NCEA Level 1 Achievement Standard 1.1 (91944) PDF

Summary

This document provides assessment materials for the NCEA Level 1 Achievement Standard 1.1 (91944) for 2025. The materials outline the subject learning outcomes and what is expected of students in exploring data using a statistical enquiry process. This includes statistical methods and real-world applications in New Zealand.

Full Transcript

NCEA Level 1 Assessment Materials for 2025 Achievement Standard 1.1 (91944): Explore data using a statistical enquiry process What is being Subject Learning Outcome...

NCEA Level 1 Assessment Materials for 2025 Achievement Standard 1.1 (91944): Explore data using a statistical enquiry process What is being Subject Learning Outcome Notes assessed Exploring data using a Students are able to: Although not required by the structured approach (a explore data, which could include: standard, it is likely that many statistical enquiry o CensusAtSchool New Zealand — TataurangaKiTeKura Aotearoa schools will base investigations on process) (censusatschool.org.nz) The Statistical Enquiry Cycle when o Kaggle: Your Machine Learning and Data Science Community (kaggle.com) looking at a completed process. o Gapminder (gapminder.org) o NZ.Stat (stats.govt.nz). Students are not required to use a statistical inquiry process, including The Statistical Enquiry Cycle (PPDAC formulate their own correctly worded — Data Detective Poster (UPDATED JULY 2023!) – CensusAtSchool New question or investigative statement Zealand) for any levels of achievement. communicate findings in context, for example, in a verbal presentation with Teachers should ensure that supporting graphics, or a written report. students are working with well- formed questions or investigative For Merit, students are able to: statements. For examples of the complete a statistical inquiry process – a completed process is required. This will questions or investigative include an introduction or purpose and a conclusion. The introduction or purpose statements, refer to the teacher must include the investigative statement or question, which may have been guidance section for each internal supplied by the teacher. The student may write about where the data comes assessment activity (Explore data from, how it was collected (which may lead to a discussion on sources of using a statistical enquiry process | variation), why the data was collected, who will benefit from the investigation, or NCEA (education.govt.nz)). what they might expect to see in their findings (hypothesis thinking rather than a formal hypothesis statement). In writing a conclusion, the context must be used to answer the investigative question correctly or address the investigative statement. Page 27 NCEA Level 1 Assessment Materials for 2025 For Excellence, students are able to: incorporate contextual and statistical thinking — this needs to be shown in at least two places. These two types of thinking are likely (but not required) to be woven together. This does not mean a minimum of two separate instances of contextual thinking and two separate instances of statistical thinking, but the student work should be considered holistically. Students also need to reflect on the inquiry process that they have undertaken. Source of the data Students are able to: explain the source of the data. For primary data or data collected as part of the Assessment activities should be activity, explanation can include why the information to be collected was chosen chosen carefully and allow students and how it will be collected. For secondary data or existing data from a source, to access the information needed to explanation can include where it came from and how reliable it is. explore the source of the data. explain factors that influence the quality and reliability of the data. This may For primary data: include sources of variation and how it was managed for primary data or how it Students will have to think about may have been managed for a secondary data. how they will be collecting data. They can work as part of a group to plan how the data will be collected and to collect the data. As part of this process, they can discuss with others which sources of variation can and should, or should not, be managed as part of the collection process. For secondary data: Students should have ready access to how the data was collected, Page 28 NCEA Level 1 Assessment Materials for 2025 including the metadata. They may identify sources of variation that were managed, or likely managed in the collection. They may also suggest what they would have done or what could have been done. They may also explain what sources of variation may still be present in the data. There is no requirement in the standard to locate this explanation at any fixed point in the enquiry process. Explanations should be holistically looked at across the student evidence. Relationships between Students are able to: Data — numeric data must be used 2 numeric variables understand and answer questions about data, which could include the following: for a relationship investigation. o How can numeric and categorical data be collected? Continuous data is not required, but o What is the context of the data (including the overall context of the variables, the data must contain enough how the data was collected, dependent and independent variables)? natural variation within the values to o What types of variation occur in the collection of this type of data? allow for meaningful relationship o How can or should (or not) this variation be managed? analysis. Students may consider o What types of visualisations support this type of data? different sources of variation as part o What measures, including statistics, are useful for this type of data? of the discussion on the source of o What makes a good scatter graph? (y vs x in the title) the data, but this is not a requirement for achieving the standard. Page 29 NCEA Level 1 Assessment Materials for 2025 describe features of visualisations (and justify in context with measures for Merit): Assessment activities should be o direction and strength of relationship (Direction — positive or negative based chosen carefully. They should lead on bottom left to top right for positive or reverse for negative, quadrant count to an investigation that shows