Nuffield Mathematics teaching resources are for use in secondary and further education

FSMQ Level 2 Data handling scheme of work

Before starting this Higher (Level 2) FSMQ students should be able to:

  • calculate with large numbers, fractions, decimals and percentages, including expressing one quantity as a fraction orpercentage of another
  • round values to the nearest whole number, 10, 100, \frac {1}{10} (0.1),  \frac {1}{100} (0.01) etc.
  • substitute into formulae expressed in words or symbols.

A suggested work scheme showing topic areas and methods to be covered is given below. This recommends a total of 60 guided learning hours that could be used in a variety of ways, such as 2 hours per week for 30 weeks, 4 hours per week for 15 weeks, or 5 hours per week for 12 weeks.  Although the topic areas are listed separately below, it would be beneficial at times to use a variety of skills within a piece of work.    

The following techniques should be introduced as soon as possible and used throughout the course:

  • using tables to record results
  • using a calculator effectively and efficiently, recording the working as well as the results and rounding values appropriately
  • using spreadsheets to sort data into increasing or decreasing order, carry out calculations and display results in tables and statistical charts and graphs
  • checking calculations using estimates, inverse operations and alternative methods (by hand and mentally).

Although the topics are listed separately, it would be beneficial to follow a number of statistical investigations through from the initial collection and organisation of data to an analysis of the situation making use of statistical charts and measures. Where possible these investigations should reflect the students’ other areas of work and interests.

Note that although the AMP resources in the list below were not written especially for this FSMQ, they include worksheets and notes you may find very useful.

Note that the assessment of this AQA FSMQ is by examination only and you should disregard any references to Coursework Portfolio requirements in the assignments which have not been updated. These are included for possible use as classroom activities but will not form part of the assessment of this FSMQ.

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

 

Define hypotheses, collect and organise data
(5 hours)

Define a hypothesis, and decide what data needs to be collected or measured in order to test it. Differentiate between discrete and continuous data.

Select a suitable sample considering in general terms what would be its appropriate characteristics. Identify appropriate values to measure.

Design a questionnaire (ensuring that questions are not biased, leading, complex or offensive) and other data collection forms for data from observation and measurement. 

Transfer data from data collection forms to tables produced by hand and into a spreadsheet. Include use of tally charts and frequency tables and grouping data using equal and unequal intervals.

 

Sports questionnaire responses    
Set of 50 responses in questionnaire form and as a spreadsheet. Teacher notes include short exercises giving practice in statistical techniques.

Cemetery mathematics (AMP)  
Learners collect data from a local graveyard or cemetery to test a hypothesis they themselves have chosen (such as people live longer than they used to or women live longer than men)

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Statistical charts 
(9 hours)

Draw by hand and interpret:
· pictograms
· bar charts
· ordered stem and leaf diagrams (including back-to-back diagrams)
· histograms (with equal and unequal class widths)
· pie charts, including comparative pie charts (using the area of the pie charts to compare the characteristics of two different populations)
· line graphs

Use a spreadsheet to draw bar charts, pie charts and line graphs. 

Interpret what the diagrams tell you about the situation.

Discuss the use of scales, area (etc) to exaggerate findings.

Solar eclipse   
Lots of data for discussion and suggestions for analysis.

Draw histograms in Excel   
Instructions explaining how to construct an accurate histogram and frequency polygon in Excel.

Draw pie charts in Excel   
Activity that shows students how to draw a pie chart in Excel and change its appearance.

Pie charts   
Activity showing students how to draw a pie chart by hand. Also includes practice exercise with real data – can be used as follow up to ‘Draw pie charts in Excel’ activity. 

Draw line graphs in Excel  
Activity showing students how to draw line graphs in Excel.

Interpreting curves   
Discussion sheets and exercise on interpreting and sketching line graphs. Focuses on the shape of graphs.

Safety on the roads   
Graphs and charts for interpretation.

Statistical measures  |
(8 hours)

Find the sum, mean, mode (or modal group), median and range (raw data and grouped data).

This includes finding the mean using a formula in words:

\frac {\textup{sum~of~observed~values}}{\textup{number~of~observations}}

or \frac {\textup{sum~of~(mid - value~of~group} \times \textup{frequency})}{\textup{number~of~observations}}

or symbols:

\bar{x} = \frac {\sum x}{n}  or \frac {\sum \left ( xf\right )}{n}  where n =\sum f .

