The purpose of this unit, which provides an integrated social sciences/statistics and probability context, is develop students' understandings of skills and knowledge of interpreting statistical and chance situations. Within this, students investigate flooding as an example of a natural catastrophe.
In this unit, students solve theoretical and model practical probability problems in the context of natural disasters. This encompasses the following mathematical ideas:
This cross-curricular, context-based unit aims to deliver mathematics learning, whilst encouraging differentiated, student-centred learning.
The learning opportunities in this unit can be further differentiated by providing or removing support to students, and by varying the task requirements. Ways to differentiate include:
With student interest engaged, mathematical challenges often seem more approachable than when presented in isolation. Therefore, you might find it appropriate to adapt the contexts presented in this unit. For example, instead of investigating floods, you might investigate earthquakes or forest fires. Consider how the type of natural disaster that you chose to investigate might make links to current events, other curriculum areas (e.g. shared texts, science foci), and your students' lived experiences. Your students might be further engaged by investigating the probability of these events occurring, in relation to specific locations.
The first session is an introductory activity that is aimed to spark the imagination of students, to introduce the need for a particular idea or technique in mathematics that would enable them to explore deeper into that context. It is expected that rich discussion may be had around the context and around the nature of the mathematics involved.
Following the introductory session, each subsequent session in the unit is composed of four sections: Introducing Ideas, Building Ideas, Reinforcing Ideas, and Extending Ideas.
Introducing Ideas: It is recommended that you allow approximately 10 minutes for students to work on these problems, either as a whole class, in groups, pairs, or as individuals. Following this, gather the students together to review the problem and to discuss ideas, issues and mathematical techniques that they noticed during the process. It may be helpful to summarise key outcomes of the discussion at this point.
Building Ideas, Reinforcing Ideas, and Extending Ideas: Exploration of these stages can be differentiated on the basis of individual learning needs, as demonstrated in the previous stage of each session. Some students may have managed the focus activity easily and be ready to attempt the reinforcing ideas or even the extending ideas activity straight away. These could be attempted individually or in groups or pairs, depending on students’ readiness for the activity concerned. The students remaining with the teacher could begin to work through the building ideas activity together, peeling off to complete this activity and/or to attempt the reinforcing ideas activity when they feel they have ‘got it’.
It is expected that once all the students have peeled off into independent or group work of the appropriate selection of building, reinforcing and extending activities, the teacher is freed up to check back with the ‘early peelers’ and to circulate as needed.
Importantly, students should have multiple opportunities to, throughout and at the conclusion of each session, compare, check, and discuss their ideas with peers and the teacher, and to reflect upon their ideas and developed understandings. These reflections can be demonstrated using a variety of means (e.g. written, digital note, survey, sticky notes, diagrams, marked work, videoed demonstration) and can be used to inform your planning for subsequent sessions.
The relevance of this learning can also be enhanced with the inclusion of key vocabulary from your students' home languages. For example, te reo Māori kupu such as tūponotanga
(probability, chance), tūponotanga whakamātau (experimental probability), tūponotanga tātai (theoretical probability), ōrau (percent), pāpono whakawhirinaki (dependent event), and pāpono wehe kē (independent event) could be introduced in this unit and used throughout other mathematical learning.
The aim of this activity, which presents an opportunity to develop the knowledge of statistical and probability processes needed to discuss the likelihood of various chance situations occurring, is to motivate students towards the integrated geographical/mathematics context, and to inform teachers of students' understandings.
Introduce the following context to students: The severity of a natural catastrophe (eg. a one in 10 year or one in 100 year event, etc.) is defined by the number of years that would be expected to elapse between two such events. A 1 in 10 year flood is expected to occur once within any given ten year period, meaning that the probability, or chance, of a 1 in 10 year flood occurring in any given year is 10%. It is unlikely, but still possible, for two such floods to occur in a given year.
Pose the following question to students: What is the probability of two 1 in 10 year floods occurring in the first two years of a ten year period?
As students work, observe their capacity for solving a problem involving combined probabilities. Use these observations to gauge your students' positions on the Interpreting Statistical and Chance Situations learning progression.
Discuss, drawing attention to the following points:
This session focuses on combining probabilities to find the probability of an outcome from a complex chance situation.
Introducing Ideas
What is the probability, or chance, of two 1 in 10 year floods occurring in two consecutive years?
Discuss, drawing attention to the following points:
How could we calculate this event occurring?
How would our answer change if the question was two such floods in three years?
Building Ideas
Reinforcing Ideas
Provide time for students to work through the following tasks:
Extending Ideas
Provide time for students to work through the following tasks:
This session focuses on running a simulation to find an experimental probability.
Introducing Ideas
Building Ideas
Reinforcing Ideas
Extending ideas
This session focuses on understanding and describing the differences and advantages between theoretical and experimental probabilities.
Introducing Ideas
Introduce the following context to students:
Discuss, drawing attention to the following points:
Building Ideas
Reinforcing Ideas
Extending ideas
This session focuses on finding a theoretical probability and expressing it as a percentage.
Introducing Ideas
Introduce the following problem to students: If the probability of a 1 in 10 year flood occurring in any given year is 10%, what is the probability of a 1 in 100 year flood occurring in any given year? Give the solution in % (as the probability is given in %).
Discuss:
What proportion is a year of the total time period specified in a 1 in 10 year event? In a 1 in 100 year event?
How does this proportion relate to a probability expressed as a percentage?
Years between events | Probability of event in a given year | Percentage probability of event in a given year |
200 | ||
100 | 1/100 | 1 % |
50 | 1/50 | |
20 | ||
10 | 1/10 | 10 % |
5 | ||
2 |
Reinforcing Ideas
Provide time for students to work through the following questions:
Extending Ideas
This session focuses on showing understanding of dependence and independence in chance situations.
Introducing Ideas
Introduce the following problem to students: If a farm experiences two 1 in 100 year floods in a single decade, should the owners rush out and buy a lottery ticket?
Discuss, drawing attention to the following points:
What is your reasoning in terms of chance situations?
Are the events of the two floods independent? This is a debatable topic given the factors involved in storm systems and the trends of global warming.
What about the following events: a flood and a lottery? Will the probability of a win on the lottery be affected by the weather? Are they independent events?
Building Ideas
Introduce the following context to students: A local raffle has 100 tickets. The probability of sunshine on the day the raffle is drawn is ½.
Provide time for students to work through the following tasks:
Reinforcing Ideas
Provide time for students to work through the following tasks:
Extending Ideas
Dear parents and whānau,
Recently we have been exploring statistics and chance in the context of flooding. Ask your child to share their learning with you.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/flooding-likely at 8:54pm on the 26th February 2024