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

# Using data

##### FSMQ Level 1 scheme of work

A suggested work scheme for this Level 1 (Foundation) FSMQ is given below. This recommends a total of 60 guided learning hours (such as 2 hours per week for 30 weeks, 4 hours per week for 15 weeks, 5 hours per week for 12 weeks). There is plenty of scope for varying the order and time allocation.

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

• using tables to record results
• using spreadsheets to carry out calculations and display results in tables and statistical charts and graphs
• using a calculator to carry out simple calculations such as finding a fraction of a quantity
• checking calculations using estimates, inverse operations and different methods.

The scheme of work below divides the content into topic areas. Although the topic areas 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.

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

The AMP resources in the list below were not written specially for this FSMQ and may include some topics that are not in the FSMQ specification

 Topic area Content Nuffield resource Collecting and organising data (7 hours) Collect data (including tally charts).  Organise data on paper and spreadsheets (compare different ways of doing this).  Express one quantity as a proportion (fraction, decimal, %) of another. Write two quantities as a ratio and reduce it to its simplest form. Divide a quantity in a given ratio (such as dividing £50 in the ratio 2:3). Coffee shop  Table of information about customers at a coffee shop.  Use on paper or in spreadsheet form for discussion and practice of statistical techniques. Ratio bingo and matching cards  Activities giving learners practice in simplifying ratios. Fractions, decimals and percentages      Slideshow shows the relationship between fractions, decimals and percentages.  Follow me game and worksheets provide practice. Statistical charts (10 hours) Draw pictograms and bar charts by hand.  Draw bar charts and pie charts using a spreadsheet. Draw pie charts by hand – include calculating the size of a sector using a fraction of 360° and using 1% represented by 3.6°. Common equivalencies for simple fractions, decimals and percentages $\frac&space;{1}{2}$ = 0.5 = 50%,  $\frac&space;{1}{4}$= 0.25 = 25%, $\frac&space;{1}{3}$ = 33%,  $\frac&space;{1}{10}$ = 0.1 = 10%, $\frac&space;{1}{5}$ = 0.2 = 20% & multiples of these) Draw line graphs in Excel  Activity showing students how to draw line graphs in Excel. Draw pie charts in Excel  Activity showing 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 – this can also be used as follow up to ‘Draw pie charts in Excel’ activity. Acid rain   Worksheet explains how acid rain is produced and requires students to analyse thedata given in the accompanying spreadsheet. Heights and weights (assignment)    Data set of girls’ and boys’ heights and weights from which students select data, then calculate statistical measures and draw statistical diagrams.

 Topic area Content Nuffield resource Statistical measures (9 hours) Find sum, mean, mode, median and range of data with and without a calculator.  (Include use of the calculator’s memory.) Use a spreadsheet to sort data and find the sum, mean, median, mode and range. Print out spreadsheet formulae. On average Examples and exercises on mean, mode and median. Election results   Spreadsheet containing the 2005 and 2010 General Election results.  Select local data for practice in drawing charts, finding percentages, and so on. Body Mass Index (assignment)   Involves collecting and illustrating data using a spreadsheet. Football figures   Excel spreadsheet containing 2007-8 data for each premier league club.  Teacher Notes suggest uses. Computer survey (assignment)   Students design a questionnaire about computer usage, carry out a survey and analyse the results Part-time work survey    Investigation into students’ paid employment (questionnaires, averages and range, charts and graphs). Outdoor gig    Students use weather data to consider which month would be the best to hold an outdoor gig. (Calculator and spreadsheet versions.) Cemetery mathematics (AMP activity)  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) Reaction times (AMP activity)  Learners design an experiment to measure reaction times and are asked to display results in a clear and interesting way.

 Topic area Content Nuffield resource Line graphs and proportionality (9 hours) Recognise when one set of data is proportional to another by considering step changes (approximate for real data).  Draw line graphs by hand, scaling axes (for data not necessarily starting at zero).  Join data points where appropriate.  Show a trend by drawing a straight line if appropriate. Using a spreadsheet to draw a scatter diagram to obtain a line graph.  Recognise the graph of data that is directly proportional: straight line passing through the origin. Find the gradient of a graph of a situation involving direct proportionality. Find the equation relating two variables that are directly proportional from a graph or information given in words. Currency conversion    Introduction to conversion graphs and direct proportionality in the context of currency conversion  Includes use of a spreadsheet. Reaction rates    Drawing and interpreting graphs using data provided from chemical reactions. Requires graphs to be drawn using spreadsheet and by hand. Plumbers’ call-out  Students complete data tables, then draw, read and interpret linear graphs where the intercept on the y axis is not zero. Interpretation includes finding where two linear graphs meet. House prices   Two versions, both with large data sets of house prices showing how they have changed in different locations over long and short periods of time. In Version A, students draw and interpret statistical diagrams and calculate statistical measures by hand. In Version B, students use a spreadsheet to create the statistical diagrams and calculate statistical measures, then interpret them. Matching graphs and scenarios     Twelve pairs of cards for students to match.  One card in each pair shows a graph and the other gives a description of the real situation that the graph represents.  Slide presentation to aid discussion (same graphs with titles and labels). Shorter by helicopter     Students plot graphs of real data to compare the straight-line distances between towns with the distances by road. Circles (assignment)    Students measure circular objects and find $\pi$ from the gradient of a graph. Melting and freezing points (assignment)   Students draw and interpret a graph using data from an experiment to find the melting point of wax Interpreting graphs (6 hours) Interpret line graphs, making sense of what is happening in the real situation where the graph cuts the axes Make sense in general terms of the gradient of graphs (steep, shallow, horizontal and vertical gradients only, i.e. calculation of gradients not included except for direct proportion) College trip   Includes a distance-time graph for interpretation. Crushed calcium carbonate   Data and line graph of a chemical reaction for interpretation. Interpreting curves   Discussion sheets and exercise on interpreting and sketching line graphs. Focuses on the shape of graphs.

 Topic area Content Nuffield resource Interpreting statistical charts (6 hours) Interpret pictograms, bar charts and pie charts. Use words to describe what the statistical diagrams indicate about the situations they represent. Eclipse    Data sheets about eclipses, discussion sheet and exercise involving interpretation of statistical diagrams. Mineral water (assignment)   Tabulated data and charts about the mineral content of various bottled waters.  Students are asked to interpret and analyse this information. Safety on the roads     Graphs and charts for interpretation. Timetables (3 hours) Read and use timetables given in 24 and 12 hour clock Find the length of time of journeys. Day out    Students plan a day out using local rail timetables. Probability (4 hours) Express the numerical values associated with events having low, equally likely and high probabilities as fractions, decimals and percentages (understanding that the probability that an event occurs lies between 0 and 1). Find the probability that an event A does not occur using 1 – P(A). Estimate probabilities from real data.  Discuss the idea of, and limitations of, probability as relative frequency. Three dice (AMP activity)   Learners investigate the most likely total scores for three dice in the context of a game. 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.) Revision (6 hours) Revise topics and try past papers. Discuss data sheet – make up and try questions based on it. Making sense of data revision guide

Page last updated on 03 August 2017