ࡱ> mojkl ;KbjbjBrBr <  @|NN!!"""49"9"9"h"5#9"aT`$(9$p$$$/ 0LU0(SSSSSSSVcYS"}0.@/}0}0S!!$$ T444}0!R$"$S4}0S44ntP!"HS$@3N9"G1|Q S%T<aTQ}Z1 }Z@HSHS}Z"\S}0}04}0}0}0}0}0SS4}0}0}0aT}0}0}0}0}Z}0}0}0}0}0}0}0}0}0N W :  Internal Assessment Resource Mathematics and Statistics Level 3 This resource supports assessment against: Achievement Standard 91581 Investigate bivariate measurement dataResource title: Subspecies4 creditsThis resource: Clarifies the requirements of the standard Supports good assessment practice Should be subjected to the schools usual assessment quality assurance process Should be modified to make the context relevant to students in their school environment and ensure that submitted evidence is authentic Date version published by Ministry of EducationDecember 2012 To support internal assessment from 2013Quality assurance statusThese materials have been quality assured by NZQA. NZQA Approved number A-A-12-2012-91581-01-6204Authenticity of evidenceTeachers must manage authenticity for any assessment from a public source, because students may have access to the assessment schedule or student exemplar material. Using this assessment resource without modification may mean that students work is not authentic. The teacher may need to change figures, measurements or data sources or set a different context or topic to be investigated or a different text to read or perform. Internal Assessment Resource Achievement Standard Mathematics and Statistics 91581: Investigate bivariate measurement data Resource reference: Mathematics and Statistics 3.9B Resource title: Subspecies Credits: 4 Teacher guidelines The following guidelines are supplied to enable teachers to carry out valid and consistent assessment using this internal assessment resource. Teachers need to be very familiar with the outcome being assessed by Achievement Standard Mathematics and Statistics 91581. The achievement criteria and the explanatory notes contain information, definitions, and requirements that are crucial when interpreting the standard and assessing students against it. Context/setting This activity requires students to investigate possible relationships between variables relating to head measurements for Hectors dolphins. They then need to decide if the classification of North Island dolphins as a new subspecies from South Island dolphins can be supported by the findings of the investigation. Before the assessment, students need to research the context, including details about the variables. Time needs to be set aside for this purpose before the assessment. Conditions This assessment activity requires multiple sessions. Confirm the timeframe with your students. Students must work independently. The students need to use appropriate technology, for example, statistical software. The format of the presentation could be, but is not restricted to, a written report. Resource requirements Provide the students with the data file. Additional information The endemic New Zealand dolphin Cephalorhynchus hectori has been shown through genetic analyses to consist of four regional populations separated to various degrees both geographically and reproductively. A study of skull and mandible features was undertaken to examine variation between the most genetically distinct population, which occurs on the west coast of the North Island, and the populations around the South Island. The North Island population of Hectors dolphin is classified as a new subspecies, C. hectori maui, and the South Island population is classified as C. hectori hectori. Further information about the research can be found from the Journal of The Royal Society of New Zealand, Volume 32, Issue 4, December 2002, pp 713-727 at  HYPERLINK "http://www.tandfonline.com/doi/abs/10.1080/03014223.2002.9517717" http://www.tandfonline.com/doi/abs/10.1080/03014223.2002.9517717 The emphasis for this task is on investigating possible relationships. This means that the definition of the explanatory and response variables is not crucial. However, for a task where regression and the making of predictions is the emphasis it would be expected that appropriate explanatory and response variables are clearly identified. For this data set the possible relationships tend to be linear. This activity can be adapted to use another existing data set. Any data set provided needs to have appropriate motivation, contextual depth and relevance to the students. Details about the data need to be provided to enable students to inform themselves about the context. Internal Assessment Resource Achievement Standard Mathematics and Statistics 91581: Investigate bivariate measurement data Resource reference: Mathematics and Statistics 3.9B Resource title: Subspecies Credits: 4 Achievement Achievement with Merit Achievement with ExcellenceInvestigate bivariate measurement data.Investigate bivariate measurement data, with justification.Investigate bivariate measurement data, with statistical insight. Student instructions Introduction A subspecies is a population that has a biological classification distinguishing it from other populations of the same species, on the basis of genetic differences. Subspecies usually occur because of isolation within a species. This activity requires you to carry out a bivariate data investigation using at least two variables relating to head measurements for Hectors dolphins and to write a report of your findings. You need to decide if the classification of North Island dolphins as a new subspecies from South