Internal Assessment Resource for Achievement Standard 91035 V2

Internal Assessment Resource for Achievement Standard 91035 V2

<p>Internal assessment resource for Achievement Standard 91035 v2 PAGE FOR TEACHER USE Internal Assessment Resource</p><p>Mathematics and Statistics Level 1</p><p>This resource supports assessment against:</p><p>Achievement Standard 91035</p><p>Investigate a given multivariate data set using the statistical enquiry cycle</p><p>Resource title: Driven to distraction</p><p>4 credits</p><p>Quality assurance status These materials have been quality assured by NZQA.</p><p>QAAM number 3063 </p><p>Authenticity of evidence Teachers must manage authenticity for any assessment from a public source, because students may have access to the assessment schedule or student exemplar material.</p><p>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.</p><p> www.education.nzta.govt.nz Internal assessment resource for Achievement Standard 91035 v2 PAGE FOR TEACHER USE</p><p>Internal Assessment Resource Achievement Standard Mathematics and Statistics 91035 v2: Investigate a given multivariate data set using the statistical enquiry cycle Resource Title: Driven to distraction Level: 1 Credits: 4</p><p>Teacher guidelines</p><p>The following guidelines are designed to ensure that teachers can 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 91035. The achievement criteria and the explanatory notes contain information, definitions, and requirements that are crucial when interpreting the standard and assessing students against it.</p><p>Context/setting This activity involves students using the statistical enquiry cycle to make comparisons between groups in a population. The context for this resource is a sample of 120 reaction test and typing test results from students at Te Horo High School in 2014. This task could be adapted to fit another similar data set with at least two category variables and three numerical variables. The sample must be big enough so that for any category variable there are about 25 - 30 records in each category.</p><p>Conditions This activity requires at least two separate sessions. Confirm the timeframe with your students. Students must work independently. In the first session, students familiarise themselves with the data and pose two comparison investigative questions. Check students’ investigative questions and, if required, give them time to correct or improve them before they begin the second session. If they are unable to produce at least one suitable investigative question, give feedback of a general nature indicating which of the question criteria have not been met – do not provide the question. If more than minimal feedback is needed, the student is not ready for assessment against this standard. The second (and subsequent) sessions are for students to carry out the analysis and write conclusions. Any technology is allowed for the analysis. </p><p>Resource requirements</p><p>Provide students with an electronic and hard copy (Resource B) version of the data set for their analysis. </p><p> www.education.nzta.govt.nz Internal assessment resource for Achievement Standard 91035 v2 PAGE FOR STUDENT USE Internal Assessment Resource Achievement Standard Mathematics and Statistics 91035 v2: Investigate a given multivariate data set using the statistical enquiry cycle Resource Title: Driven to distraction Level: 1 Credits: 4 Achievement Achievement with Merit Achievement with Excellence Investigate a given Investigate a given Investigate a given multivariate data set using the multivariate data set using the multivariate data set using the statistical enquiry cycle. statistical enquiry cycle, with statistical enquiry cycle, with justification. statistical insight.</p><p>Student instructions</p><p>Introduction Students in a Year 11 class at Te Horo High School in 2014 came across an article discussing things that impact on driving ability. They decided to carry out a survey to look at the impact that reading a text message and feeling tired has on concentration levels. The students used an online reaction test to measure reaction times and an online typing test to measure typing speed and typing accuracy. </p><p>This assessment requires you to undertake a statistical investigation using the randomly selected data from students of Te Horo High School in 2014. First you will pose two investigative questions that can be answered using the data set. Then you will analyse the sample and form a conclusion for one of your questions. This assessment is to be completed independently. The quality of your discussion and reasoning and how well you link this to the context will determine the overall grade.</p><p>Task As you carry out this task you will use the statistical enquiry cycle (Problem, Plan, Data, Analysis, Conclusion).</p><p>Problem Pose two investigative questions that can be explored using the data from students at Te Horo High School in 2014. See Resource A for part of the data and a description of the variables. Your investigative questions must be comparison questions. A suitable comparison investigative question is one that:  reflects the population  has a clear variable to investigate  compares the values of a continuous variable across different categories  can be answered with the data.</p><p>Page 3 of 13 Internal assessment resource for Achievement Standard 91035 v2 PAGE FOR STUDENT USE For each question, state the variable you are investigating and the groups you are comparing. Now choose one of your two questions for investigation using the data found in Resource B.</p><p>Plan and data The sample can be considered representative of all students attending Te Horo High School in 2014.</p><p>Analysis Draw at least two appropriate graphs that show different features of the data in relation to your investigative question. Give appropriate summary statistics. Describe features of the distributions comparatively, for example, shape, middle 50%, shift, overlap, spread, unusual or interesting features. </p><p>Conclusion Write a conclusion summarising your findings. The conclusion needs to include an informal inference in response to your investigative question and be supported with relevant evidence. </p><p>Page 4 of 13 Internal assessment resource for Achievement Standard 91035 v2 PAGE FOR STUDENT USE Resources</p><p>Resource A – Driven to distraction </p><p>Details of sample and variables</p><p>The table below shows a small part of the data set that you will be using to complete the investigation and a description of the variables. Your teacher will give you a random sample of 120 reaction test and typing test results from students at Te Horo High School in 2014 in electronic and hard copy form. </p><p>The sample in the data set was randomly selected from the students at Te Horo School in 2014. Tests of the types used in the survey can be found at http://www.bbc.co.uk/science/humanbody/sleep/sheep/reaction_version5.swf and http://10fastfingers.com/typing-test/english.</p><p>Tired Texting Rxn time Speed Accuracy (ms) (characters per minute) (%) NotTired NotText 207 181 99.2 NotTired Text 304 199 94.6 Tired Text 558 138 87.6 NotTired Text 304 199 94.6 NotTired Text 450 176 84.6</p><p>Variable Description of variables Tired Self-assessment as to whether or not the student is tired (Tired or NotTired) Texting Whether or not the student was reading a text message while taking the tests: Text = were reading a text message, NotText = were not reading a text message Rxn time (milliseconds) Reaction time as measured on an online reaction test site Speed (characters per Speed as measured on an online typing site minute) Accuracy (% of words Accuracy rate as measured on an online typing site correct)</p><p>Page 5 of 13 Internal assessment resource Mathematics and Statistics 1.10 for Achievement Standard 91035 v2 PAGE FOR STUDENT USE</p><p>Resource B – Driven to distraction Tired Texting Rxn time Speed Accuracy NotTired NotText 202 178 98.7 NotTired NotText 207 181 99.2 NotTired NotText 237 195 95.6 NotTired NotText 238 195 96.8 NotTired NotText 177 212 93.2 NotTired NotText 227 191 94.6 NotTired NotText 226 197 92.8 NotTired NotText 211 184 92.1 NotTired NotText 316 228 98.4 NotTired NotText 211 197 93.6 NotTired NotText 259 204 97.3 NotTired NotText 197 178 98.5 NotTired NotText 247 199 96.1 NotTired NotText 216 186 94.0 NotTired NotText 228 192 96.9 NotTired NotText 274 210 96.0 NotTired NotText 228 201 95.2 NotTired NotText 228 202 96.2 NotTired NotText 228 189 89.1 NotTired NotText 218 187 98.2 NotTired NotText 235 194 89.8 NotTired NotText 218 244 89.5 NotTired NotText 187 174 87.9 NotTired NotText 237 195 91.4 NotTired NotText 217 243 86.7 NotTired NotText 288 216 85.9 NotTired NotText 227 192 87.5 NotTired NotText 295 219 96.5 NotTired NotText 217 236 98.0 NotTired NotText 213 185 91.6 NotTired Text 372 167 93.9 NotTired Text 372 161 94.9 NotTired Text 397 156 93.2 NotTired Text 287 158 92.7 NotTired Text 473 165 88.8 NotTired Text 382 165 92.2 NotTired Text 501 153 88.5 NotTired Text 439 171 87.2 NotTired Text 471 187 94.0 NotTired Text 459 156 89.2 NotTired Text 294 160 91.6 NotTired Text 324 151 81.3 Tired Texting Rxn time Speed Accuracy</p><p>Page 6 of 13 Internal assessment resource Mathematics and Statistics 1.10 for Achievement Standard 91035 v2 PAGE FOR STUDENT USE</p><p>NotTired Text 325 156 93.5 NotTired Text 294 167 90.6 NotTired Text 417 198 91.2 NotTired Text 449 166 91.5 NotTired Text 372 159 92.3 NotTired Text 380 180 90.1 NotTired Text 424 182 85.7 NotTired Text 304 199 94.6 NotTired Text 450 176 84.6 NotTired Text 434 162 84.7 NotTired Text 381 167 82.7 NotTired Text 364 168 86.7 NotTired Text 459 176 82.3 NotTired Text 459 172 79.9 NotTired Text 364 194 83.8 NotTired Text 441 163 91.9 NotTired Text 412 162 87.8 NotTired Text 334 165 87.1 Tired NotText 261 202 89.3 Tired NotText 293 176 94.3 Tired NotText 299 183 90.8 Tired NotText 272 160 92.2 Tired NotText 329 167 88.4 Tired NotText 299 163 89.8 Tired NotText 376 163 87.7 Tired NotText 282 170 87.0 Tired NotText 238 181 93.5 Tired NotText 274 154 88.9 Tired NotText 331 171 90.8 Tired NotText 288 154 92.8 Tired NotText 354 190 91.6 Tired NotText 264 157 90.2 Tired NotText 302 153 92.3 Tired NotText 292 194 91.5 Tired NotText 309 170 90.4 Tired NotText 334 172 90.6 Tired NotText 321 166 85.7 Tired NotText 295 161 94.0 Tired NotText 299 199 84.8 Tired NotText 248 159 84.9 Tired NotText 346 170 82.1 Tired NotText 220 158 86.3 Tired NotText 295 176 82.1 Tired NotText 309 167 79.7 Tired Texting Rxn time Speed Accuracy Tired NotText 337 157 83.6 Tired NotText 457 162 91.9</p><p>Page 7 of 13 Internal assessment resource Mathematics and Statistics 1.10 for Achievement Standard 91035 v2 PAGE FOR STUDENT USE</p><p>Tired NotText 309 169 93.1 Tired NotText 409 167 86.9 Tired Text 472 160 88.4 Tired Text 463 142 89.6 Tired Text 598 164 89.4 Tired Text 541 147 88.9 Tired Text 341 140 83.4 Tired Text 331 146 87.9 Tired Text 500 156 84.3 Tired Text 577 172 84.9 Tired Text 551 143 88.6 Tired Text 586 134 83.8 Tired Text 588 139 86.7 Tired Text 594 140 76.1 Tired Text 567 144 89.7 Tired Text 519 142 86.5 Tired Text 579 147 82.7 Tired Text 560 141 85.9 Tired Text 586 168 88.1 Tired Text 556 146 86.0 Tired Text 577 153 82.0 Tired Text 569 122 89.3 Tired Text 449 157 81.1 Tired Text 428 143 79.9 Tired Text 557 152 77.8 Tired Text 456 135 83.3 Tired Text 448 128 77.4 Tired Text 557 137 74.9 Tired Text 567 142 78.8 Tired Text 558 138 87.6 Tired Text 528 175 85.4 Tired Text 567 154 83.9</p><p>Page 8 of 13 Internal assessment resource Mathematics and Statistics 1.10 for Achievement Standard 91035 v2 PAGE FOR STUDENT USE</p><p>Page 9 of 13 Internal assessment resource Mathematics and Statistics 1.10 for Achievement Standard 91035 v2 PAGE FOR STUDENT USE</p><p>Assessment schedule: Mathematics and Statistics 91035 Driven to distraction</p><p>Teacher note: You will need to adapt this assessment schedule to include examples of the types of responses that can be expected.</p><p>Evidence/Judgements for Achievement Evidence/Judgements for Achievement with Evidence/Judgements for Achievement with Merit Excellence The student shows evidence of investigating a given The student shows evidence of investigating a given The student shows evidence of investigating a given multivariate data set using each component of the multivariate data set using each component of the multivariate data set using each component of the statistical enquiry cycle. statistical enquiry cycle with justification. statistical enquiry cycle with statistical insight. The student: The student: The student:  poses an appropriate comparison question  poses an appropriate comparison question  poses an appropriate comparison question  draws graph(s) and gives summary statistic(s)  draws graph(s) and gives summary statistics  draws graphs and gives summary statistics that allow features of the distributions to be that allow features of the distributions to be which allow features of the distributions to be described in relation to the question described in relation to the question described in relation to the question – at least  writes statements which describe comparative  writes statements, with evidence, which two different graphs showing different features features of the distributions in context – at least describe comparative features of the are expected two statements, describing different features, distributions in context – at least two  writes statements with evidence that describe are expected statements, describing different features, are key comparative features of the distributions in  answers the comparison question in the context expected context – at least three statements describing of the investigation or makes a correct  makes a correct informal inference about