In this unit students construct, administer and analyse a survey to consider what constitutes a typical Year 8 student.
Surveys are increasingly important in modern life. Surveys such at the national census are important for government planning. Surveys of teenage smoking tell organisations such as ASH how successful their programmes are. Surveys of the performance of political parties help the government to see how their policies are working and enable predictions of who might form the next government. Clearly it is important to be able to design, collect and analyse these surveys to get information which is as accurate as possible. This unit concentrates on these three facets of surveys to produce information about the typical Year 8 student.
At Level 5, students build on the ideas from Level four about different aspects of the PPDAC (Problem, Plan, Data, Analysis, Conclusion) cycle. The key transition at this level is the acknowledgement that samples can be used to answer questions about populations. See Statistical Investigations for further information around Level 5 statistics investigations.
Knowledge of the following ideas will support your students' thinking throughout this unit. Consider planning short whole-class or small group lessons to address any gaps in these areas of knowledge
Mean, median, mode: The mean and median are both measures of central tendency (or central location), meaning they describe the centre or most typical value of a data set. The mean is found by taking the sum of a set of numbers and then dividing that sum by the total number of numbers (i.e. n). The media is the middle value found the numbers in a data set are ordered and the median is the most commonly occurring value.
Data displays - Bar graphs, Pie graphs, Stem and leaf plots, Histograms: Data can be displayed in a variety of ways, but whatever way is chosen the key intention of using some form of data display is to make the data more readily accessible or more understandable to the viewer. Category data might best be displayed by pictograms or bar graphs. Whole number data can be displayed by block graphs, pictographs, tally charts, bar graphs, pie graphs and stem and leaf graphs. Also possible are dot plots, strip graphs and time series graphs. Measurement data can be displayed with histograms.
Range: The range is a measure of spread, meaning it measures the degree of variability in a set of data and can be used as an indicator of the dispersion of a set of data. The range is identified by finding the difference between the largest and smallest numbers in a data set.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
The context for this unit can be adapted to suit the interests and experiences of your students. The statistical enquiry process can be applied to many topics and selecting ones that are of interest to your students should always be a priority. Other contexts might include students exploring a typical year 8 student in another country or culture, or variables including cultures, languages spoken at home, values etc. Consider what contexts will be most meaningful and engaging for your students, and whether you can make any links with other curriculum areas.
Te reo Māori kupu such as tūhuratanga tauanga (statistical investigation), tirohanga tauanga (statistical survey), raraunga (data), kohikohi raraunga (data collection) and taurangi (variable) could be introduced in this unit and used throughout other mathematical learning
In this session students being posing questions and developing ideas to help them find out what is a typical Year 8 student. (Reference is to Year 8 students but should be changed for the appropriate year level.)
In this session students prepare for, and carry out, a process of data collection.
Set up data cards to use to collect data. An example is shown below.
Name (optional): | |
Gender: | |
Age (years): | |
Birth month: | |
Colour of eyes: | |
Colour of hair: | |
Left or right handed: | |
Length of right foot (cm): | |
Height (cm): | |
Arm span (cm): | |
Sports played: | |
Hobbies: | |
Hours spent watching TV last week: | |
Etc. |
Name | Gender | Age | Birth month | Colour of eyes | Colour of hair | Left/ right hand | Length of right foot | Height | Arm span | Sports played | Hobbies Hours of TV |
In these sessions students collate and reclassify the data in order to start to develop ideas about what a typical year 8 student is.
Students might work on one particular area, for example ‘interests and hobbies’. They will need to decide what features they want to look at, what appropriate displays they could use, and what statistics they might need to calculate. For example, if they ask what sports are played they might describe the number of sports played and then the types of sports played from this question. It would be appropriate to give some average for the number of sports (mean or median), it could also be appropriate to compare this with the mode. They might also think about how outliers should be treated and about how the data represents the people who play two or more sports (e.g. is there a commonality amongst them?) It might be that if they are a boy and play two or more sports it is likely that one of the sports is soccer or if they are a girl and play two or more sports it is likely that one of the sports is netball.
In this session students consider what a typical student at another year level would be like.
Dear families and whānau,
Recently we have been investigating what constitutes a "typical" Year 8 student. We have investigated many different variables as part of this, and have used our results to create presentations. Ask your child to share their presentation and learning with you.
Printed from https://nzmaths.co.nz/resource/what-typical-year-8-student at 12:28am on the 25th April 2024