickly generated (Watson, 2007). The learning object may also act as a motivator engaging students and enhancing learning (Yanik, 2009).

Modifications for Stage 2:

Students create a customisable spinner. They list all of the possible outcomes and label them with the terms likely, unlikely and equally likely. Students predict what the outcome will be if they spin the spinner 6 times before undertaking the investigation and recording their results. Students discuss the reasons for discrepancies between their predication and results.

  • MA2-19SP Describes and compares chance events in social and experimental contexts

Assessment:

Students demonstrate their understandings through spoken language used during interviews and questioning, and conversations observed between peers. Assessment is also made using analysis of students written work samples in their maths notebooks.

Resources:

 

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