The purpose of this unit is to engage the student in carrying out the steps of a statistical investigation in a context from the science learning area; predator control.
Students develop their skills and knowledge on the mathematics learning progressions statistical investigations and interpreting statistical and chance situations.
Students will carry out the steps of a statistical investigation in the context of predator control; predator and wildlife population counts.
Structure
This crosscurricular, context based unit has been built within a framework that has been developed with input from teachers across the curriculum to deliver the mathematics learning area, while meeting the demands of differentiated studentcentred learning. The unit has been designed around a six session focus on an aspect of mathematics that is relevant to the integrating curriculum area concerned. For successful delivery of mathematics across the curriculum, the context should be meaningful for the students. With student interest engaged, the mathematical challenges often seem more approachable than when presented in isolation.
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.
The following five sessions are each based around a model of studentcentred differentiated learning.
 There is a starting problem to allow students to settle into the session and to focus on the mathematics within the chosen context. These starting problems might take students around ten minutes to attempt and/or to solve, in groups, pairs or individually.
 It is then expected that the teacher will 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.
 The remaining group of activities are designed for differentiating on the basis of individual learning needs. 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.
Introductory session
(This activity is intended to motivate students towards the context/integrated learning area and to inform teachers of each student’s location on the learning progressions):
The Department of Conservation is working to make New Zealand ‘predator free’ by 2050.
 What is meant by ‘predator free’?
 What data might this decision be based on?
 How can they measure their effectiveness?
 How can we (at school, at home, around the community) assist in achieving this goal?
In this activity, the teacher(s) will be able to locate their students on the statistical investigations and interpreting statistical and chance situations learning progressions as they work through the stages of a statistical investigation. The activities within this unit treat the individual steps of an investigation in isolation, with the amount of guidance needed to be provided by the teacher dependant on the location of the student on the learning progression(s). It should be noted that the intention of the NZ Curriculum achievement objective ‘plan and conduct investigations using the statistical enquiry cycle’ is for students to carry out a complete statistical investigation. This unit of activities serves to provide the learning opportunity to allow students to explore each of the stages of a statistical investigation with the outcome of an understanding of the whole process and the ability to carry out their own investigation afterwards.
Mathematical discussion that should follow this activity involve:
 What variables might have been measured to suggest the need for the ‘predator free by 2050’ pledge?
 What are the variables should be measured to recognise the success of the goal to be predator free?
 What data collection methods can the Department of Conservation use to count wildlife and predator populations over the next 30 years?
Session 2
Focusing on comparing the distribution of predators over time from a visual graph display.
Activity
A local bird sanctuary is protected from predators by good fencing and a trapping project run by volunteers. A record is kept of all the predators caught in the traps and when the traps are sprung (by a predator that ‘got away’). Looking at the graph of the data for the first five years of the trapping programme as shown below:
 Describe the overall trend in trapping success shown in this graph.
 Which type of predator is the most prevalent in the traps.
 In early 2016, the bird sanctuary operated a poison drop as well as the trapping programme. Use the data below to comment on the effectiveness of the the poison drop in terms of predator control.
Discussion arising from activity:
 Does the data tell you how many predators are present in the bird sanctuary?
 The graph shown above has the data grouped by trap contents. Why is this a useful choice of grouping?
 If the data was grouped by year, what trends/patterns would be more obvious to see?
Building ideas
The table below shows the raw data (number of animals caught per calendar year) from a local bird sanctuary’s predator trap programme.

2013

2014

2015

2016

2017

Rat

502

340

461

253

120

Possum

50

47

130

68

53

Stoat/weasel

35

32

20

12

14

Other

12

15

18

8

20

Sprung

86

82

73

50

62

 If a trap has been sprung, we can assume that a predator was present but cannot count it as caught. Why not?
 Find the total number of predators caught in traps each year.
 Graph the total number of predators caught in traps each year.
 Comment on the overall trend of the total number of predator’s caught in in traps each year.
Reinforcing ideas
In the year following the poison drop, the bird sanctuary decided to further reduce the rat population with better management of visitor behaviour. They did this by banning food consumption within the predator controlled area and removing the rubbish bins (as they were no longer needed).
Use the data below to comment on the effectiveness of the management of visitor food and rubbish.

