Name: Martina SellarsDay 1:

Curriculum Area: Mathematics Specific Topic: Data and Chance/Measurement Year Level: 9

Essential Learnings ( knowledge, understandings, and ways of working) to be addressed:

Knowledge and Understandings Data can be gathered from samples and surveys, experiments and simulations, published data and databases, and used

to estimate probabilities of events and to respond to claims and questions Sample spaces can be specified for single events and straightforward compound events using tables and tree diagrams,

and probabilities can be determined using different methods, including counting, measuring and symmetry

Ways of Working Analyse situations to identify the key mathematical features and conditions, strategies and procedures that may be

relevant in the generation of a solution Evaluate their own thinking and reasoning, considering their application of mathematical ideas, the efficiency of their

procedures and opportunities to transfer results into new learning Reflect and identify the contribution of mathematics to their own and other people’s lives

General Teaching Aim or Goal: To enable students to apply their basic knowledge of probability in a range of real world situations To reinforce that probability can be used to ‘strategise’, but the outcome cannot be accurately predicted To allow students to develop and test a hypothesis To provide students with the necessary skills to complete the web quest activity

Students’ Prerequisite knowledge / understanding / concepts / skills: Basic concept of probability Basic recording skills Analysis of results to come to a conclusion

Specific Learning Outcomes for this

Lesson

Time Req.

Teaching / Learning Strategies

Organisation Resources Type of formative or summative assessment

Orientating Phase / IntroductionStudents should be able to:

Accurately record the results of the experiment.

Work as a group to discuss findings.

Works as a group to develop a hypothesis.

25 mins

Before the lesson: have the instructions for the dice rolling activity up on the board for students to refer to when completing the activity.

Discuss the concept of probability and how it relates to events in the student’s lives – eg. When flipping a coin to do the dishes at home, what are the odds of winning in the student’s favour?

With the class divided into 4 groups, explain the task of rolling the dice and ask students to refer to the board when ensuring they have completed the task properly. (1. Assign one team member to be the ‘results recorder’, one member to be the ‘teacher liaison’ and one member to be the ‘presenter’. 2. Roll a dice 20 times, with the ‘results recorder’ keeping record of the results. 3. As a team, discuss your findings (the order, how often a number appears, what the overall result was). 4. Prepare to communicate your findings to the class.)

Divide the class into 4 even groups, with the desks/seats clumped together appropriately.

Record instructions for dice activity on the board, with a step by step list for the students to follow.

Dice (at least 4 – one for each group).

Paper and pens to records and analyse findings.

Board utensils should the team presenters need them.

Formative: Informal

questioning. Observation of

group participation.

Observation of presentation.

Enhancing Phase / BodyStudents should be able to:

Relate the theory of independent events, and associate this back to their dice activity.

Accurately record the results of the experiment.

Work as a group to discuss findings.

Works as a group to develop a hypothesis.

15 mins

Have a group discussion, facilitated by the teacher, comparing the findings of the 4 groups – looking at differences and similarities in the data and theories.

Explain and demonstrate how the rolling of the die is an independent event – it does not affect the next result. Also explain the difference between a simple and a compound event. Explain the trends in the results, and how the probability can be calculated given this knowledge (emphasise that it is only the probability – not the certainty).

Using the same teams, ask the students to now analyse a bag of 5 marbles (2 red and 3 green marbles). Ask them to randomly draw out the marbles one by one (keeping the marble removed once drawn) and records the results. Ask the students to repeat the experiment, again recording the results, although using the tree diagram this time.

The students will now perform the same analysis activity that they

Use the same table groupings as before.

Add notes to the dice activity to ensure the students understand to use the same instructions for the marbles activity.

Bag of 2 red marbles and 3 green marbles (at least 4 – one for each group).

Paper and pens to records and analyse findings.

Board utensils should the team presenters need them.

Formative: Informal

questioning. Observation of

group participation.

Observation of presentation.

performed on the dice activity, and again present to the class.

Synthesising Phase / Conclusion Students should be able to:

Relate the theory of dependent events, and associate this back to their marble activity.

Communicate the difference between dependent and independent probability events, and how that affects the outcome (guesswork).

10 mins

Have a group discussion, facilitated by the teacher, comparing the findings of the 4 groups – looking at differences and similarities in the data and theories.

Explain and demonstrate how marble activity is a dependent event – the outcome is conditional upon the previous events. Examine the trends in the results, and ask students whether they thought it was possible to ‘guess’ the order they would come out.

Ensure all students understood the tree diagram.

Describe the relationship between strategies and probability and the outcome.

Ask students to consider events of probability in their day to day lives, and how they may use this acquired knowledge to their advantage.

Ask students to face their chairs forward, while maintaining the group formation.

Formative: Observation of

discussion participation.

Informal questioning.

Assessment Strategies (link to Learning Outcomes): Only formative assessment at this stage Observe students’ responses to informal questionings Observe students’ participation in the group activities

What’s next? Where to from this lesson? This lesson was intended to provide/reinforce students

with the necessary skills to complete a web quest that has been designed around this topic

The next two lessons are for the completion of the web quest, which will provide students with the opportunity to apply their learning to an authentic task

Name: Martina SellarsDay 2:

Curriculum Area: Mathematics Specific Topic: Data and Chance/Measurement WebQuest – Guess Who Year Level: 9

Essential Learnings ( knowledge, understandings, and ways of working) to be addressed:

Knowledge and understandings: Data can be gathered from samples and surveys, experiments and simulations, published data and databases, and used

to estimate probabilities of events and to respond to claims and questions Sample spaces can be specified for single events and straightforward compound events using tables and tree diagrams,

and probabilities can be determined using different methods, including counting, measuring and symmetry

Ways of Working: Analyse situations to identify the key mathematical features and conditions, strategies and procedures that may be

relevant in the generation of a solution Plan and conduct activities and investigations, using valid strategies and procedures to solve problems Communicate thinking, and justify and evaluate reasoning and generalisations, using mathematical language,

representations and technologies

General Teaching Aim or Goal: To provide the students with the opportunity to successfully navigate a Web Quest To demonstrate how mathematics can be applied to activities in the ‘real world’ To provide the students with the opportunity to experiment and problem solve with their peers To provide students with the opportunity to justify their reasoning

Students’ Prerequisite knowledge / understanding / concepts / skills: Basic knowledge of computer skills (mouse, keyboard, links and printing) Basic concept of probability Basic recording skills Analysis of results to come to a conclusion

Specific Learning Outcomes for this

Lesson

Time

Req.

Teaching / Learning Strategies

Organisation Resources Type of formative or summative assessment

Orientating Phase / Introduction Recall their

prior knowledge regarding probability.

Successfully navigate the Web Quest.

10 mins

Before the lesson: ensure that each computer is working and the games tables are set up.

Reminding the students specifically of the activities already undertaken in the last lesson, facilitate a conversation with the students about the types of probability.

Ask students about any encounters with probability in the ‘real world’.

Introduce the students to the concept of the Web Quest.

Explain that the class will be working on this Web Quest for the next two lessons, and the set up of the classroom.

Equitably divide the previous groups of 4 into pairs, and take them to the computers.

Students will then browse the Introduction, Task, Process, Evaluation and Conclusion sections of the Web Quest, with questions directed to teacher as they arise. Answers that will need to

Students share a computer with one other person.

Using the same 4 groups as the last lesson, the groups will all be sitting beside each other at the computers (in a row).

Each group will also have a ‘games’ area (where the tables are arranged in a group) with each group having a Guess Who? Game.

URL of Web Quest written clearly

For a class of 20, 10 computers are required with internet access.

4 games of ‘Guess Who?’.

Paper and pencils for any additional notes.

Formative: Informal

questioning. Observation of

participation within each pair of students.

be commonly known will be written on the board for the class’ reference.

visibly on the board.

Enhancing Phase / BodyStudents should be able to:

Design and conduct experiments to investigate and model the probabilities.

Keep an accurate record of the results.