the different features are expected, key features comparison using an informal inference about population from the sample data which shows include: middle 50%, shift and overlap, shape, the population. an understanding of sampling variability or of spread, any unusual or interesting features For example: the context  makes a correct informal inference about the  answers the comparison question, with at least population from the sample data which shows The student poses an appropriate comparison one statement of supporting evidence. an understanding of sampling variability and of question: For example: the context Do the reaction times of students from Te Horo The student poses an appropriate comparison  answers the comparison question with High School in 2014 who are reading a text question: reference to the population and key supporting message tend to be slower than the reaction times evidence summarised in context – what the of students from Te Horo High School in 2014 who Do the reaction times of students from Te Horo statistical basis for the claim is and the effect of are not reading a text message? High School in 2014 who are reading a text sampling variability or does the claim make message tend to be slower than the reaction times The student draws at least one graph, for example, sense considering the actual situation is of students from Te Horo High School in 2014 who a dot plot or a box plot and provides at least one expected. are not reading a text message? summary statistic for each group, for example, a For example: modal group. The student draws at least one graph, for example, The student poses an appropriate comparison a dot plot or a box plot and gives summary </p><p>Page 10 of 13 Internal assessment resource Mathematics and Statistics 1.10 for Achievement Standard 91035 v2 PAGE FOR STUDENT USE</p><p>The student describes at least two comparative statistics. question: features of the distributions in context: The student describes, with evidence, at least two Do the reaction times of students from Te Horo High The box and whisker graph shows that the centre of comparative features in context: School in 2014 who are reading a text message the distribution of reaction times (median reaction The interquartile range of the reaction times for tend to be slower than the reaction times of time) for those reading a text message is longer those not reading a text message (73 ms) is less students from Te Horo High School in 2014 who are than for those who are not reading a text message. than half the interquartile range of reaction times for not reading a text message? The box and whisker graph also shows that the those who are reading a text message (176 ms). The student draws at least two graphs, for example, interquartile range for those reading a text message This means that there is more spread for the middle a dot plot and a box plot and provides summary is also longer, which suggests that spread of the 50% of reaction times for those reading text statistics. messages than for those students who are not middle 50% of reaction times is greater when The student reflects on at least three features of the reading text messages. reading a text message. distribution comparatively. The box and whisker graph shows that the centre of The student answers the comparative question in The median reaction time for those not reading a context. the distribution of reaction times (median reaction time) for those not reading a text message is much text message is much faster (263 ms) than the Overall, reaction times tend to be longer when faster (263 ms) than the median reaction time for median reaction time for those who are reading a reading a text message compared to when not those who are reading a text message (458 ms). I text message (458 ms). I can see from the box and reading a text message. can see from the box and whisker graph that the whisker graph that the median reaction time for median reaction time for each group is well outside each group is well outside of the middle 50% of of the middle 50% of reaction times for the other reaction times for the other group. group. I can see from the box and whisker graph that there is no overlap of the middle 50% of reaction times for those who are reading a text message with the The student makes a correct informal inference middle 50% of the reaction times for those who are about the population from the sample data which not reading a text message. The lower quartile for shows an understanding of sampling variability or of those reading a text message is a much slower the context. reaction time (381 ms) than the upper quartile of the AND reaction times for those who were not reading a text The student answers the comparison question, with message (300 ms). This tells me that the at least at least one statement of supporting evidence. 