ࡱ> %` bjbjٕ ;`0PPPP  |2|2|282T3 33333;P;P;P_aaaaaa$hd (QO|;P(Q(QPP33TTT(QvP3 3_T(Q_TT| 33 P_B|2Qj}";$0~fZR&ZDZ ;P"]PTuPP;P;P;P.T;P;P;P(Q(Q(Q(Q t D* t * PPPPPP Title: 8 Glasses per day? Achievement Objectives: S4-1A Determining appropriate variables and data collection methods S4-1B Gathering, sorting and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationship and trends S4-1C Comparing distributions visually S4-1D Communicating findings, using appropriate displaysKey Competencies: Thinking: Co-construct knowledge Select appropriate methods Relating to Others: Listen actively Using Language, Symbols and Texts: Interpret statistical information Interpret visual representations such as graphs, diagrams Managing self: Reflect Participating and Contributing: Build on prior knowledge This activity explores the following key ideas: Sampling (What is a sample? What is a population?) Variability between samples of different sizes Distribution of data (discussing the shape) Predicting the population distribution from sampling distribution Resources OHT of samples n=10, n=27, n=67 OHT of shapes OHT of graph of all students Worksheet for each studentPrior Knowledge: Possibly dot plots, although you could use this task to introduce dot plots. Adapting for ICTIntroduction/Background as appropriate The context for this activity is How many glasses of water do you drink in a day? Students will be aware that drinking water regularly helps to keep our bodies hydrated. This helps to keep our brains functioning well. Many students have drink bottles of water on their desks. Discuss what they know about the benefits of drinking water. How many glasses of water do they drink each day? Do other drinks count? How big is one serving of water? Problem What would a graph of the number of glasses of water that NZ students drink per day look like? How much water do NZ students drink (each day)? Plan Ask the class: How many glasses of water did you drink yesterday? Record the results of the class on the board. Illustrate that these results can be shown on a dot plot.  This lesson will cycle through prediction and comparison with actual samples. In each cycle the sample size will be increased. Finally students will predict what the graph for all students in New Zealand would look like. The students who participated in the 91 Survey were asked What did you drink yesterday? Write the number of glasses/cups beside each type of drink A random sample of the water results can be produced using the Random sampler. The graphs available with this activity were made using random samples of data from the 91 website. Graphs could be prepared beforehand and shown on the OHT or they could be created live using a data projector. The live option has the benefit of students seeing the sample taken and multiple samples of each size can be easily taken to really demonstrate how variable the samples can be. 91  Cycle 1: Ask the students to make a prediction of what the graph will look like for 10 students using a dot plot. Give students a master sheet with the axes already drawn. Show the students the several dot plots for sample size 10 made from the data on the 91 website. Discuss how each sample is different. Cycle 2: Using a new axis ask the students to make a dot plot to represent all the students in the classroom next door (sample size 27) and another for prediction for a couple of classes in another school (sample size 67). Show the students several dot plots for samples size 27 and 67 taken from the 91 data. Cycle 3: Using a new axis ask the students to make a graph showing data of all students in their city, town or district, not necessarily with dots. Encourage students to think about the shape of the graph. Analysis  Emphasise that each sample is different from all the others. As the sample size increases the graphs of the samples are more similar (i.e. there is less variation between the samples). Most students will accept that the sample size of 10 is too small to make conclusions for the whole population. Encourage students to use statistical language when they describe the graphs. Write key words (majority, outliers, spread, skew and average) on the board for students to refer to. Discuss the shape that the points make on each of the graphs. To encourage more discussion about the shape of the graph show the following sketches of graph shapes.  Ask students which drawing they think is the best shape for the data they have been looking at. Discuss which shape it definitely is not. Explore the students reasoning. Conclusion  Cycle 1: Guide students towards conclusion that the sample is too small to really get a feeling for the shape of the graph. Cycle 2: Students should hopefully conclude that the sample of n= 67 gives them a better idea of what the shape of the graph is. Ask the students to make a sketch, based on the shape they have chosen in the analysis. Cycle 3: Finally ask the students to make a sketch of the shape for all the students of New Zealand. They should record why they choose this shape.  Show the students the graph for all the students who completed the 91 survey. Reflection Would the shape be similar for different drinks? E.g. fizzy drinks What other factors could influence the shape of the graph? To extend this activity What do students notice about the average and spread of the sampling distributions in relation to the sample size? Investigate medians/middle 50% from dot plot to dot plot with increasing sample sizes.      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