OCR GCSE Year 8-01 Shape and Skew PDF

Unit of Learning: Year 8 – 01. Shape and skew Duration 5 weeks Start date: Completed date: Outcomes: MAO-WM-01, MA4-DAT-C-01, MA4-DAT-C-02...

Unit of Learning: Year 8 – 01. Shape and skew Duration 5 weeks Start date: Completed date: Outcomes: MAO-WM-01, MA4-DAT-C-01, MA4-DAT-C-02 Life skills: MALS-PAT-01, MALS-LEN-01 MA4-DAT-C-01: classifies and displays data using a variety of graphical representations MALS-PAT-01: recognises and applies patterns in everyday contexts MA4-DAT-C-02: analyses simple datasets using measures of centre, range and shape of the data MALS-LEN-01: measures and uses length in everyday contexts This program of learning addresses content from the focus areas of Data classification and visualisation and Data analysis. The lessons and sequences in this program of learning are designed to allow students to explore how to analyse frequency distribution graphs using measures of centre and spread, and shape and skew of a graph. Core Syllabus Content Background Knowledge Data classification and visualisation (partial) Classify data as either numerical (discrete or continuous) or categorical (nominal or ordinal) variables Define a variable in the context of statistics as any characteristic, number or quantity that can be measured or counted Display data using graphical representations relevant to the purpose of the data Represent single datasets using graphs, including frequency histograms and polygons, dot plots, stem-and-leaf plots, divided bar graphs, column graphs, line graphs, sector graphs and pictograms, with or without digital tools Select the type of graph best suited to represent various single datasets and justify the choice of graph Interpret data in graphical representations Key Terms Identify and interpret data displayed on graphs Identify features of graphical representations to draw conclusions Data analysis (partial) Calculate and compare the mean, median, mode and range for simple datasets Describe and interpret data displays using mean, median and range Assessment Identify and describe datasets as having no modes (uniform), one mode (unimodal), 2 modes (bimodal) or multiple modes In-class assessment: Interprets and analyses (multimodal) data by calculating key statistics and assessing Compare simple datasets using the mean, median, mode and range Interpret the effect individual data points have on measures of centre and range the impact of individual data points Informally identify clusters, gaps and outliers in datasets and give reasons for their occurrence in the context of the data Identify and explain the impact of adding or removing data values that are clustered at one end of a dataset on the measures of Summative assessment: Exam centre Identify and explain the impact of outliers on the measures of centre and range Determine and justify the most appropriate measure of centre to summarise the data in its context Analyse datasets presented in various ways and draw conclusions Identify and describe the shape and distribution of a dataset using the terms symmetrical, negatively skewed and positively skewed Define a census as a study of every unit, everyone or everything in a population Define a sample as a subset of units in a population selected to represent all units in a population of interest Draw conclusions and make informed decisions about data gathered using data-collection techniques, including census and sampling, which is then presented in tables, graphs and charts Lesson sequence Duration Additional resources Lesson Teaching and Learning Activity (no. of lessons) 01. broccoli soup Students will explore the first steps of a statistical investigation by considering when a census is 1 needed and how to avoid bias when selecting a sample to collect data. 02. goal-free soccer Students learn how to draw and interpret histograms and polygons in reference to statistics in 1 sport. 03. the big sick Students determine whether a company should pay for the flu vaccine by analysing data to 1 determine the mean number of sick days used by staff each year. 04. shooting hoops Students learn how to find median and range from a frequency table and graphs by testing 1-2 their skills of throwing scrunched paper into a bin from a distance. 05. footy fit Students will draw a stem-and-leaf plot using data from NRL player statistics. They will then 1 analyse the data using the range, mode, median and mean and draw conclusions based on their findings. 06. picture perfect Students describe the skewness of frequency histograms and polygons in reference to exposure 1-2 in photographs. 07. pass it on graph Students play a game of ‘Pass it on’, using different graphs to highlight the need for shared 1 Digital device style terminology of the features to describe them. 08. wisdom of the Students explore the effect on measures of centre and spread when data is added or removed. 1 crowd 09. the best centre Students explore how the location of the mean, median and mode in frequency graphs to 1 determine the best measure of centre. 10. random samples Students explore why we can trust sample data and how collection bias can appear when using 1-2 samples. 