Use a calculator to find the standard deviation.

Use a spreadsheet to sort data and find the sum, mean, median, mode and range.  Print out spreadsheet formulae.

Choose appropriate measures of location and spread to represent and compare different sets of data (raw or grouped data).

Election results  
Spreadsheet containing the 2005 and 2010 General Election results. Select data for practice in drawing charts, finding percentage, and so on.

Average limits (AMP)
Learners choose two numbers X and Y and find their average, then replace X with Y and replace Y with the average and find the average of these two numbers. Using an interative process, they investigate what happens.

Reaction times (AMP)   
Learners design an experiment to measure reaction times and are asked to display results in a clear and interesting way.

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Cumulative frequency graphs
(4 hours)

Draw cumulative frequency graphs, indicating the range, median, quartiles, inter-quartile range and percentiles. Could be drawn on a spreadsheet as well as by hand.  Use cumulative frequency graphs to estimate values.

Pay rates for men and women  
Activity showing students how to draw a cumulative frequency graph in Excel.

Box and whisker diagrams
(4 hours)

Draw and interpret box and whisker diagrams.

Use box and whisker diagrams to compare two data sets.

Box and whisker plots  
Students can use this Excel spreadsheet to draw up to four box and whisker plots. Includes instructions.

Scatter diagrams
(5 hours)

Understand ideas of positive correlation, negative correlation, strength of correlation and no correlation. 

Draw a line of best fit by eye through the mean point.

Use the line of best fit to estimate missing values.

 

Probability 
(5 hours)

 

Express probabilities as fractions, decimals and percentages.  Understand that probabilities lie between 0 and 1 and understand the numerical values associated with events having low, equally likely and high probabilities. Use P(not A) = 1 – P(A)

Estimate probabilities from real data, understanding the idea of, and limitations of, probability as relative frequency for simple situations. 

Draw probability diagrams to illustrate results.

Use probabilities from small data sets to project to larger populations, understanding the limitations resulting from factors such as sample profile, when the data was collected, and so on.

A risky business
Data sheet and probability worksheet involving accidents in the home and at work and leisure.

Sports injuries    
Discuss the use of real data (gives age and gender, also included on spreadsheet.)

Crime in the regions (assignment)  
Assignment in which students compare crime figures for their region with other regions. 

Probability   
Students use relative frequency to estimate probability. They find theoretical probabilities including probabilities of combined events. They use probabilities to predict the expected number of trials in which an event will occur. 

Three dice (AMP) 
Learners investigate the most likely total scores for 3 dice in the context of a game.

 

Interpret and compare data sets
(6 hours)

 

Use measures of location and spread and probability, together with statistical and probability diagrams, to come to conclusions about data and compare similar data sets.

Music Festival 
Students use weather data to decide which is the best month for an outdoor event. Two versions – for use with calculator or spreadsheet.

House prices  
Spreadsheet containing house price data from 1983 to 2011 for each country and region of the UK. Introduction suggests uses.

Football figures  
Excel spreadsheet containing 2007-8 data for each premier league club.

Heart rate  
Students are shown how to measure heart rate and then asked to plan and carry out an investigation.

HE applications  
Data sheets and spreadsheet giving gender, age, ethnic origin and other information about HE applicants. 

Five a day   
An investigation to find out to what extent people understand and follow government advice to eat 5 portions of fruit and vegetables per day.

Larks and owls  A very open investigation in which students may set their own statistical tasks based on sleep requirements. 

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.

Critical analysis
(6 hours)

 

Critically examine statistical work done by other people.

· Consider the use of diagrammatic representations of data in order to bias findings (such as by manipulation of axes or use of area to exaggerate findings).

· Question if the data used has been selected to strengthen a case (such as a sub-set of data may have been used or certain data discarded).

· Consider whether alternative measures and diagrams would have been more or less useful in highlighting findings.

· Identify what it is not possible to conclude from the data and consider what extra information or data is needed.

Global warming (assignment) 
Gives a list of websites that have reports or articles about global warming including statistical evidence. Students analyse one of these reports to meet the second portfolio requirement.

Revision
(8 hours)

Revise topics and try past papers.

Discuss data sheet – make up and try questions based on it.

 

 

 

Page last updated on 22 March 2012