ࡱ>  NbjbjVV ;h<<04<<8;4oAcccccxxxAAAAAAAC#FhAx^xxxAcc3A"   xccA xA  6>@?<A?F@F8@F@$xx xxxxxAA xxxAxxxxFxxxxxxxxx< E: Title: Rumbling Tummy Achievement Objectives: S4-1A Determining appropriate variables and data collection methods Key Competencies: Thinking: Discern if answers are reasonable Design investigations Managing self: Seek understanding This activity explores the following key ideas: What sample size is appropriate? Resources Access to internet for students Prior Knowledge: Percentages Adapting for ICTIntroduction/Background Allow 60 minutes for this lesson. The focus of this lesson is to determine how sample size influences the accuracy of a survey. Students will take random samples of various sizes using the Random Sampler tool on the CensusAtSchool website. They will compare the results of these samples with the overall population statistics. The context of this lesson is: Where do teenagers get their lunch from? Discuss this issue with the class. Can they list all the possible responses that students are likely to give? Does everyone always have a lunch? What do they think the most common source of lunch is? What other factors influence where students get their lunch from?Problem Its lunchtime and Jackson is looking forward to his lunch. His dad made his lunch for him today. Jackson made a quick survey of the friends he sits with at lunchtime. Jerry, Hemi and Tony also have lunches from home. Daniel and Leo bought their lunch at the tuckshop. Harrison bought his lunch at the Dairy on the way to school. Based on his quick survey 4 out of 7 (57%) of his group get their lunch from home. Jackson wonders whether 57% of New Zealand students get their lunch from home. Harrison is concerned that his quick survey is not accurate enough. How can Jackson make a more accurate survey so that he can find out the where New Zealand school students get their lunch from?Plan Discuss the opening scenario. Is Jacksons quick survey of his friends accurate? Can he say that 57% of NZ teenagers get their lunch from home? Ask students to brainstorm how they could improve his survey. The brainstorm may bring up a number of issues. His friends are not representative of all NZ teenagers. What about girls? What about students from other schools?... other parts of NZ?... other ethnicities?... The sample was not random. The sample size is only 7. This is not big enough. This raises the question of how big should a sample be. To investigate this further, explain to the class that we will take a number of different samples, of different sample sizes from the CensusAtSchool website. Then they will compare their sample results with the population results. We hope to determine what would be a sensible sample size so that the sample results are representative of the whole population. Allocate sample sizes to groups. Students could work in small groups of 2-3 students. Note that the group with a sample size of 200 will have a lot more work to collate results than a group with a sample size of 20. Suggested allocation of sample sizes:  Make more cards if you have more groups in your class. Some sample sizes are doubled up. We will be able to show that different samples of the same size will give different results. This variation is an important for students to experience. Students will then graph their results and compare their graphs. Data  Introduce the Random Sampler on the CensusAtSchool website. The students enter the following fields:  The results can then be imported into Excel and manipulated to give a frequency table. Where did you get todays lunch from? Frequency Percentage Home Dairy Tuckshop Friend Provided by School No lunch Analysis  Each group need to graph their results. A Bar graph of the percentage would be an appropriate graph for this activity. Use the activity sheet so that each group draws their graph with using the same axes. This will make comparison easier. Discuss the advantage of using percentages rather than the frequency. If the students draw their graph on a OHT they can be displayed to the whole class. Arrange the graphs so that they can be compared easily. Sort the samples so that the graphs of samples with the same sample size are together. This could be done on butcher paper and displayed round the room. Allow the students to view all the graphs. Ask students to summarise their analysis using two sentence starters: I notice I wonder Share the students statements. Display the graph of the population frequency. Which sample gives a graph which is similar to the population graph?  Issues to discuss: Variation. Each sample gives different results. The smaller samples tend to be more variable. The larger samples will be more similar to each other and more similar to the population graph. What is the smallest sample which gives results similar to the population graph? What other factors influence how big the sample size should be? Conclusion What sample size should Jackson use for his survey? What other factors should Jackson consider when he is planning his survey? These questions will encourage students to think about sampling methods. Reflection Encourage students to think of surveys that they or their family have been involved in, e.g. CensusAtSchool, magazine surveys, Man on the street surveys, telephone surveys, product surveys. How do these surveyors choose who is in their sample? To extend this activityWork at differences between year levels primary, intermediate, secondary for example.     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