11. survival of the Students revise measures of centre and spread by splitting people into teams for the television 1 fittest show ‘Survivor’. Learning episode 1 – broccoli soup Teaching and learning activity Students will explore the first steps of a statistical investigation by considering when a census is needed and how to avoid bias when selecting a sample to collect data. Syllabus content Define a census as a study of every unit, everyone or everything in a population Define a sample as a subset of units in a population selected to represent all units in a population of interest Table 1 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes Broccoli soup (DOCX 430.7 KB) Class set of Appendix A and C, Duration: 1 lesson printed Learning intention Appendix B, printed (one per pair of To be able to understand factors to consider when collecting students) data. Appendix D, printed and cut into Success criteria individual cards (one card per pair I can explain the difference between a census and a of students) sample. Broccoli soup (PPTX 3.0 MB) I can identify when a census is needed in data PowerPoint collection. I can avoid bias when selecting a sample to collect data. Learning episode 2 – goal-free soccer Teaching and learning activity Students learn how to draw and interpret histograms and polygons in reference to statistics in sport. Syllabus content Represent single datasets using graphs, including frequency histograms and polygons, dot plots, stem-and-leaf plots, divided bar graphs, column graphs, line graphs, sector graphs and pictograms, with or without digital tools Select the type of graph best suited to represent various single datasets and justify the choice of graph Table 2 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes Goal-free soccer (DOCX 1.0 MB) Appendix A and Appendix B, Duration: 1 lesson printed (one per pair of students) Learning intention Goal-free soccer (PPTX 4.1 MB) To be able to draw and interpret a frequency histogram PowerPoint and polygon. Success criteria I can draw a frequency histogram from a dataset. I can draw a frequency polygon from a dataset. I can interpret a frequency histogram and polygon to draw conclusions. Learning episode 3 – the big sick Teaching and learning activity Students determine whether a company should pay for the flu vaccine by analysing data to determine the mean number of sick days used by staff each year. Syllabus content Define a variable in the context of statistics as any characteristic, number or quantity that can be measured or counted Describe and interpret data displays using mean, median and range Compare simple datasets using the mean, median, mode and range Table 3 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes The big sick (DOCX 571.7 MB) Class set of Appendix A, B, and C, Duration: 1 lesson printed Learning intention The big sick (PPTX 2.3 MB) To be able to find the mean from a frequency table and PowerPoint graphs. Success criteria I can record data in a frequency. I can create and complete an 𝒇𝒙 column in a frequency table. I can find the mean from a frequency table. I can use the mean from a dataset to inform decisions. Learning episode 4 – shooting hoops Teaching and learning activity Students learn how to find median and range from a frequency table and graphs by testing their skills of throwing scrunched paper into a bin from a distance. Syllabus content Describe and interpret data displays using mean, median and range Compare simple datasets using the mean, median, mode and range Table 4 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes Shooting hoops (DOCX 1.4 MB) Class sets of Appendix A, B and C, Duration: 1–2 lessons printed Learning intention Shooting hoops (XLSX 104.2 MB) To be able to find the median and range from a Excel Spreadsheet frequency graph. Waste bin (one per 4–5 students) Success criteria Masking tape (one per 4–5 I can draw a dot plot from a frequency table. students) I can find the range from a frequency table and graph. Tape measures (one per 4–5 I can find the median from a frequency graph. students) A piece of A4 paper (one per student) Learning episode 5 – footy fit Teaching and learning activity Students will draw a stem-and-leaf plot using data from NRL player statistics. They will then analyse the data using the range, mode, median and mean and draw conclusions based on their findings. Syllabus content Describe and interpret data displays using mean, median and range Compare simple datasets using the mean, median, mode and range Table 5 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes Footy fit (DOCX 442.4 KB) Appendix A, B and D, printed (one Duration: 1 lesson per group of 3) Learning intention Appendix C, printed A3 (one per To be able to analyse data in a stem-and-leaf plot. group of 3) Success criteria Footy fit (PPTX 3.8 MB) PowerPoint I can draw a stem-and-leaf plot. Adhesive putty I can calculate the range, mode, median and mean from A3 plastic pockets (one per group a stem-and-leaf plot. of 3) I can use data from a stem-and-leaf plot to justify a decision. Learning episode 6 – picture perfect Teaching and learning activity Students describe the skewness of frequency histograms and polygons in reference to exposure in photographs. Syllabus content Identify and interpret data displayed on graphs Identify features of graphical representations to draw conclusions Describe and interpret data displays using mean, median and range Identify and describe the shape and distribution of a dataset using the terms symmetrical, negatively skewed and positively skewed Table 6 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes Picture perfect (DOCX 4.5 MB) Appendix A, printed (one per pair Duration: 1–2 lessons of students) Learning intention Appendix B, printed in colour (one To know about the shape of a frequency graph. per pair of students) Success criteria Picture perfect (PPTX 10.5 MB) I can describe the skewness of a frequency graph. PowerPoint I can explain whether to use the median or mean as a measure of centre for different shaped frequency graphs. I can interpret a frequency graph to draw conclusions. Learning episode 7 – pass it on graph style Teaching and learning activity Students play a game of ‘Pass it on’, using different graphs to highlight the need for shared terminology of the features to describe them. Syllabus content Identify and interpret data displayed