a ratio. Strength — a visual indicator and comment on low, medium, or high relationship to allow students to give scattering. Examples of visual indicators include brush stroke, rectangle, good evidence against the standard. cigar/sausage/oval shape, shading in/out, train tracks) o clusters (circling them on the graph and giving x interval and y interval for the When sourcing visualisations cluster) (compare with creating o unusual or interesting data points (state the co-ordinates, could comment on visualisations) students need to vertical distance from trend line or distance from the rest of the data ensure that they will be able to read patterns). sufficient information from the graph when looking for measures, such as consider different sources of variation in the data collection process for primary being reasonably able to read data data collection, for example: points and calculate gradient and o natural or real variation — the data needs to contain sufficient variation to intercept of a trend line. allow for analysis. For example, when looking discrete data such as age or shoe sizes 3 or 4 response options would not produce a viable data set. A line of best fit (including equation) o occasion-to-occasion variation — examples include blood pressure, speed of is not required to meet the standard object, blood sugar, height, heart rate, memory tests, activity where but if included can be done so continued practise would lead to increased ability, such as throwing a new or manually or digitally. Care should be foreign object like a gumboot — the more you do it the better your technique taken with the scale for each axis. becomes, so considering “how much practise” or “how many attempts” becomes a source of variation Formal regression analysis o measurement variation — examples include height, foot length, throwing (explaining least squares regression distance, speed, reaction time, time from planting to germination, seed size or using r2) is not required at this o induced variation — examples include the consistency of conditions at the level. time of data collection including wind, temperature, weight of objects thrown, and/or watering procedures. Page 30 NCEA Level 1 Assessment Materials for 2025 A prediction can be made using either visual inspection of the graph or substitution into the line of best fit equation. The exemplar marking schedules found in Teacher Guidance offer a single example of what a student may do in the lower section of the table titled “For example (description of possible student response to this activity)”. It does not define what is required for the standard, but it exemplifies what a student may do. In this case, for this exemplar, the student has decided to manually add “train tracks” to their graph. This is an example of what the student may have done. This is not a requirement for the standard. Comparison of one Students are able to: When sourcing visualisations numeric variable understand and answer questions about data which could include the following: (compare with creating between two o How can numeric and categorical data be collected? visualisations) students need to categories o What is the context of the data (including the overall context of the variables, ensure that they will be able to read how the data was collected, dependent and independent variables)? sufficient information from the graph o What types of variation occur in the collection of this type of data? when looking for measures, such as o How can or should (or not) this variation be managed? summary statistics. Page 31 NCEA Level 1 Assessment Materials for 2025 o Why is random sampling important? o What effect does sample size have? Choosing a sample — for digital or o What types of visualisations support this type of data? readily available data sets, samples o What measures, including statistics, are useful for this type of data? of size 100 or 1000 are o What makes a good visualisation? recommended. describe features of visualisations (and justify in context with measures for A box and whisker graph is needed Merit): for all levels of achievement, and o centre (median, mean) dot plots are strongly o spread (interquartile range, range) recommended. These can be o shape (uniform, rectangular, modality, skew) supported by other visualisations, o shift and overlap of two groups (position of the middle 50% sections through for example stem and leaf, or use of quartiles, ¾ - ½ rule, distance between the median as a proportion of histogram. overall visible spread, applied visually) o clusters (location of data points given) Summary statistics are not required o unusual or interesting data points (specific values given). by the standard for Achieved but should be included for good For Merit and Excellence: statistical practice. They are needed make a call for a sample to population using the following information: when justifying for Merit and o the sample must be random Excellence. o in all cases, if there is no overlap between the middle 50% sections, a call can be made Making a call — in order to o in samples of size 20-40, a call should be made using the ¾ - ½ rule, where complete an enquiry process, clear students will need to make a sample o in samples of size 100 or more, a call should be made visually using the to population inference. The distance between the medians as a proportion of overall visible spread. process for making the call is o the size of the smaller group in the sample should be used as the basis for determined by the sample size. making the call. Page 32 NCEA Level 1 Assessment Materials for 2025 consider different sources of variation in the data collection process, for Students may consider different example: sources of variation as part of the o natural or real variation — discussion of this may show up in a reflection on discussion on the source of the the process, particularly where the samples do not show a difference, there data, but this is not a requirement may be strong overlap with sampling variation in comparison investigations. for achieving the standard. o occasion-to-occasion variation – examples include speed or aptitude tests where practising the tasks leads to better performance, weight of an animal, body temperature. o measurement variation — examples include weight, cubit