2013

2014

2015

2016

2017

Rat

502

340

461

253

120

Possum

50

47

130

68

53

Stoat/weasel

35

32

20

12

14

Other

12

15

18

8

20

Sprung

86

82

73

50

62

Extending ideas
The graph below shows the data from a local bird sanctuary’s predator trap programme, grouped by year.
 How is the effectiveness of the poison drop early in 2016 shown in the graph?
 Initially, possum hunters were contracted to manage the numbers of possums. This contract was cancelled for various reasons. Suggest when the hunters’ contract was cancelled. Support your suggestion with evidence from the graph.
Session 3
Focusing on communicating findings from a statistical investigation, using appropriate displays.
Activity
A year 8 class has been taking part in a ‘predator free’ programme. It has made 12 traps from plastic milk bottles and set these up around the school grounds. Over one week, the class have caught the following predators:

Monday

Tuesday

Wednesday

Thursday

Friday

Rats

3

1

0

2

0

Mice

2

3

3

2

2

Other

0

0

1

1

0

Sprung

2

4

2

4

5

Nothing

5

4

6

3

5

What conclusions can you draw about the predators around the school grounds from these data?
Discussion arising from activity:
 How many traps are accounted for each day?
 What might be in the ‘other’ category? Would it be useful to list these by name?
 What precautions will the class need to have taken to run this programme safely?
Building ideas
Look at the data collected by the year 8 class over the week of predator trapping. The data in this table are grouped by trap results, including predator type, over time. A line graph, with a differently coloured line for each row in the table is a suitable method of graphing.
 Construct a line graph of the data in this table.
 Describe the trends shown by the lines in your graph. You may like to use terms such as; increasing, decreasing, constant, fluctuating, no clear trend.
Reinforcing ideas
Look at the data collected by the year 8 class over the week of predator trapping.
 To show the trend of predator numbers over time, which type of graphs are the most appropriate for these data?
 Graph the data in the table.
 Describe the trends shown in your graph. You may like to use terms such as; increasing, decreasing, constant, fluctuating, no clear trend.
Extending ideas
Look at the data collected by the year 8 class over the week of predator trapping.
 Does the table format show the trends in the data?
 What is the daily count total? Why?
 To show the total count for each day, with the trapped predator, missed predator and inactive traps separated, a stacked column graph could be used. Graph the data in this way.
 Describe the trends shown in your graph. You may like to use terms such as; increasing, decreasing, constant, fluctuating, no clear trend.
Session 4
Focusing on gathering a range of data to support a more informed predator survey.
Activity
The year 8 class has been taking part in a ‘predator free’ programme wanted to know if they were effective in reducing the number of wildlife predators around the school. They have been collecting data on the activity in their 12 tunnel shaped predator traps. The students want to find out more about any predators that had not been caught in the traps.
They have prepared inkpads and plain cards for the entrance to each of the trap tunnels. The predators entering the tunnels will get ink on their paws/feet as they enter the tunnel and will leave a footprint record of their visit.
Suggest a method of recording the footprint data along with the existing method of recording the trap data.
Discussion arising from activity:
 How will the class distinguish between different species visiting the same trap?
 Is it possible for the class know how many of the same species have visited the same trap?
Building ideas
Thinking about the footprint cards in front of the traps, which of the following are valid statements? Give reasons for your choices.
 The footprint record can be used to count how many wildlife predators visit the traps.
 The footprint record will show how many wildlife predators are in the area.
 The footprint cards could be used to identify the predators that are springing the traps and escaping.
 Different species will leave a different coloured footprint.
 The footprint cards will help the class work out which are the most prevalent species of predator.
Reinforcing ideas
After a week of using the footprint cards, the class recorded the following data:

Caught

Footprints

Visited but not trapped

Rats

5

12


Mice

8

10


Other

2

5

 Can you complete the section ‘visited but not trapped’?
 What percentage of each type of wildlife predator has been successfully caught in the trap it enters?
 Can the class use this information to estimate the wildlife predator population in the area?
 How can the class use this information to improve their traps?
 How can the class use this information to evaluate the effectiveness of their 12 traps over time?
Extending ideas
After a week of using the footprint cards, the class recorded the following data:

Caught

Footprints

Rats

5

12

Mice

8

10

Other

2

5

 Estimate the total number of predators that visited traps but were not caught.
 Why can you not be certain of the total number of predators that visited traps but were not caught?
 Find the ratio of the total number of caught to visiting (but not caught) predators.
 Looking at the data for one week, can you make the call that the traps work better for any one species of predator? Explain your answer.
Session 5
Focusing on communicating findings using suitable displays.
Activity
Before the year 8 class implemented a ‘predator free’ programme, it took part in Landcare New Zealand’s garden bird survey. The class were interested to learn that over the past ten years in their area, there has been an 11% increase in the tui count but a 13% decline in the fantail count and a 27% decline in the kereru count. Show this information on a suitable chart, diagram or graph.
Discussion arising from activity:
 How have the birds been counted in the ‘garden bird survey’?
 The ‘garden bird survey’ is carried out on the same date each year. Why is this important?
 How reliable are the trends shown from the results of the ‘garden bird survey’?
 What other methods of tracking bird populations are there in New Zealand?
Building ideas
In the same region, some species of bird have shown an increase in population while others have shown a decrease. For each of the following factors, suggest how this might affect the population. Where possible, explain your suggestions.
 Reducing predator numbers.
 Reducing food supply.
 Reducing predator numbers and reducing food supply.
 An increase in the populations of other species of birds.
 Decreasing available habitat (e.g. clearing bush and building more houses)
Reinforcing ideas
Find out about the trends in population of the birds in your region as measured in the Landcare Research New Zealand garden bird survey. How are the native bird counts trending compared with the introduced species? Show this information on a suitable chart.
Extending ideas
Predators such as rats and mice, possum and cats are not the only threats to native bird populations. Find out about other possible threats. Which of the threats to native birds are of particular relevance to your community? Which of threats can be mitigated – and how? Create an infographic to display what you have found.
Session 6
Focusing on communicating findings using suitable displays.
Activity
To measure the effectiveness of their predator traps on the bird population at their school, the year 8 class have taken a bird count for one day each month, over a period of five months. The results are as follows:

One Day Count



Tui

Fantail

Kereru

July

0

1

6

August

2

0

8

September

0

1

5

October

4

3

6

November

4

2

8

Construct a suitable graph so that:
 a sense of a time series trend is shown,
 the total number of these three types of bird sighted at each survey is shown,
 the count for each species is also shown.
Discussion arising from activity:
 How might the seasons affect the trend shown in these data?
 What other possible factors might affect the reliability of these data?
 From these data, can you say that one type of bird is more prevalent than another?
 From these data, can you comment on any trends in the population of the tui, fantails or kereru?
Building ideas
The class wanted to compare the one day bird surveys with the monthly total predator catch numbers from their trapping programme. The results are shown below:

One Day Count

Monthly Count



Tui

Fantail

Kereru

Predator Catch

July

0

1

6

35

August

2

0

8

31

September

0

1

5

26

October

4

3

6

15

November

4

2

8

18

 Construct a line graph to show the monthly predator catch count from July to November.
 Describe the trend of the monthly predator catch count from July to November as either increasing, decreasing, constant or no clear trend shown.
 Construct a line graph to show the one day total* bird count from July to November.
 Describe the trend of the one day total* bird count from July to November as either increasing, decreasing, constant or no clear trend shown.
*note that this total is of the three species counted and not of all birds present that day.
Reinforcing ideas
The class wanted to compare the one day bird surveys with the monthly total predator catch numbers from their trapping programme. The results are shown below:

One Day Count

Monthly Count



Tui

Fantail

Kereru

Predator Catch

July

0

1

6

35

August

2

0

8

31

September

0

1

5

26

October

4

3

6

15

November

4

2

8

18

Noting that the class collected data on the tui, fantail and kereru sightings over just one school day, and the predator catch over a full month…find a suitable way of graphing these data to identify the trends in bird (sightings) and predator (catch) numbers.
Extending ideas
Evaluate the reliability of the data collected by the class. The data on bird populations and predator catch numbers was recorded over a period of five months.
 Was this a suitable period of time for trends to become apparent?
 What effect would the seasons during which the data were collected have on the apparent trends?
What would you expect the trends in bird population and predator catch numbers to be over a longer period of time (ie, more than a year)? What other factors would come into play over this longer period?