on graphs Identify features of graphical representations to draw conclusions Identify and describe datasets as having no modes (uniform), one mode (unimodal), 2 modes (bimodal) or multiple modes (multimodal) Informally identify clusters, gaps and outliers in datasets and give reasons for their occurrence in the context of the data Table 7 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes Pass it on graph style (DOCX 678.2 KB) Appendix A, printed and cut into Duration: 1 lesson individual cards (one per pair of Learning intention students) (if not using technology) To be able to describe the features of a graph. Pass it on graph style (XLSX 227.5 KB) Success criteria Excel Spreadsheet I can identify clusters, gaps and outliers in graphs. Digital device per pair of students I can describe a dataset as having no modes, one mode, (optional) 2 modes or multiple modes. Learning episode 8 – wisdom of the crowd Teaching and learning activity Students explore the effect on measures of centre and spread when data is added or removed. Syllabus content Identify and explain the impact of adding or removing data values that are clustered at one end of a dataset on the measures of centre Identify and explain the impact of outliers on the measures of centre and range Table 8 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes Wisdom of the crowd (DOCX 416.1 KB) Class set of Appendix A and B, Duration: 1 lesson printed Learning intention Wisdom of the crowd (PPTX To understand how data affects the mean, median, 1.9 MB) PowerPoint range and mode. Success criteria I can explain what happens to the mean, median, range and mode when an outlier is added. I can explain what happens to the mean, median, range and mode when a cluster of numbers is added or removed from a dataset. I can add or remove data to increase or decrease the mean, median and mode. Learning episode 9 – the best centre Teaching and learning activity Students explore how the location of the mean, median and mode in frequency graphs to determine the best measure of centre. Syllabus content Describe and interpret data displays using mean, median and range Determine and justify the most appropriate measure of centre to summarise the data in its context Table 9 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes The best centre (DOCX 773.8 KB) Class set of Appendix A, printed. Duration: 1 lesson Appendix B, printed and cut into Learning intention individual cards (one per 5 To be able to select the best measure of centre to students) represent a dataset. Appendix C and D, printed (one per Success criteria 3 students) I can explain how an outlier affects the measure of The best centre (PPTX 1.4 MB) centre of a dataset. PowerPoint I can explain how a cluster affects the measure of centre of a dataset. I can select and explain the best measure of centre given the graph of its data. Learning episode 10 – random samples Teaching and learning activity Students explore why we can trust sample data and how collection bias can appear when using samples. Syllabus content Describe and interpret data displays using mean, median and range Compare simple datasets using the mean, median, mode and range Draw conclusions and make informed decisions about data gathered using data-collection techniques, including census and sampling, which is then presented in tables, graphs and charts Table 20 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes Random samples (DOCX 718.5 KB) Appendix A, printed (one per 3 Duration: 1–2 lessons students) Learning intention Appendix B, printed and cut into 3 To understand how to use sample data to represent a pieces (one per 3 students) population. Appendix C, printed (one per pair Success criteria of students) I can explain the potential bias that can occur when Random samples (PPTX 1.5 MB) using a sample. PowerPoint I can explain why a variation in measures of centre occur when using a sample. I can justify why I can draw valid conclusions from sample data. Learning episode 11 – survival of the fittest Teaching and learning activity Students revise measures of centre and spread by splitting people into teams for the television show ‘Survivor’. Syllabus content Select the type of graph best suited to represent various single datasets and justify the choice of graph Calculate and describe the mean, median, mode and range of a dataset Compare simple datasets using the mean, median, mode and range Table 31 – lesson sequence and details Teaching and learning activities Required resources Registration, adjustments and evaluation notes Survival of the fittest (DOCX 444 KB) Appendix A and B, printed (one per Duration: 1 lesson 3 students) Learning intentions To be able to use data displays to compare datasets. To be able to use measures of centre and spread to compare datasets. Success criteria I can find the measures of centre and spread. I can create data displays from data to help inform decisions. I can explain the decisions I make using mathematical evidence.  UNIT EVALUATION Teacher Evaluation Comments / variations How does the unit rate in these areas? Google link – click here Time Allocation and Pacing Record any variation made: Resources appropriate Cognitive Load Theory considered Use of Digital Technologies Cross-Curriculum Integration Differentiation for Diverse Learners Use of Numeracy Strategies Recommendations to improve this program: Literacy Strategies & activities Formative Assessment Strategies Student Engagement Levels Connects concepts to real-world contexts Incorporation of group activities Feedback strategies Data monitoring of student progress Date commenced: / / Date completed: / / Teacher name: _____________________________ Head Teacher name: ___________________________ Teacher’s signature: Head Teacher’s signature: