Download Modular Higher Unit 1 (old Unit 2)

HIGHER UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
HIGHER CHAPTER 1
COLLECTING DATA
Time: 3–4 hours
SPECIFICATION REFERENCE
– Grouping discrete and continuous data, formulating questions
– Censuses; choosing samples to minimise bias
– Random, stratified and selective (systematic) sampling
HD1a/2c/d/e/3a/c/d
HD2c/d/5j
HD2c/d
PRIOR KNOWLEDGE
Experience of simple tally charts
Experience of inequality notation
An awareness of the different types of data: continuous, discrete, categorical
Concept of a random number
OBJECTIVES
By the end of the chapter the student should be able to:
– Collect data using a tally chart
– Complete a two-way table
– Understand the difference between a census and a sample
– Design a suitable question for a questionnaire
– Understand the difference between: primary and secondary data; discrete and continuous data
– Design suitable data capture sheets for surveys and experiments
– Understand about bias in sampling
– Choose an appropriate sampling scheme, including random, stratified and systematic sampling
DIFFERENTIATION AND EXTENSION
– Carry out a statistical investigation of their own, including designing an appropriate means of gathering the data
– An investigation into other sampling schemes, such as cluster and quota sampling
– Do ‘Activity – Collecting continuous data’
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Higher
See the Teaching and Learning Software for the activities linking to this chapter.
Chapter/section: 1.1–1.3
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 data collection exercise and statistical project.
HINTS AND TIPS
– Students may need to be reminded 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–1C for practice. Use Mixed Exercise 1 for consolidation.
HIGHER UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
HIGHER CHAPTER 2
REPRESENTING AND PROCESSING DATA
Time: 3–4 hours
SPECIFICATION REFERENCE
– Drawing and Interpreting pie charts and stem and leaf diagrams
– Drawing histograms and frequency polygons
– Frequency density; drawing and interpreting histograms
HD4a/5b
HD4a/5b
HD4a/5b
PRIOR KNOWLEDGE
Experience of inequality notation
Ability to plot points
Understanding how to find the median and range for small data sets
Understanding the difference between discrete and continuous data
Measuring and drawing angles
Ability to multiply a number by a fraction
OBJECTIVES
By the end of the chapter the student should be able to:
– Draw and interpret pie charts for categorical data
– Draw a histogram (with equal class intervals)
– Draw a frequency polygon
– Use a stem and leaf diagram to sort data
– Complete a histogram from a frequency table
– Complete a frequency table from a histogram
– Use a histogram to work out the frequency in part of a class interval
DIFFERENTIATION AND EXTENSION
– Carry out a statistical investigation of their own and use an appropriate means of displaying the results
– Investigate how the choice of class width affects the shape of a distribution
– Use stem and leaf diagrams with unusual stems
– Do ‘Drawing histograms (an investigation)’
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Higher
See the Teaching and Learning Software for the activities linking to this chapter.
Chapter/section: 2.1–2.3
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
– Stem and leaf diagrams should have a key.
– Angles for pie charts should be within 2°.
– Label clearly all axes on graphs (frequency density).
– Emphasise the difference between a histogram and bar charts/graphs that pupils have previously encountered.
– Use Exercises 2A–2C for practice. Use Mixed Exercise 2 for consolidation.
HIGHER UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
HIGHER CHAPTER 3
AVERAGES AND SPREAD
Time: 4–5 hours
SPECIFICATION REFERENCE
– Mean, median, mode, range and interquartile range for grouped discrete data
– Grouped continuous data, estimating the mean, modal class, the class that contains the median
– Drawing and interpreting cumulative frequency graphs and box plots
– Comparing two cumulative frequency graphs or two box plots
HD4e/j
HD4a/e/5a/b
HD3b/4a/5a/b
HD4a/e/5a/b/d
PRIOR KNOWLEDGE
Knowledge of finding the mean for small data sets
Ability to find the mid-point of two numbers
Plotting coordinates
An understanding of the concept of a variable
Recognition that a change in one variable can affect another
OBJECTIVES
By the end of the chapter the student should be able to:
– Use the mid-interval value to find an estimate for the mean of data given in a grouped frequency distribution
– Understand and use the sigma notation for the mean of grouped and ungrouped data
– Find the median and quartiles for large sets of ungrouped data
– Draw a cumulative frequency table for grouped data (using the upper class boundary)
– Write down the modal class
– Write down the class containing the median
– Use a cumulative frequency curve to find an estimate for the median and the quartiles of a distribution
– Use a cumulative frequency curve to solve problems, e.g. how many greater than a particular value
– Draw a box plot to summarize the information given by a cumulative frequency curve
– Compare pairs of both cumulative frequency diagrams and box plots to make inferences about populations
DIFFERENTIATION AND EXTENSION
– Use statistical functions on calculators and spreadsheets
– Use statistical software to calculate the mean for grouped data sets
– Estimate the mean for data sets with ill-defined class boundaries
– Investigate the effect of combining class intervals on estimating the mean for grouped data sets
– Identify and represent outliers in box plots
– Compare more than two distributions using box plots
– 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
– Do ‘Activity – Comparing the performance of male and female athletes’
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Higher
See the Teaching and Learning Software for the activities linking to this chapter.
Chapter/section: 3.1–3.4
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.
Completing of data handling coursework; completion of simple statistical project.
HINTS AND TIPS
– Students should understand that finding an estimate for the mean of grouped data is not a guess.
– Some students may find the sigma notation difficult to understand at first.
– The connection between sigma f and n should be established clearly
– Clearly label all axes on graphs and use a ruler to draw straight lines.
– Use Exercises 3A–3D for practice. Use Mixed Exercise 3 for consolidation.
HIGHER UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
HIGHER CHAPTER 4
RELATIONSHIPS AND TRENDS IN DATA
Time: 4–5 hours
SPECIFICATION REFERENCE
– Drawing and interpreting scatter graphs and lines of best fit
– Calculating and plotting moving averages to identify trends
– Calculating price changes in line with RPI
HD4a/i/5c/f
HD 4a/f/5b/c
HD5j
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
– Find an equation for the line of best fit
– Use a line of best fit for estimation
– Draw a time series graph
– Calculate and plot moving averages to identify trends in data
– 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 – Do taller people have bigger feet?’
– Do ‘Activity – House prices’
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Higher
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
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 4A–4C for practice. Use Mixed Exercise 4 for consolidation.
HIGHER UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
HIGHER CHAPTER 5
PROBABILITY
SPECIFICATION REFERENCE
– Mutually exclusive outcomes
– Using sample space diagrams to calculate probabilities
– Using tree diagrams to calculate probabilities for independent events
Time: 4–5 hours
HD2a/4d/5g/h/i
HD2a/4c
HD2a/4d/g/h
PRIOR KNOWLEDGE
Understanding that a probability is a number between 0 and 1
Knowing how to add and multiply fractions and decimals
Experience of expressing one number as a fraction of another number
Recognise the language of statistics, e.g. words such as likely, certain, impossible, etc.
OBJECTIVES
By the end of the chapter the student should be able to:
– List all the outcomes from mutually exclusive events, e.g. from two coins, and sample space diagrams
– Write down the probability associated with equally likely events, e.g. the probability of drawing an ace from a pack of cards
– Estimate the number of successful events given the number of trials of an experiment and the probability of a successful
event
– Know that if the probability of an event occurring is p then the probability of it not occurring is 1 – p
– Find the missing probability from a list or table
– Know that the probability of either A or B is P(A) + P(B)
– Know that the probability of A and B is P(A)  P(B)
– Draw and use tree diagrams to solve probability problems (including examples of non-replacement)
DIFFERENTIATION AND EXTENSION
– Binomial probabilities
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Higher
See the Teaching and Learning Software for the activities linking to this chapter.
Chapter/section: 5.1–5.3
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
– Students should express probabilities as fractions, percentages or decimals.
– Probabilities expressed as fractions need not be cancelled to their lowest terms.
– Written testing can be used to assess knowledge of content.
– Use Exercises 5A–5C for practice. Use Mixed Exercise 5 for consolidation.
HIGHER UNIT 1 (OLD UNIT 2) SCHEMES OF WORK
HIGHER CHAPTER 6
MORE PROBABILLITY
Time: 2–3 hours
SPECIFICATION REFERENCE
– