Lesson Plan 1 - Save a Baby Kangaroo

TL1: How is the teacher's preparation different for this case compared to the preparation for traditional classes?

This vignette is written by a member of the writing team who had previously experienced teaching the case and subsequently observed a colleague teaching the case. It highlights the difference in mental preparation and focus required to teach problem-based lessons rather than traditional Maths lessons.

Chris is a young teacher in his second year of teaching and with minimal Maths teaching training. When I mentioned we had a series of lessons he may like to try, he was very keen to give something different a go. We spent a fair bit of time prior to Chris commencing the lessons discussing activities, expected pupil questions etc. Despite this preparation, in discussion following each of the first two lessons Chris expressed that he felt he had not got the most out of the lesson. Comments included, “I don’t think I had thought about the depth of some of the ideas in that lesson enough”, “I probably could have got the pupils to do some more thinking”, “There were probably some better questions I could have asked”, and “I felt under prepared”.

We had a long discussion about what preparation may make this type of lesson richer. We discussed the idea that standard preparation for a traditional Maths class was focussed on ensuring the teacher could clearly explain a new Mathematical process for that day. Chris said his focus in preparing for the first two lessons of this Case was similar, concentrating on the Maths skills required. Going into these lessons with traditional teacher preparation ensured pupils were able to perform accurate percentage calculations and draw carefully and correctly labelled graphs during the first two lessons. However, it was felt that through this traditional preparation and focus, pupils did not get as much out of the lessons as they might. It was felt the pupils –

considered the activities complete when they had the right answer
considered each activity an individual unit
didn’t see the bigger picture of how we were using the result of each activity to help us with the overall aim of saving the joey, and
didn’t see the links from one activity to another and how they were sequentially working towards the overall aim of the Case.

Chris said next time he taught a problem based learning lesson, while ensuring pupils could capably complete all the required maths, he would prepare by carefully considering some closed and open ended questions that could follow the traditional maths part of each activity. By being prepared to get pupils to consider their results from the ratio worksheet, the pupils may have developed a better of just how small a joey is. By being prepared to get pupils to carefully analyse their graphs, Chris felt he could encourage pupils to identify key stages in their growth which could later affect the joey’s feeding patterns. He also felt that preparing for the lessons by carefully considering the order of the activities and the links between them, he could continually encourage pupils to understand where the Case was heading and encourage pupils to be part of the design process of the activities that they need to do to achieve the overall aim of saving the joey.

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TL2: What is different about this approach to teaching maths compared to the more traditional approach to teaching maths?

The quotes used in this vignette are taken from two teachers who trialled this case with Year 9 classes. L is in her second year of teaching. M has been teaching for a number of years and brings industry experience to his teaching career. P is the interviewer, one of the teacher writers who also trialed the case with her class.

L was amazed at how much the pupils were discussing their maths, and the depth to which they were doing this.

Some differences in using this approach to learning:

Strong focus in discussion
No set exercises for the pupils to do
There is not a definitive answer – this is an open-ended Case
Generate the need to know the skill in order to find a solution to the problem
Show the pupils that we are assessing their contributions to their own learning, which indicates what we value in the learning process. Assessment Rubric
M – “Having something different to start to the year was great, it was a neat way to start the year”
L – “This was a good way to get to know the pupils strengths and weaknesses in terms of maths and cooperative group skills. I was looking at the whole group dynamic -looking at who was leading and who was struggling”
Pupil 1 - “It was an interesting activity to do and I learnt a lot of new things”
Pupil 2 - “I enjoyed it – it was interesting and straightforward”

Pupil 3 - “This is not maths – as it does not involve the textbook”

In one of the lessons, M noticed that some of his pupils were saying, “We are getting a bit bored with this, this is not maths”. He took an ‘in-the-moment decision’ and sat down with the pupils, commenting, “Let’s stop here and reflect upon what we are doing” and asking, “Where do you think the maths has come out of this lesson?” M observed,” Most kids in most subjects want to get away from using textbooks, but if they are not using textbooks in maths, then they feel that they are not learning maths”. M says that he wanted to point out to his pupils that they were actually still doing maths, even though they were not using the textbook. “When the pupils are not doing text work, it is easy for them to forget that they are doing maths. It is our job as teachers to try to refocus the pupils”.

P - “In this sort of open-ended, non textbook lesson, kids are going to throw ideas and questions at you. How do you deal with that – being out of your depth in terms of this different teaching method?”

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TL5: Keeping the overall Case firmly in mind

The tasks that pupils do in most maths lessons are extremely short term – completing exercises that take only minutes. It is foreign, therefore, to spend several lessons, on several tasks, that are cohered by an overall goal such as saving a baby kangaroo. During the first two lessons of this case, it is important for teachers to help pupils see how and what they are doing relates to an overall goal that is fixed for five lessons, not five minutes. The following incident occurred half way through the first lesson in one of the trials. It describes a pupil who has lost track of how the task at hand connects to the overall goal.

‘This is boring. I’m not doing it’. Jake’s head goes down on the desk.

I kneel down next to him. ‘Can you and me have a quick chat outside?’.

Jake nods and leaves the room.

Leaving the class with clear instructions to sensibly carry on with the task, I follow him out of the room.

‘It’s taking ages and I don’t even understand it. Why can’t we do normal maths?’

As calmly as I can and with a sympathetic face I start to explain to Jake that he has been chosen to do this because of his enthusiasm towards maths. In the end he’ll actually be able to save the life of a baby joey. Just think how exciting that will be. This part of the task is only one tiny part. I coaxed him into continuing with the task and challenged him to find the biggest percentage for me. ‘The biggest percentage means that that animal grows the least between when it is born an adulthood. Try and predict what you think it might be and work out that percentage. You might even find it first!’

Jake appeared much happier and went back into the room with a real focus.

On re-entry to the room the observations begin; ‘Miss a horse grows the least’ and then Jake comments ‘Miss Kangaroos grow the most. Their percentages are really small’.

I smile. ‘I’m really glad you noticed that Jake because that’s why what we are going to do today is so important. If we give the wrong type of food or too much of it, the joey will not survive because of its size. If our maths is wrong, the consequences are very serious’.

The pupils now look excited and are ready for the next stage of the project. I have learnt a valuable lesson: pupils can sometimes lose sight of what they are doing and get bogged down with maths processes. I found that reminding them of their final aim and that the project is like a big jigsaw puzzle with lots of separate parts helps them to get back on track. Each step fits into a bigger and more important picture. Next time I will make this clearer from the outset.

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TL3: How do I redirect pupils who are not effectively engaging with the scenario?

The following vignette is written by one of the teachers who helped develop the case and who trialled the first version of the case with her Year 7 class. The vignette illustrates how she tried to keep the discussion in Lesson 1 focused on saving the joey. There was an important lesson that emerged from this experience, which is reflected in the current materials

Several suggestions are given at the end of the vignette for different pupil reactions to TL3

Prior to the first lesson, I had set up the room with posters of kangaroos and wallabies and I had the scenario ready to show on the overhead projector. The pupils did not notice the posters until I pointed them out. I told the pupils that we were going to do something a little different for the next five lessons and asked them to be prepared to go out of their comfort zone. I did not give them any clues – but asked them to try to ‘go with the flow of the lesson’ and discover as we went along.

I showed them the scenario and then asked the class for initial comments..…then waited. I had hoped that the pupils would come up with a key question – what would need to be done to save the kangaroo? Instead, they observed that if we did save the joey that we would not be allowed to keep it anyway, so wouldn’t you just take it to the nearest vet or police station? Good point, I said to the class.

I had to think quickly on my feet here and came up with the idea that they needed to change from school pupils into wildlife officers (ie role play) – to a give a valid reason for the Task. I sought and gained general agreement from the class that they would role-play for the next few lessons.

The next problem, which I encountered, was pupils who did not want to be putting their hands in to a kangaroo pouch to check for a joey. We discussed this as a class and eventually decided that if we really wanted to help the joey, we would need to find it first. We then came up with what you would do/need to get the joey out of the pouch– eg gloves/another person/torch/old rag to keep it warm.

I still did not feel that I had them interested; rather, I felt they were really going along with the discussion as I had asked them to do so. Some boys were starting to offer silly suggestions and I could see the class going off-track again.

In an effort to engage each pupil fairly quickly, and again thinking on my feet, we then focused in on the 12 cm and 60 grams in the scenario – I asked the pupils to estimate the length 12 cm with their hands and to have a friend measure it with a ruler. This hands-on activity was very successful (and very obviously mathematical, in the pupil’s eyes). Many pupils were surprised at how incorrect their estimation was. I then asked them, for homework, to define the weight of 60 grams in everyday terms. Their answers the next lesson included an egg, a small Mars bar and 60 ml water.

The lessons which the developers learnt from this initial trialing of the case, were incorporated into subsequent developments and writing.

With hindsight, it became obvious that one of the reasons for the pupil’s lack of focus on the Case, and their puzzlement as to why we were talking about kangaroos in a maths classroom, was that they did not realize that the ‘maths was coming’. The pupils needed explicitly to know that they were going to use some maths skills in solving this problem and that a major component of this case, was to identify the maths skills as they emerged. Subsequent trials were adjusted so that teachers did highlight to the pupils that there was a great deal of maths that was involved.