Island dolphins can be supported by the findings of your investigation. Your overall grade will be determined by how well you carry out your investigation and how well you apply the statistical enquiry cycle. You will work independently over a period of <> to complete this task. Task The North Island population of Hectors dolphins has been classified as a new subspecies, C. hectori maui, and the South Island population as C. hectori hectori. This classification has been made on the basis of measurements taken from various parts of the head. You have been given data relating to head measurements for Hectors dolphins from both the North and South Islands and information that can be used to interpret the measurements (see Resource A). Use the statistical enquiry cycle to carry out a statistical investigation to determine if there is a relationship between at least one pair of variables. Write a report describing the investigation. Pose an appropriate relationship question that can be answered using variables in the data set. The variables you choose must be numerical, and the variable you use as your response variable must be continuous. You may choose to investigate more than one pair of variables. Select appropriate display(s) to graph your data. Identify features in the data, including the nature and strength of the relationship. Find an appropriate model. Use your model to make prediction(s). Write a conclusion answering your question. Use the results of your investigation to decide if the classification of North Island dolphins as a new subspecies from South Island dolphins can be supported. Support your conclusion by referring to your analysis and/or features of the visual display(s). Include a reflection on your process, which could consider other relevant variables, or evaluate the adequacy of your model(s). In writing your report, link your discussion to the context and support the statements you make by referring to statistical evidence. Resource A The endemic New Zealand dolphin Cephalorhynchus hectori has been shown through genetic analyses to consist of four regional populations separated to various degrees both geographically and reproductively. A study of skull and mandible features was undertaken to examine variation between the most genetically distinct population, which occurs on the west coast of the North Island, and the populations around the South Island. The North Island population of Hectors dolphin is classified as a new subspecies, C. hectori maui, and the South Island population is classified as C. hectori hectori. Further information about the research can be found from the Journal of The Royal Society of New Zealand, Volume 32, Issue 4, December 2002, pp 713-727 at  HYPERLINK "http://www.tandfonline.com/doi/abs/10.1080/03014223.2002.9517717" http://www.tandfonline.com/doi/abs/10.1080/03014223.2002.9517717 The data set provides information about dolphin measurements. Explanation of column headers in the data set: Selected measurementsSimplified definitionsRWMrostrum width at mid-lengthRWBrostrum width at baseRLrostrum lengthZWzygomatic widthCBLcondylobasal lengthMLmandible lengthIslandNorth = 1; South = 2 Assessment schedule: Mathematics and Statistics 91581 Subspecies Teacher note: You will need to adapt this assessment schedule to include examples of the types of responses that can be expected. Evidence/Judgements for Achievement Evidence/Judgements for Achievement with MeritEvidence/Judgements for Achievement with ExcellenceThe student investigated bivariate measurement data. They have shown evidence of using each of the following components of the statistical enquiry cycle. The student has: posed an appropriate relationship question For example, chosen appropriate variables to investigate a possible relationship with respect to the purpose of trying to establish if a bivariate investigation can provide supporting evidence for the classification. selected and used appropriate display(s) For example, produced appropriate scatter graph(s) with axes labelled. The explanatory and response variables are clear. identified features in the data and described the nature and strength of the relationship For example, stated from a visual inspection that the trend is linear rather than non-linear. They have described the strength with references to visual aspects of scatter about the regression model and the nature, in context, by stating that as one variable increases the other also tends to increase. Other features of the data have been described. found an appropriate model For example, fitted an appropriate regression model to the data. made a prediction For example, used the model to make a prediction for the response variable. The prediction is sensible with respect to the context and uses units and sensible rounding. communicated findings in a conclusion: For example, clearly communicated each component of the cycle. They have made a conclusion which is consistent with the purpose of investigating if possible relationships can support the classification. The examples above are indicative of the evidence that is required. The student investigated bivariate measurement data, with justification. They have shown evidence of linking components of the statistical enquiry cycle to the context and made supporting statements by referring to evidence such as statistics, data values, trends or features of visual displays. The student has: posed an appropriate relationship question For example, chosen appropriate variables to