FOUNDATION UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
FOUNDATION CHAPTER 1
COLLECTING DATA
Time: 3–4 hours
SPECIFICATION REFERENCE
– Types of samples
– Writing questions for questionnaires; eliminating bias
– Designing and using data capture sheets
– Designing and using two-way tables for data capture
HD1a/2c/5k
HD2c/d/e
HD3a
HD3c
PRIOR KNOWLEDGE
An understanding of why data needs to be collected
Some idea about different types of graphs
OBJECTIVES
By the end of the chapter the student should be able to:
– Understand the difference between: primary and secondary data; discrete and continuous data
– Understand the difference between a census and a sample
– Design a suitable question for a questionnaire
– Design suitable data capture sheets for surveys and experiments
– Understand about bias in sampling
– Use a two-way table to record or display data that is grouped into categories
DIFFERENTIATION AND EXTENSION
– Carry out a statistical investigation of their own, including designing an appropriate means of gathering the data
– Do ‘Activity – Pastimes’
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Foundation
Chapter/section: 1.1–1.4
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
The students’ own data collection exercise
GCSE coursework – data handling project
HOMEWORK
Homework at each stage could comprise consolidation of work by completion of exercises 1A–1D set in class, or additional work
of a similar nature, or extension work detailed above.
Completion of data collection exercise statistical project.
HINTS AND TIPS
– Students may need reminding about the correct use of tallies.
– Emphasise the differences between primary and secondary data.
– If students are collecting data as a group, they should all use the same procedure.
– Emphasise that continuous data is data that is measured.
– Use Exercises 1A–1D for practice. Use Mixed Exercise 1 for consolidation.
FOUNDATION UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
FOUNDATION CHAPTER 2
REPRESENTING AND PROCESSING DATA
Time: 3–4 hours
SPECIFICATION REFERENCE
– Drawing and interpreting bar charts and pictograms
– Drawing and interpreting pie charts and line graphs
– Drawing and interpreting stem and leaf diagrams
– Drawing and interpreting frequency polygons
HD4a/5b
HD4a/5b
HD4a/5b
HD4a/5b
PRIOR KNOWLEDGE
An understanding of why data needs to be collected and some idea about different types of graphs
Experience of collecting, interpreting, displaying and calculating with data
Ability to measure and draw angles
Ability to multiply a number by a fraction
OBJECTIVES
By the end of the chapter the student should be able to represent data as:
– A bar chart
– A pictogram
– A line graph
– A histogram (with equal intervals)
– A frequency polygon
In addition, students should be able to:
– Use a stem and leaf diagram to sort data
– Choose an appropriate way to display discrete, continuous and categorical data
DIFFERENTIATION AND EXTENSION
– Carry out a statistical investigation of their own and choose an appropriate way to display the results
– Use a spreadsheet to draw different types of graphs
– Collect examples of charts and graphs in the media which have been misused, and discuss the implications
– Use stem and leaf diagrams with unusual stems e.g. 234.1, 234.6, 235.1 ….
– Do ‘Activity – Investigating height’
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Foundation
Chapter/section: 2.1–2.4
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
The students’ own statistical investigation
GCSE coursework – data handling project
HOMEWORK
Homework at each stage could comprise consolidation of work done in class by completion of exercises set, additional work of a
similar nature, or extension work detailed above.
Completion of a simple statistical project.
HINTS AND TIPS
– Clearly label all axes on graphs and use a ruler to draw straight lines.
– Most students enjoy drawing statistical graphs for classroom displays.
– Stem and leaf diagrams should have a key.
– Angles for pie charts should be within 2°.
– Use Exercises 2A–2D for practice. Use Mixed Exercise 2 for consolidation.
FOUNDATION UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
FOUNDATION CHAPTER 3
AVERAGES AND SPREAD
Time: 5–6 hours
SPECIFICATION REFERENCE
– Calculating statistics for small data sets
– Calculating statistics for discrete frequency distributions
– Calculating statistics for continuous grouped data
HD4b/j
HD4b/g
HD4b/g
PRIOR KNOWLEDGE
Some experience of the measures of averages
Ability to order numbers
OBJECTIVES
By the end of the chapter the student should be able to:
– Find the mode, median, mean and range for a small set of data
– Find the modal class for grouped data
– Find the median by using (n+1)/2, where n is the number of data
 fx
f
–
Find the mean from a frequency table by using
–
Use the mid-point of equal class intervals to find an estimate for the mean of grouped data
DIFFERENTIATION AND EXTENSION
– Collect data from class – children per family etc.
– Discuss occasions when one average is more appropriate, and the limitations of each average
– Compare distributions and make inferences, using the shapes of distributions and measures of average and spread, e.g.
‘boys are taller on average but there is a much greater spread in heights’
– Do ‘Activity – Estimating the mean (an investigation)’
– Use statistical functions on a calculator or computer to find measures of average and spread
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Foundation
Chapter/section: 3.1–3.3
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
A group work assessment through selected questions and mini-projects
Data-handling project coursework task
HOMEWORK
Homework at each stage could comprise consolidation of work done in class by completion of exercises set, additional work of a
similar nature, or extension work detailed above.
Collect data at home for processing in class.
HINTS AND TIPS
– Students identify a modal class using the frequency rather than the class interval.
– Explain that the median of grouped data is not necessarily in the middle class interval.
– Students have difficulty understanding what is meant by ‘estimate’ when finding an estimate for the mean of grouped data.
– Use Exercises 3A–3C for practice. Use Mixed Exercise 3 for consolidation.
FOUNDATION UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
FOUNDATION CHAPTER 4
INTERPRETING DATA
Time: 3–4 hours
SPECIFICATION REFERENCE
– Interpreting databases, tables and mileage charts
– Interpreting line graphs and bar charts
– Comparing distributions using measures of average and spread
HD3b
HD5a/b/c/d
HD5a/d
PRIOR KNOWLEDGE
Chapter 2 Representing and processing data
Chapter 3 Averages and spread
OBJECTIVES
By the end of the chapter the student should be able to:
– Use a mileage chart
– Interpret information from a database
– Interpret information from a line graph
– Interpret information from comparative line and bar charts
– Understand the need for both a measure of average and a measure of spread when comparing sets of data
DIFFERENTIATION AND EXTENSION
– Find the mean for grouped continuous data with unequal class intervals
– Read and interpret a variety of graphs presented in newspapers or on the Internet
– Use combinations of mileage charts to plan routes, e.g. fly to Los Angeles via New York
– Do ‘Activity – Country facts database’
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Foundation
Chapter/section: 4.1–4.3
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Test a given hypothesis either using data provided or by collecting data from the class
GCSE coursework
HOMEWORK
Homework at each stage could comprise consolidation of work done in class by completion of exercises set, additional work of a
similar nature, or extension work detailed above.
Completion of a simple statistical project.
HINTS AND TIPS
– There are plenty of examples in the media where averages are used without spread. Students should be encouraged to
question these statistics.
– Use Exercises 4A–4C for practice. Use Mixed Exercise 4 for consolidation.
FOUNDATION UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
FOUNDATION CHAPTER 5
SCATTER GRAPHS, CORRELATION AND TIME SERIES
Time: 4–5 hours
SPECIFICATION REFERENCE
– Investigating the relationship between two sets of data; correlation and lines of best fit
– Drawing and interpreting time series
– Interpreting social statistics; calculating prices in line with RPI
HD4a/h/5b/c/f
HD4a/5b/j/k
HD5k
PRIOR KNOWLEDGE
Plotting points on a grid
An understanding of the concept of a variable
Recognition that a change in one variable can affect another
Linear graphs
OBJECTIVES
By the end of the chapter the student should be able to:
– Draw and produce a scatter graph
– Appreciate that correlation is a measure of the strength of association between two variables
– Distinguish between positive, negative and zero correlation using a line of best fit
– Appreciate that zero correlation does not necessarily imply ‘no correlation’ but merely ‘no linear relationship’
– Draw a line of best fit by eye and understand what it represents
– Use a line of best fit for estimation
– Draw a time series graph
– Identify trends in data over time
– Understand how prices change over time (inflation)
– Calculate a new price given the old price and the RPI
DIFFERENTIATION AND EXTENSION
– Vary the axes required on a scatter graph to suit the ability of the class
– Carry out a statistical investigation of their own, including designing an appropriate means of gathering the data, and an
appropriate means of displaying the results
– Use a spreadsheet, or other software, to produce scatter diagrams/lines of best fit; investigate how the line of best fit is
affected by the choice of scales on the axes
– Make predictions by considering trends of line graphs for time series
– Collect data from the Internet (e.g. RPI) and analyse it for trend
– Do ‘Activity – Fishing in the North Sea’
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Foundation
Chapter/section: 5.1–5.3
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
Testing a given hypothesis either using data provided or by collecting data from the class
The students’ own statistical investigation
HOMEWORK
Homework at each stage could comprise consolidation of work done in class by completion of exercises set, additional work of a
similar nature, or extension work detailed above.
Completion of a simple statistical project.
HINTS AND TIPS
– Clearly label all axes on graphs and use a ruler to draw straight lines.
– Use Exercises 5A–5C for practice. Use Mixed Exercise 5 for consolidation.
FOUNDATION UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
FOUNDATION CHAPTER 6
PROBABILITY
Time: 2–4 hours
SPECIFICATION REFERENCE
– Representing probabilities on scales labelled in words and numbers; equally likely outcomes
– Identifying mutually exclusive outcomes; adding simple probabilities
– Systematic listing and sample space diagrams
– P(event does not happen) = 1 – P(event happens)
– Predicting results based on theoretical probabilities
HD4c/5g
HD4c/d
HD4e
HD4c
HD4d/5g
PRIOR KNOWLEDGE
Some idea of chance and the likelihood of an event happening; and recognition that some events are more likely than others
Experience of using the language of likelihood
OBJECTIVES
By the end of the chapter the student should be able to:
– Use the language of probability to describe the likelihood of an event
– Represent and compare probabilities on a number scale
– List outcomes for single mutually exclusive events and write down their probability
– Write down the theoretical probability for an equally likely event
– Estimate a probability by relative frequency
– Know that a better estimate of probability is achieved by increasing the number of trials
– Use and interpret sample space diagrams
– Know that the sum of probabilities is 1
– Add probabilities
DIFFERENTIATION AND EXTENSION
– Write down probabilities of events that may or may not happen
– Play simple probability games, predicting outcomes; e.g. horse race for sum of two dice
– Do ‘Activity – Drawing pin’
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Foundation
Chapter/section: 6.1–6.6
See the Teaching and Learning Software for the activities linking to this chapter.
ASSESSMENT ISSUES
Written testing to assess knowledge of content
HOMEWORK
Homework at each stage could comprise consolidation of work done in class by completion of exercises set, additional work of a
similar nature, or extension work detailed above.
HINTS AND TIPS
– Where possible introduce practical work to support the theoretical work.
– Only fractions, decimals or percentages should be used for probability.
– Use Exercises 6A–6E for practice. Use Mixed Exercise 6 for consolidation.