What is a typical Year 8 student?

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Purpose

In this unit students construct, administer and analyse a survey to consider what constitutes a typical Year 8 student.

Achievement Objectives
S5-1: Plan and conduct surveys and experiments using the statistical enquiry cycle: determining appropriate variables and measures; considering sources of variation; gathering and cleaning data; using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets; comparing sample distributions visually, using measures of centre, spread, and proportion; presenting a report of findings.
Specific Learning Outcomes
  • Plan an investigation.
  • Choose and construct appropriate data displays.
  • Discuss features of data displays using mean, median and mode and looking at the range.
  • Where appropriate, state implications from their investigation.
  • Look at possible further investigations or improvements to their investigation.
Description of Mathematics

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.

Opportunities for Adaptation and Differentiation

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:

  • adjusting expectations regarding the type of analysis to be carried out by students – and the support given to do the analysis
  • providing pre-prepared graph templates to support developing scales for axes
  • constraining the number of graph types students are asked to select from
  • modelling the construction and filling out of data cards, tables, and graphs
  • providing prompts for writing descriptive statements
  • grouping your students strategically to encourage tuakana-teina (peer learning) and mahi-tahi (collaboration)
  • providing small group teaching around the different mathematical processes involved at each stage of this investigation, in response to demonstrated student need
  • providing teacher support at all stages of the investigation.

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

Required Resource Materials
  • Big sheets of paper
  • Tape measures
Activity

Session 1

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.)

  1. Explain to students: We have been asked to describe a typical Year 8 student.
    What sorts of things would we need to know to be able to describe a typical Year 8 student?
  2. Get students to brainstorm all of their ideas. Starter ideas might include: 
  • physical attributes – hair and eye colour; height, arm span, length of legs, arms, gender
  • interests and hobbies – what sports they play, how much time spent watching TV, time on other activities, cultural and other activities …
  • school - related ideas – time spent on homework, what is their favourite subject (avoid topics that may be upsetting to some students, especially weight).
  1. In groups get students to predict what they think a typical Year 8 student might be like using the main categories they have brainstormed above.
  2. Discuss how they will find out what a typical Year 8 student is like.
    What data will they need to collect?
    Who will they collect the data from?
    How do they know that their sample is representative of all Year 8 students? (In their school? In their city/town? In NZ?)
  3. Discuss practical matters.
    Which attributes and information should be collected in order to describe a typical Year 8 student?
    Will we survey our class only or do we need to survey other classes as well (this requires some organisation with other teachers – or other schools).
    How will the data be collected?
    How will the data be analysed? (Histograms? Mean? Etc.)
    What might be the limitations of the data we collect?
    How will we deal with outliers?

Session 2

In this session students prepare for, and carry out, a process of data collection.

  1. 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. 
  2. Spend the rest of this session on completing the data cards and collating the information into some sort of summary table. This will most probably be a multivariate table (use excel or paper version). An example is shown below. You might want to warn the students ahead of time so that they can collect accurate data on things like the number of hours of TV watched in a week. You might also let the students work in pairs so that they can measure each others height, etc.
NameGenderAgeBirth monthColour of eyesColour of hairLeft/ right handLength of right footHeightArm spanSports playedHobbies Hours of TV
            
            
            
            
            
            
            
            
            
            
            

Sessions 3/4

In these sessions students collate and reclassify the data in order to start to develop ideas about what a typical year 8 student is.

  1. Split students up into groups or pairs to explore different parts of the picture.

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.

  1. Students should clarify what question(s) they are trying to answer, draw appropriate displays and then answer their question(s) showing some insight/depth in their response.
    Going back to the sports example, it is not sufficient to say that a typical Year 8 student plays two sports, it is better to go into more detail about what those sports might be and how it might differ for boys and girls.
  2. Students will need to present their results to the class. Support them to present their results using tools and representations that allow them to express their mathematical understanding in a variety of ways (e.g. as a video, poster, verbal presentation and infographic, PowerPoint). Links to transactional writing could be made here. Display these presentations for other students to view.
  3. With the class, synthesise (pull together) a number of ideas from the class results. Try to draw a picture to represent a typical Year 8 student.
  4. Now that we have done all of this, what questions do we still have?
    Is there information that we now need that we didn’t realise we needed when we started?
    Could we have asked for different information that would have given us a better picture?
    Would students in another part of the country have produced the same results?

Session 5

In this session students consider what a typical student at another year level would be like.

  1. If they are in Year 8 then it would be good to discuss how a Year 7 student might differ or be the same?
    Then discuss how a Year 9 student might be the same or differ?
    How confident are you on your ideas about Year 7? (Given that they have already been in Year 7)?
    How confident are you on your ideas about Year 9? (Given that they have not yet been in Year 9)?
  2. Pick one or two attributes that they want to explore the differences/similarities between levels. If it is possible see if you can survey the other year levels and make comparisons.
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Level Five