length, standing time, leaf width/length/weight, energy consumption, mass of any object, jumping distance. o induced variation — examples include consistency of the conditions at the time of data collection including type of activity undertaken to raise heart rate, oxygen saturation levels, water temperature, size of objects tested. o sample variation — examples include sampling method, size of sample, expected results for different samples, variation within each sample. Time series Students are able to: When sourcing visualisations investigations understand and answer questions about data including the following: (compare with creating o How can data be collected over time? visualisations) students need to o What is the context of the data (including the time periods and the values ensure that they will be able to read being recorded)? sufficient information from the graph o What types of variation occur in the collection of this type of data? when looking for measures, such as o How can or should (or not) this variation be managed? start-and-end points or the points o What types of visualisations support this type of data? needed to calculate gradient and o What measures, including statistics, are useful for this type of data? intercept of a trend line. Page 33 NCEA Level 1 Assessment Materials for 2025 o What makes a good time series graph? When using technology students describe features of visualisations (and justify in context with measures for can add a digital trend. Merit): o trend of time series (direction, gradient) Students are not required to o unusual or interesting data points, spikes, or troughs (specific points given) calculate seasonal effects. o seasonality, cycles (timeframes) o patterns (timeframes) Time series investigations are useful for making future forecasts. A consider different sources of variation in the data collection process, for completed investigation needs to example: include a forecast. Forecasts could o occasion-to-occasion variation — examples include temperature during the be made using a visual inspection of day (determining at which point it will be measured), blood pressure, heart the graph including use of any trend rate, height, weight line. o measurement variation — examples include height of pole vault, distance of javelin throw, waterflow rate, canteen food waste, city recycling levels Formal long-term trend line analysis o induced variation — examples include consistency of the conditions at the lies outside the scope of this time of data collection including rainfall/watering levels, ambient Achievement Standard. temperature, wind assistance. As part of their investigation students may reason that a forecast is not useful. For Merit, this should be with justification. For Excellence, this should be with non-trivial explanations and extended abstract thinking. Care should be taken when using student collected data. Students Page 34 NCEA Level 1 Assessment Materials for 2025 should have access to data for assessment that will allow them to sufficiently demonstrate all their learning. Data without a clear trend might make this difficult. Students may consider different sources of variation as part of the discussion on the source of the data, but this is not a requirement for achieving the standard. Probability Students are able to: The intent of an experimental investigations understand and answer questions about data including the following: probability investigation is to o What types of experiment can be conducted to collect data? conduct an experiment to collect o What is the context of the data? data and describe observed o What types of variation occur in the collection of this type of data? probabilities in context. In some o How can or should (or not) this variation be managed? situations, with theoretical o What types of visualisations support this type of data? probabilities it may be appropriate to o What makes a good visualisation? use simple simulations. Simulations o What measures, including statistics, are useful for this type of data? could also be run with collected data where a theoretical model does not describe features of visualisations (and justify in context with measures for exist. An experiment using a tool Merit): with a simple outcome (dice, o clusters (location of data points given) spinner) needs to use digital o unusual or interesting data points (specific values given) simulation to be at the right level. o centre (mean, median, mode) o spread (interquartile range, range) o shape (uniform, rectangular, modality, skew) o unusual or interesting data points (specific values given) Page 35 NCEA Level 1 Assessment Materials for 2025 o patterns. Achievement Standard 1.2 (91945): Use mathematical methods to explore problems that relate to life in Aotearoa New Zealand of the Pacific What is being Subject Learning Outcome Notes assessed Number Students are able to: From Conditions of Assessment: operate with more complex rates and ratios involving metric unit conversions to solve problems — examples include blood-alcohol levels, speed, heart rate, pay Number: rates, density, scale factor or unit cost. For example, A car travels from A to B in o Reasoning with linear proportion, 25 minutes at 100 kilometres per hour. How long will the trip take at 80 kilometres including inverse percentage per hour? This can be represented as 25 x 100 = 80x. change or more complex rates and ratios. operate with percentages, which includes: o Integer exponents or scientific o using percentages to solve problems — for example, calculating percentage form. of a quantity, expressing a ratio as a percentage o using percentages in both directions — for example, inverse percentages or Linear proportion also includes the finding the original amount examples shown on the left. o examples from TKI Senior Secondary guide include the following: ▪ which is the stronger concentration of syrup to water, 2:7 or 3:11? This can be represented as 2/9 > 3/14 (the fractions represent the part to whole relationships). ▪ for what positive integer values of x is this inequality true, 2/5 > 6/x? ▪ calculate GST inclusive and exclusive values ▪ using ratios with objects or pictures. operate on very large and on very small numbers using scientific notation Page 36

Use Quizgecko on...
Browser
Browser