investigate a possible relationship with respect to the purpose of trying to establish if a bivariate investigation can provide supporting evidence for the classification. They have justified the question and choice of variables with reference to the context. selected and used appropriate display(s) For example, produced appropriate scatter graph(s) with axes labelled. The explanatory and response variables are clear. identified features in the data and described the nature and strength of the relationship. For example, stated from a visual inspection, with evidence, that the trend is linear rather than non-linear. They have described the strength with references to visual aspects of scatter about the regression line. They have described, in context, the nature by stating that as one variable increases the other also tends to increase and justified this with reference to visual aspects of the display(s). Other features of the data have been discussed with supporting comments which refer to the context. They may have acknowledged that they have found only a statistical relationship between the variables but that this does not imply causation. They may acknowledge that other factors (named) would impact on the variable. found an appropriate model For example, fitted an appropriate regression model to the data. The appropriateness of the model is justified by discussion of fit throughout the range of x-values in the data or the number of data points. made a prediction For example, used the model to make a prediction for the response variable. The prediction is interpreted in context with the use of units and sensible rounding. It is justified with discussion on how precise it might be and has supported comments with references to statistical evidence from the analysis. communicated findings in a conclusion For example, clearly communicated each component of the cycle. They have used the results of their investigation with at least one pair of variables to decide if the classification of North Island dolphins as a separate subspecies can be supported. There is contextual support for the conclusion. The examples above are indicative of the evidence that is required. The student has investigated bivariate measurement data, with statistical insight. They have shown evidence of integrating statistical and contextual knowledge throughout the process. They may have reflected on the process, considered other relevant variables, or evaluated the adequacy of any models. The student has: posed an appropriate relationship question For example, chosen appropriate variables to investigate a possible relationship with respect to the purpose of trying to establish if a bivariate investigation can provide supporting evidence for the classification. They have considered other possible variables and reflected on them with reference to the scientific report before deciding on ones that are appropriate with respect to their question. selected and used appropriate display(s) For example, produced appropriate scatter graph(s) with axes labelled. The explanatory and response variables are clear. identified features in the data and described the nature and strength of the relationship For example, stated from a visual inspection, with evidence, that the trend is linear rather than non-linear. They have described the strength with detailed references to visual aspects of scatter about the regression line. They have described, in context, the nature by stating that as one variable increases the other also tends to increase and justified this with reference to visual aspects of the display(s). Other features of the data have been discussed with supporting comments which reflect aspects which have been discussed in the scientific report. They have reflected on the strength and nature of the relationship with contextual comments. They may have acknowledged that they have found only a statistical relationship between the variables but that this does not imply causation. They may acknowledge that other factors (named) would impact on the variable. They may have reflected on features by discussing their relevance to a wider population. found an appropriate model For example, fitted an appropriate regression model to the data. The appropriateness of the model is justified by discussion of fit throughout the range of x-values in the data. Consideration has been given to aspects such as the number of data points. made a prediction For example, used the model to make a prediction for the response variable. The prediction is interpreted in context with the use of units and sensible rounding. It is justified with discussion on how precise it might be and has supported comments with references to statistical evidence from the analysis. They may have reflected on predictions by discussing their relevance to a wider population. communicated findings in a conclusion For example: clearly communicated each component of the cycle. They have used the results of their investigation for at least two pairs of variables to decide, with supporting comments from their analysis, if the classification of North Island dolphins as a separate subspecies can be supported. There are contextual references to the scientific report as part of the reflection on the process. The examples above are indicative of the evidence that is required. Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against the criteria in the Achievement Standard.     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