75% of reaction times for those reading a text message are slower than the fastest 75% of the reaction times for those students not reading a text Because there is no overlap of the middle 50% of message. reaction times for those who are reading a text message and those who are not, and the median The middle 50% of reaction times when reading a score for each group is outside of the middle 50% of text message are from 381 to 557 ms, which are reaction times for the other group, I can make the further up the scale (slower times) than the middle claim that the reaction times of students from Te 50% of reaction times when not reading a text Horo High School in 2014 who are reading a text message, which are 227 to 300 ms There is also a message do tend to be slower than the reaction bigger spread in the middle 50% of reaction times </p><p>Page 11 of 13 Internal assessment resource Mathematics and Statistics 1.10 for Achievement Standard 91035 v2 PAGE FOR STUDENT USE</p><p> times of students who are not reading a text when reading a text message. message. In the dot plot, the reaction times for those students This claim seems reasonable as I know that I am not reading a text message seem to have two distracted when I am reading a text message and peaks, one centred around 220 ms and the other at the law is that you cannot text while driving so I approximately 300 ms. This bimodal nature would would expect that reading a text message would be consistent with the data which has two groups mean a slower reaction time. within those not reading a text message: students who assessed themselves as tired and those who said they were not tired. The tired students are likely to have slower (longer) reaction times. The two groups (tired and not tired) are not apparent in the reaction times for students who are reading a text message, although there is a cluster of reaction times centred around 580 ms which may be due to those who are tired. For example the reaction times of 588 ms and 594 ms both correspond to times for students who assessed themselves as being tired. The student makes a correct informal inference about the population from the sample data, which shows an understanding of sampling variability and of the context, and answers the comparison question with reference to the population and key supporting evidence summarised in context. The students at Te Horo High School in 2014 who are reading a text message do tend to have slower (longer) reaction times than the students who are not reading a text message. This claim is based on the fact that in the sample the median for the students’ reaction times who are reading a text message is higher than the middle 50% of reactions times for the students who aren’t reading a text message. This evidence is sufficient to suggest that what I see in my samples is what is happening back in the population (students at Te Horo High School in 2014). The claim about reaction times makes sense as it would be difficult to concentrate on a reaction time </p><p>Page 12 of 13 Internal assessment resource Mathematics and Statistics 1.10 for Achievement Standard 91035 v2 PAGE FOR STUDENT USE</p><p> test and read a text message at the same time so it would take longer to react. This also makes sense as texting was identified in the article read by the Year 11 students at Te Horo High School as something which impacted on driving ability as it makes it difficult to concentrate on driving and it is something which is banned when driving. If I was to repeat this sampling process with a new sample from Te Horo High School in 2014, I would expect there to be some differences in the sample statistics and graphs due to sampling variability. Even so, I would expect to see reactions times for those who were reading a text message tending to be longer than those who were not reading a text message, as the distance between the medians in my original sample is sufficiently large, with the median reaction time for students reading a text message being 458 ms, which is 158 ms higher than the upper quartile of reaction times for those not reading a text message. So I would not expect my claim to change.</p><p>Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against the criteria in the Achievement Standard.</p><p>Page 13 of 13</p>

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