30 mins

Facilitate group decision on roles within the groups as necessary to ensure roles are equitable and use group member’s strengths.

Monitor the group work and analysis undertaken to ensure activity instructions are being adhered to.

Students will move between the computer area and games area as necessary, therefore ensure clear pathways.

As above.

Formative: Informal

questioning. Observation of

group participation.

Note of role within the group, and the subsequent contributions.

Synthesising Phase / Conclusion Students should be able to:

Justify statements and decisions.

Communicate their conclusions clearly and concisely.

10 mins

Ask students to begin their analysis work from the Web Quest, and facilitate any teams that are left behind.

Ensure each group has a shared understanding of their outcomes, but each group member to write their own conclusion.

Keep a count-down on the board of time remaining for the task.

Ensure all group working and individual conclusions are grouped together and handed in before the end of class.

Communicate the place that papers will need to be left.

As above.

In-tray for completed papers.

Formative: Informal

questioning. Observation of

group participation.

Summative: Completion of

individual conclusions and group working to be handed in to teacher for review.

Assessment Strategies (link to Learning Outcomes): Students are formatively assessed on their participation

with the group and their contribution to the group as directed by their role.

Students are able to be summatively assessed on their ability to draw logical conclusions from analysis, and to clearly and concisely communicate these conclusions.

What’s next? Where to from this lesson? The next lesson will focus on the other type of

probability taught using similar themes and activities – independent probability. It will also include a component on measurement.

The lesson after that will give the students a chance to present and demonstrate their findings to the class and thereby share their accumulated learnings.

Name: Martina SellarsDay 3:

Curriculum Area: Mathematics Specific Topic: Data and Chance/Measurement WebQuest – RouletteYear Level: 9

Essential Learnings ( knowledge, understandings, and ways of working) to be addressed:

Knowledge and understandings: Data can be gathered from samples and surveys, experiments and simulations, published data and databases, and used

to estimate probabilities of events and to respond to claims and questions Sample spaces can be specified for single events and straightforward compound events using tables and tree diagrams,

and probabilities can be determined using different methods, including counting, measuring and symmetry Relationships exist between units of equivalent measure and are used to make conversions of Units Lengths and angles that cannot be measured directly can be investigated using scale, similarity or trigonometry

Ways of Working: Analyse situations to identify the key mathematical features and conditions, strategies and procedures that may be

relevant in the generation of a solution Plan and conduct activities and investigations, using valid strategies and procedures to solve problems Select and use mental and written computations, estimations, representations and technologies to generate solutions

and to check for reasonableness of the solution Communicate thinking, and justify and evaluate reasoning and generalisations, using mathematical language,

representations and technologies

General Teaching Aim or Goal: To provide the students with the opportunity to successfully navigate a Web Quest To demonstrate how mathematics can be applied to activities in the ‘real world’ To provide the students with the opportunity to experiment and problem solve with their peers To provide students with the opportunity to justify their reasoning

Students’ Prerequisite knowledge / understanding / concepts / skills: Basic knowledge of computer skills (mouse, keyboard, links and printing) Basic concept of probability Basic recording skills Analysis of results to come to a conclusion

Specific Learning Outcomes for this

Lesson

Time

Req.

Teaching / Learning Strategies

Organisation Resources Type of formative or summative assessment

Orientating Phase / IntroductionStudents should be able to:

Design and conduct experiments to investigate and model the probabilities.

Keep an accurate record of the results.

Model and determine probabilities for single events to justify statements and decisions.

Communicate their conclusions clearly and concisely.

30 mins

Roulette Facilitate group

decision on new roles within the group to ensure fair workloads.

Monitor the group work and analysis undertaken to ensure activity instructions are being adhered to.

Ensure teams are running on schedule to finish the task on time, with a count-down written on the board.

Ensure each group has a shared understanding of their outcomes, but each group member to write their own conclusion.

Students will move between the computer area and games area as necessary, therefore ensure clear pathways.

For a class of 20, 10 computers are required with internet access.

4 games of ‘Roulette’.

Printer for worksheets from Web Quest.

