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, $\frac&space;{1}{10}$ (0.1),  $\frac&space;{1}{100}$ (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: $\frac&space;{\textup{sum~of~observed~values}}{\textup{number~of~observations}}$ or $\frac&space;{\textup{sum~of~(mid&space;-&space;value~of~group}&space;\times&space;\textup{frequency})}{\textup{number~of~observations}}$ or symbols: $\bar{x}&space;=&space;\frac&space;{\sum&space;x}{n}$  or $\frac&space;{\sum&space;\left&space;(&space;xf\right&space;)}{n}$  where $n&space;=\sum&space;f$ . 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.