The following comment on this vignette is written by one of the academic observers.

The teacher wanted to use the scenario and posters to initiate a somewhat free flowing discussion with minimum direct teacher control. The teacher had a clear vision, about where she wanted the discussion to go, but the pupils were very much ‘in the dark’ as to the direction of this and subsequent lessons, and so found it difficult to remain focused and engaged in the discussion.

These two intentions were likely to clash and indeed, resulted in the pupils going “off track”. The scenario provided a context and set of issues that were intended, in a short period, to stimulate some general real-life discussion with possibilities of how one could use maths to help solve the problem. This was a maths class, in which these types of discussions rarely occurred. The teacher had less ability to be able to use unexpected pupils comments, than if this discussion occurred in a subject where kangaroos or road kill etc were of more general interest, and perceived to be more relevant to the subject matter.

This dilemma will be most acute the first time a class engages in this sort of activity, but will be much easier to manage the second time, when the pupils can envisage how this sort of introduction can lead to some fun/interesting/relevant maths.

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TL6: Why is it important to reflect at the end of each lesson?

This vignette is written by the author and outlines the value both to the pupil and to the teacher in taking time at the end of each lesson to reflect on what has taken place.

This case has been developed with the specific aim of introducing the pupil, and perhaps the teacher also, to a fresh approach to learning mathematics. This involves the use of open-ended problem-solving Tasks in an engaging practical scenario.

The author, the trialing teachers and the writing team believe that, managed well, this approach can lead to a marked improvement in both interest and confidence in the processes of learning and applying mathematics.

A central and key factor in this approach to learning is to develop in the pupil an awareness of:

how each activity in the sequence leads naturally and logically to the next;
how each activity or lesson contributes to the overall aim (in this case, to save the joey);
what is learned from each activity.

For pupils who are accustomed to teacher and/or textbook-centred learning approaches, this will be a challenging and demanding change from the normal. It might be akin, for comparison, to asking teenagers not only to keep their bedrooms tidy, but to remain aware of exactly what is making them untidy in the first place. (Teenagers tend to reflect on such matters fairly infrequently.)

It is thus recommended to teachers that time be set aside at the end of each lesson to reflect on the events in that lesson, as well as the mathematics that has been learnt (or at least used) in the process. This needs only be three or four minutes, and in fact pupils should be encouraged to develop this as an efficient skill – to reflect briefly and personally without the Task becoming laborious.

Teachers are encouraged to conduct this activity with some or all of these questions in mind:

What did we do in this lesson?
Can you see how the previous lesson was preparation for this?
What maths did we use and learn today?
How did the maths help us work towards saving the joey?
What might we be going to do in the next lesson?
How has this been similar to and different from our usual maths lessons?

This will have been a successful activity if the pupils leave the classroom knowing what they have done and why. A good way for teacher and pupil to monitor this is through these questions:

“If you go home tonight and mum or dad asks you what you did in maths today, what will you tell them? And if they ask why you did that, what will you say?”

Provision is made in the workbook for pupils to record their reflections. These can be revisited later.

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TL4: The following IF/TRY points are strategies which could be used to counteract other diversions

IF/TRY points to note from this vignette:

IF the pupils stray from the Case, eg start talking about trucks or holidays etc

TRY refocusing the group – eg scribe on board for suggestions from class

TRY “Think, Pair, Share” – pupils Think of ideas on their own for 30 secs, then Pair with a partner for 30 seconds, then Share with the class

IF the pupils show an aversion to the Case eg feeling for the joey

TRY talking different strategies of getting joey out with them, eg gloves/another person

TRY “OK, let’s suppose that someone else has rescued the joey and has brought it to your place for you to take care of it”

IF the pupils do not appear to be engaged in the Case

TRY asking them to come up with a series of questions, which are important to answer if they are to look after a joey hence giving them ownership of the Case. These questions could then form the direction which the subsequent lessons could take

TRY reminding them about the overall Case Big Question

TRY finding an example in the class where someone has had to look after an orphaned animal eg bird, kitten and ask that person to relate their story

IF The pupils say “what has this got to do with maths?” OR “When are we going to do some maths”

TRY We will be doing some maths, but this time it will not be so obvious. I want you to try to be on the lookout for when the maths happens. When it does happen, put your hand up and tell the rest of the class.

TRY Most of the time we do maths from our textbook. But this time we are going to see where and how maths can be used in our everyday lives. Your job is to try to discover how maths is used to help us work out the best way to help an orphaned joey

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	LESSON PLANS
	DETAILED LESSON PLAN 1
	(DETAILED LESSON INFORMATION FOR TEACHERS LESS FAMILIAR
	WITH PROBLEM-BASED LEARNING)

AIMS	ACTIVITIES	NOTES	TEACHING AND LEARNING ISSUES (TL)
To develop pupils’ awareness that this is a new approach to the learning of mathematics, and that the mathematics will emerge through the activities and will be discussed at the end of the lesson.	1. Brief introductory discussion of the nature of the lesson ahead, of how this approach might be different to the usual mathematics lessons, and that this will be discussed (and recorded) at the end of the lesson. 2. Show pupils the scenario and discuss the basic outline of the sequence of lessons. 3. Distribute Record booklets and instruct pupils on the use of these over the five lessons. 4. Ensure pupils have a clear overview of the sequence and a clear understanding of the three components of the Case – a record booklet, a “how to” rescue poster and a simulated rescue.	This should be kept brief, and the pupils given assurance that there will be an opportunity throughout the lesson to share their thoughts about how the Task is being approached.	TL3: How do I redirect pupils who are not effectively engaging with the scenario? TL3: How do I redirect pupils who are not effectively engaging with the scenario? The following vignette is written by one of the teachers who helped develop the case and who trialled the first version of the case with her Year 7 class. The vignette illustrates how she tried to keep the discussion in Lesson 1 focused on saving the joey. There was an important lesson that emerged from this experience, which is reflected in the current materials Several suggestions are given at the end of the vignette for different pupil reactions to TL3 Prior to the first lesson, I had set up the room with posters of kangaroos and wallabies and I had the scenario ready to show on the overhead projector. The pupils did not notice the posters until I pointed them out. I told the pupils that we were going to do something a little different for the next five lessons and asked them to be prepared to go out of their comfort zone. I did not give them any clues – but asked them to try to ‘go with the flow of the lesson’ and discover as we went along. I showed them the scenario and then asked the class for initial comments..…then waited. I had hoped that the pupils would come up with a key question – what would need to be done to save the kangaroo? Instead, they observed that if we did save the joey that we would not be allowed to keep it anyway, so wouldn’t you just take it to the nearest vet or police station? Good point, I said to the class. I had to think quickly on my feet here and came up with the idea that they needed to change from school pupils into wildlife officers (ie role play) – to a give a valid reason for the Task. I sought and gained general agreement from the class that they would role-play for the next few lessons. The next problem, which I encountered, was pupils who did not want to be putting their hands in to a kangaroo pouch to check for a joey. We discussed this as a class and eventually decided that if we really wanted to help the joey, we would need to find it first. We then came up with what you would do/need to get the joey out of the pouch– eg gloves/another person/torch/old rag to keep it warm. I still did not feel that I had them interested; rather, I felt they were really going along with the discussion as I had asked them to do so. Some boys were starting to offer silly suggestions and I could see the class going off-track again. In an effort to engage each pupil fairly quickly, and again thinking on my feet, we then focused in on the 12 cm and 60 grams in the scenario – I asked the pupils to estimate the length 12 cm with their hands and to have a friend measure it with a ruler. This hands-on activity was very successful (and very obviously mathematical, in the pupil’s eyes). Many pupils were surprised at how incorrect their estimation was. I then asked them, for homework, to define the weight of 60 grams in everyday terms. Their answers the next lesson included an egg, a small Mars bar and 60 ml water. *The lessons which the developers learnt from this initial trialing of the case, were incorporated into subsequent developments and writing.* With hindsight, it became obvious that one of the reasons for the pupil’s lack of focus on the Case, and their puzzlement as to why we were talking about kangaroos in a maths classroom, was that they did not realize that the ‘maths was coming’. The pupils needed explicitly to know that they were going to use some maths skills in solving this problem and that a major component of this case, was to identify the maths skills as they emerged. Subsequent trials were adjusted so that teachers did highlight to the pupils that there was a great deal of maths that was involved. *The following comment on this vignette is written by one of the academic observers.* The teacher wanted to use the scenario and posters to initiate a somewhat free flowing discussion with minimum direct teacher control. The teacher had a clear vision, about where she wanted the discussion to go, but the pupils were very much ‘in the dark’ as to the direction of this and subsequent lessons, and so found it difficult to remain focused and engaged in the discussion. These two intentions were likely to clash and indeed, resulted in the pupils going “off track”. The scenario provided a context and set of issues that were intended, in a short period, to stimulate some general real-life discussion with possibilities of how one could use maths to help solve the problem. This was a maths class, in which these types of discussions rarely occurred. The teacher had less ability to be able to use unexpected pupils comments, than if this discussion occurred in a subject where kangaroos or road kill etc were of more general interest, and perceived to be more relevant to the subject matter. This dilemma will be most acute the first time a class engages in this sort of activity, but will be much easier to manage the second time, when the pupils can envisage how this sort of introduction can lead to some fun/interesting/relevant maths. Close Box
