Lesson Plan 2 - Save a Baby Kangaroo

TL7: How can I guide the class through designing the step by step process?

The class discussion that takes place at the start of lesson two of this sequence can provide great benefits to the pupils. It requires genuine problem solving thinking and with careful planning can result in rich mathematical conversations. These are two aspects of a sequence of lessons such as this which aren’t always present in traditional Maths lessons.

The issues below highlight the key issues from this class discussion. They are notes from a teacher who took a class through this process and aim to –

provide other teachers with the intended end point of the discussion
assist other teachers in guiding a class to the correct outcome while still engaging them in quality thinking.
highlight areas of potential for rich Mathematical experiences, encouraging pupils to think like Mathematicians.

Issue one – Imagine we have found an injured joey. What are the key factors we need to know about the joey before we can work out what to feed it?

Answer – Species and age

Notes – Two issues should be apparent from the growth and feeding charts provided at the start of the lesson. For any one species, the type of formula and volume of formula changes as the age of the joey changes. Also, for a given number of days, the type of formula and volume of formula changes across the species. Pupils should be able to identify from this that species and age are two key variables which affect the feeding of a joey. Teachers may also wish to discuss the necessary change in formula for the growing joey. Younger joeys whose energy goes mainly into growing requires more protein. As the joey grows and it spends more time outside the pouch spends more energy on movement and requires more carbohydrate and fat.

Issue two – Using the growth data for species, how can we determine the age and species of the joey?

Answer – Measure the weight and tail and foot length. Check each species to see which provides a consistent prediction of age from all three measurements.

Notes – A key problem solving step in the process. A good understanding at this stage is vital for the simulated rescue process. The pupils should identify from the new table that foot length, tail length and weight are good predictors of age. An example set of data could be provided for the class. The class may be asked if any groups feel it is highly unlikely that the joey is of their species. Different groups may be asked to predict what age the example is from their tables to identify the issue of conflicting ages being predicted. The class may then be asked if any of the groups are confident that the joey was from their species. Pupils should identify that each species has measurements in quite unique ratios.

Issue three – What problems might we have with this process? How can we fix it? What extra resources do we need?

Answer – The table only provides increments of 20 days. The joey is likely to have measurements and be of an age between the intervals listed on the table. To solve this, the relationship could be represented as a graph. With the relationship represented as continuous data, it would be possible to find any weight, foot length or tail length on the graph and determines the corresponding age.

Notes – A key opportunity for a rich mathematical discussion. Introduce the concept of interpolation and extrapolation by suggesting that it is very likely that an orphaned joey would not have measurements corresponding exactly with those on the table, but would likely fall between the intervals of ten days shown on the table. While it may be possible to work only from the table, representing the same data in graphical form would make interpolation easier and more accurate. The ability to represent data in different forms (table, graph, equation etc), understand the advantages and disadvantages of each, and know when to use them is an important mathematical skill. Real life problem solving situations such as these are powerful tools to develop such understandings in pupils. Depending on the ability of the class, the teacher may discuss the difference between discrete and continuous data. A highly capable class could consider the idea of dependent and independent variables and how they affect this situation also.

Issue four – What process will we go through to save an orphaned joey?

Answer –

1. Measure the joey’s weight, tail length and foot length.

2. Check all species and predict your joey’s age based on its measurements.

3. Decide upon species and age based on which species provides the closest three predictions of age.

4. Use the feeding table for the correct species (provided earlier to pupils) to determine a feeding plan for the joey.

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	LESSON PLANS
	DETAILED LESSON PLAN 2
	(DETAILED LESSON INFORMATION FOR TEACHERS LESS FAMILIAR
	WITH PROBLEM-BASED LEARNING)

AIMS	ACTIVITIES	NOTES	TEACHING AND LEARNING ISSUES
To clarify the outcomes from lesson 1, including the nature of this approach to learning mathematics.	1. Pupils review lesson 1 through brief discussion: a) marsupial species involved in this case, marsupial birth and development, b) aspects of this approach to learning mathematics, importance of remaining aware of and recording the mathematics as it emerges. 2. Ensure pupils are aware that the focus of today’s lesson is designing a step by step process for saving an orphaned joey, which they will use to rescue a joey in lesson four. Ensure they understand how this fits into the whole sequence.	Brief discussion only, and should involve review of notes in pupils’ record booklets from lesson 1.
To use joey feeding data to develop a step by step process that can be used to determine the species and age of individual joeys.	3. Divide pupils into five groups from the start. 4. Compile a list of factors on the board that pupils identified at the end of last lesson as being important when rescuing an orphaned animal, especially a joey. 5. Direct pupils’ attention to the fact that for the remainder of this lesson they will be focussing on developing a feeding plan for a joey. 6. Pupils are all given Feed Chart for Different Kangaroos of all species. As a class, pupils use these tables to identify that age and species are the key variables which affects a joey’s required feeding. Pupils begin to record this information in their record books (Task 2.1). 7. Teachers may wish to explore the different compositions of the four types of milk powder at Kangaroo Milk Replacer and discuss possible reasons for the changes in fat and protein levels with the class. 8. Each group is assigned one of the five species in which to become an expert. Each pupil is given the specific joey growth chart for their species. 9. As a class, pupils identify that body measurements can be used to determine an orphaned joey’s age and the ratio of these three measurements can be used to determine its species.		TL7: How can I guide the class through designing the step by step process? TL7: How can I guide the class through designing the step by step process? The class discussion that takes place at the start of lesson two of this sequence can provide great benefits to the pupils. It requires genuine problem solving thinking and with careful planning can result in rich mathematical conversations. These are two aspects of a sequence of lessons such as this which aren’t always present in traditional Maths lessons. The issues below highlight the key issues from this class discussion. They are notes from a teacher who took a class through this process and aim to – provide other teachers with the intended end point of the discussion assist other teachers in guiding a class to the correct outcome while still engaging them in quality thinking. highlight areas of potential for rich Mathematical experiences, encouraging pupils to think like Mathematicians. Issue one – Imagine we have found an injured joey. What are the key factors we need to know about the joey before we can work out what to feed it? Answer – Species and age Notes – Two issues should be apparent from the growth and feeding charts provided at the start of the lesson. For any one species, the type of formula and volume of formula changes as the age of the joey changes. Also, for a given number of days, the type of formula and volume of formula changes across the species. Pupils should be able to identify from this that species and age are two key *variables* which affect the feeding of a joey. Teachers may also wish to discuss the necessary change in formula for the growing joey. Younger joeys whose energy goes mainly into growing requires more protein. As the joey grows and it spends more time outside the pouch spends more energy on movement and requires more carbohydrate and fat. Issue two – Using the growth data for species, how can we determine the age and species of the joey? Answer – Measure the weight and tail and foot length. Check each species to see which provides a consistent prediction of age from all three measurements. Notes – A key problem solving step in the process. A good understanding at this stage is vital for the simulated rescue process. The pupils should identify from the new table that foot length, tail length and weight are good predictors of age. An example set of data could be provided for the class. The class may be asked if any groups feel it is highly unlikely that the joey is of their species. Different groups may be asked to predict what age the example is from their tables to identify the issue of conflicting ages being predicted. The class may then be asked if any of the groups are confident that the joey was from their species. Pupils should identify that each species has measurements in quite unique ratios. Issue three – What problems might we have with this process? How can we fix it? What extra resources do we need? Answer – The table only provides increments of 20 days. The joey is likely to have measurements and be of an age between the intervals listed on the table. To solve this, the relationship could be represented as a graph. With the relationship represented as continuous data, it would be possible to find *any* weight, foot length or tail length on the graph and determines the corresponding age. Notes – A key opportunity for a rich mathematical discussion. Introduce the concept of interpolation and extrapolation by suggesting that it is very likely that an orphaned joey would not have measurements corresponding exactly with those on the table, but would likely fall between the intervals of ten days shown on the table. While it may be possible to work only from the table, representing the same data in graphical form would make interpolation easier and more accurate. The ability to represent data in different forms (table, graph, equation etc), understand the advantages and disadvantages of each, and know when to use them is an important mathematical skill. Real life problem solving situations such as these are powerful tools to develop such understandings in pupils. Depending on the ability of the class, the teacher may discuss the difference between discrete and continuous data. A highly capable class could consider the idea of dependent and independent variables and how they affect this situation also. Issue four – What process will we go through to save an orphaned joey? Answer – 1. Measure the joey’s weight, tail length and foot length. 2. Check all species and predict your joey’s age based on its measurements. 3. Decide upon species and age based on which species provides the closest three predictions of age. 4. Use the feeding table for the correct species (provided earlier to pupils) to determine a feeding plan for the joey. Close Box
To identify the need for, and produce, graphs to assist in determining a feeding program for an orphaned joey.	10. As a class, pupils identify the issue of accurately predicting the age of a joey from a table and discuss the need to convert the data from tabular to graphical form. 11. Pupils now complete the Graphs for their specific species using the joey growth chart for their species provided earlier (Task 2.2). These graphs may be done by hand or on excel. It is anticipated that most pupils will complete three separate graphs, one each for weight, foot length and tail length. An advanced class or highly capable pupils may be shown how to complete a double axis graph. Pupils should draw a trend line on the graph. NOTE: If this activity is not completed in class it will need to be completed out of class before lesson 3.
To collect further information on a particular species of kangaroo or wallaby – such as photos, data or other information from library resources or the internet.	12. Discuss with pupils the posters they will be producing in the next lesson and how it fits into the overall sequence. For homework they should collect any other information they may like to include on their posters from Background on Kangaroos (Task 2.3)
To develop an awareness of the mathematics involved in this case, and of this approach to learning mathematics	13. Pupils spend a few minutes at the end of the lesson completing their Record Booklets.	This may be completed at home if the teacher is confident pupils know how to complete the Task independently.
	Homework: See steps 11-13 above.