Paper and pencils for any additional notes.

Formative: Informal

questioning. Observation of

group participation.

Note of role within the group, and the subsequent contributions.

Enhancing Phase / BodyStudents should be able to:

Use internet resources to research specific information.

Students

15 mins

One More Thing... Ensure teams are

running on schedule to finish the task on time, with a count-down written on the board.

Move around the room and be easily visible.

Games area will no longer be

As above. A 1 metre ruler

in case scale needs to be described.

Formative: Informal

questioning Observation of

participation within each pair of students.

interpret, analyse and solve the measurement problem and justify their outcome.

needed, therefore it can be tidied up if time allows.

Synthesising Phase / Conclusion Students should be able to:

Understand the differences between dependent and independent factors in probability.

Review their performance as a group and as an individual.

5 mins

Facilitate conversation with students on what they thought of their work today.

Inform students of the activities for the next day – presentation to the class with preparation time.

Ensure all group working, individual conclusions and worksheets are grouped together and handed in before the end of class.

Communicate the place that papers will need to be left.

In-tray for completed papers.

Formative: Informal

questioning.Summative:

Completion of group working, conclusion for Roulette and measurements worksheet to be handed in to teacher for review.

Assessment Strategies (link to Learning Outcomes): Students are formatively assessed on their participation

with the group, their contribution to the group as directed by their role and their participation as a pair.

Students are able to be summatively assessed on their ability to draw logical conclusions from analysis, and to clearly and concisely communicate these conclusions in regards to Roulette. They will also be summatively assessed on their ability to interpret information, scale

What’s next? Where to from this lesson? The next lesson will give the students a chance to

present and demonstrate their findings to the class and thereby share their accumulated learnings.

They will also get a chance to analyse their performance as a group and as an individual.

There will also be an emphasis on relating everything learned, back to the ‘real world’.

measurements and present their findings.

Name: Martina SellarsDay 4:

Curriculum Area: Mathematics Specific Topic: Data and Chance/Measurement WebQuest – Presentation Year Level: 9

Essential Learnings ( knowledge, understandings, and ways of working) to be addressed:

Knowledge and Understandings Data can be gathered from samples and surveys, experiments and simulations, published data and databases, and used

to estimate probabilities of events and to respond to claims and questions Sample spaces can be specified for single events and straightforward compound events using tables and tree diagrams,

and probabilities can be determined using different methods, including counting, measuring and symmetry Relationships exist between units of equivalent measure and are used to make conversions of Units Lengths and angles that cannot be measured directly can be investigated using scale, similarity or trigonometry

Ways of Working Evaluate their own thinking and reasoning, considering their application of mathematical ideas, the efficiency of their

procedures and opportunities to transfer results into new learning Communicate thinking, and justify and evaluate reasoning and generalisations, using mathematical language,

representations and technologies Reflect and identify the contribution of mathematics to their own and other people’s lives Reflect on learning, apply new understandings and justify future applications.

General Teaching Aim or Goal: Students have the opportunity to share their learnings and evaluation with their peers Students have the opportunity to reassess mathematics in their everyday life

Students’ Prerequisite knowledge / understanding / concepts / skills: Determination of key information by relevance to audience Basic presentation skills

Specific Learning Outcomes for this Lesson

Time Req.

Teaching / Learning Strategies Organisation Resources Type of formative or summative assessment

Orientating Phase / IntroductionStudents should be able to:

Reflect on their achievements and learnings, as well as recognise possible improvements.

Work as a group to develop a logical and clear presentation.

10 mins

Before the lesson: write the presentation points onto the board for the teams to work from (overview of Guess Who? Strategies, conclusion from group, overview of Roulette strategies, conclusion from group, review of how the team worked together, would they change any of the roles, and how the team felt about their progress).

Still working as the initial 4 groups, the teams will develop a presentation (to be presented in whatever form the team feels appropriate) that cover the points on the board as a minimum.

Keep the students in their group desk formation.

Pen and paper for notes.

Butchers paper and pens for presentation should they need it.