To understand the unusual nature of the marsupial birth and development process	5. Emphasise to the pupils that the focus of this lesson is on understanding the special nature of new born kangaroos compared to other species. 6. Show pupils photos of kangaroos and joeys 7. The newborn kangaroo, called a joey, is small and helpless. It is the size of a jellybean. It moves into its mother’s pouch where it will feed and grow for months. Show the video clips of a new born joey (Task 1.1). The issue that needs to emerge is that kangaroos (and other marsupials) at birth are very much less developed than other mammals and that this has important implications for caring for young joeys.	Time could be provided for pupils to explore this on-line. A short summary of what is different about marsupials from other mammals is provided at marsupial mammals.	TL4: The following strategies could be used to counteract other diversions
To use data to illustrate the nature of marsupial development compared to other more common species - to show that marsupials are born very much smaller than other mammals when birth weight is compared to adult weight.	8. Provide Animal Data: Birth to Adult Weight Ratios for Various Animals, including humans 9. Pupils calculate birth to adult weight ratios. All pupils should complete the first four Including kangaroo; after that, the data is arranged in more challenging ways that allow teachers to challenge more able pupils. If this occurs, then results should be shared so that all pupils can complete the table in Task 1.2. 10. Pupils consider the ratios table and write down observations (Task 1.3) they think are significant. Pupils then reflect on what factors would need to be considered if they found an injured animal on the side of the road. In particular, given the differences pupils have just noted between the young of a kangaroo and other animals, they are encouraged to consider what extra care a joey would need.	Different animals could be assigned to different groups for each activity, then ratios and graphs compared. Some pupils may wish to further investigate Background Information on Kangaroos before attempting some of the Maths work. Background information and links to websites can be found on the Background Information on Kangaroos page.	TL5: Keeping the overall Case firmly in mind
To understand differences between this approach and the usual approach to learning mathematics	11. Class discussion at end of lesson explores differences between this lesson and a ‘normal’ maths lesson. Ideas are recorded in their Record Booklets and retained for review at the end of the five lessons.	Pupils should be encouraged to develop their own lists of differences as they emerge through discussions.
	Home Work 1. Pupils complete reflection questions in record booklets		TL6: Why is it important to reflect at the end of each lesson? TL6: Why is it important to reflect at the end of each lesson? This vignette is written by the author and outlines the value both to the pupil and to the teacher in taking time at the end of each lesson to reflect on what has taken place. This case has been developed with the specific aim of introducing the pupil, and perhaps the teacher also, to a fresh approach to learning mathematics. This involves the use of open-ended problem-solving Tasks in an engaging practical scenario. The author, the trialing teachers and the writing team believe that, managed well, this approach can lead to a marked improvement in both interest and confidence in the processes of learning and applying mathematics. A central and key factor in this approach to learning is to develop in the pupil an awareness of: how each activity in the sequence leads naturally and logically to the next; how each activity or lesson contributes to the overall aim (in this case, to save the joey); what is learned from each activity. For pupils who are accustomed to teacher and/or textbook-centred learning approaches, this will be a challenging and demanding change from the normal. It might be akin, for comparison, to asking teenagers not only to keep their bedrooms tidy, but to remain aware of exactly what is making them untidy in the first place. (Teenagers tend to reflect on such matters fairly infrequently.) It is thus recommended to teachers that time be set aside at the end of each lesson to reflect on the events in that lesson, as well as the mathematics that has been learnt (or at least used) in the process. This needs only be three or four minutes, and in fact pupils should be encouraged to develop this as an efficient skill – to reflect briefly and personally without the Task becoming laborious. Teachers are encouraged to conduct this activity with some or all of these questions in mind: What did we do in this lesson? Can you see how the previous lesson was preparation for this? What maths did we use and learn today? How did the maths help us work towards saving the joey? What might we be going to do in the next lesson? How has this been similar to and different from our usual maths lessons? This will have been a successful activity if the pupils leave the classroom knowing what they have done and why. A good way for teacher and pupil to monitor this is through these questions: “If you go home tonight and mum or dad asks you what you did in maths today, what will you tell them? And if they ask why you did that, what will you say?” Provision is made in the workbook for pupils to record their reflections. These can be revisited later. Close Box