Each group should have their games (Guess Who? And Roulette) nearby to stimulate their memories, but they must not interfere with their work.

Formative: Informal

questions. Observation of

group participation.

Enhancing Phase / BodyStudents should be able to:

Present their learnings clearly to the class.

25 mins

Drawing the teams out of a hat to ensure the order is fair, each group will present their presentation.

A short question time will follow each presentation.

All students chairs to face the front to encourage listening.

As above. Formative: Observation of

presenter and their assistant/s.

Questioning of group during question time.

Synthesising Phase / Conclusion Students should be able to:

Analyse their learnings and learning methods.

Reflect on how this learning style assisted them.

Relate probability with their everyday life.

10 mins

Teacher to facilitate conversation around the entire activity including; how the students responded to the learning, how the groups worked together, how the different teams developed differing strategies and conclusions, how the presentations were conducted, how probability can relate back to the ‘real world’.

Allow time to tables to be put back into conventional positions.

Inform the class that the next lesson will be on another topic.

As above.

As above. Formative: Observation of

participation in discussion.

Informal questioning.

Assessment Strategies (link to Learning Outcomes): Students are summatively assessed on their ability to

work as a group and identify and justify their key learnings. They will also be assessed on their ability to identify achievements, and strengths and weaknesses with themselves and their groups.

What’s next? Where to from this lesson?

Written Rationale - Justification of Decisions

This Web Quest was designed from a Constructivist approach. The proactive nature of these activities is very much in line with the Constructivism way of thinking, and allows the students to be more actively involved with their learning. It has also been found that students are more engaged and eager to learn when the work is ‘hands-on’. The planning of these activities was also carefully crafted to link the new activities with prior learnings. Therefore the students were not starting from a blank slate, but were able to build upon their previous knowledge, understandings and skills (“A Constructivist Learning Model”, n.d.).

This Web Quest and it’s supporting lessons covered all but one level of Bloom’s Taxonomy, the synthesis stage. The knowledge was covered in the first lesson, with the students being exposed to the probability work being addressed. The comprehension was partly tested in the first lesson, but was definitely covered in the second and third (example, the pre-questions on the type of probability of each game). Most of the Web Quest was devoted to the application and analysis stages, given that they spent the whole time putting probability into practice, and then analysing the results. Finally, a good deal of the lesson was devoted to the evaluation stage, with students asked to specifically target this in their presentation and the following facilitated discussion (“Bloom’s Taxonomy of Learning Domains”, 1999).

This series of lessons incorporated a great deal of group work. This was consciously done to promote the development of social skills, team work¸ and to cater for all students. The aim was to facilitate a more supportive learning environment that didn’t leave anyone behind. The groups would work together to develop and determine their outcomes, however the individual was still accountable for their learning, as they needed to justify their decision individually. The roles incorporated in these activities also allowed individuals to contribute to the whole in a meaningful way, and they could choose roles that suited their strengths.

You will also notice that most of the lesson plans involved some type of facilitated discussion. This forum would give students the opportunity to share their learnings and misgivings. Although most classroom discussions are often dominated by the teacher, it is envisaged that the students would be more energetic after a vigorous activity, and therefore would more likely to contribute to the conversation. The teacher’s role would be

to simply keep the exchange going, while ensuring that the student’s dialogue remained on task.

The assessment for this series of lessons was mostly of a formative nature given the need to observe the students interacting with their peers. Group work is a more supportive environment, but also makes it markedly harder to assess individuals. Therefore the summative aspect of this Web Quest involved the individual justifying the group’s decision and mathematical reasoning. Therefore the student is not assessed on how they achieved the outcome, but rather that they understand the outcome and mathematical logic behind the outcome.

References

The University of Sydney. (n.d.). A Constructivist Learning Model. Retrieved May 13, 2011, from http://alex.edfac.usyd.edu.au/methods/science/Constructivist_Teaching.html

Big Dog and Little Dog’s Performance Juxtaposition. (1999). Bloom’s Taxonomy of Learning Domains. Retrieved May 13, 2011, from http://www.nwlink.com/~donclark/hrd/bloom.html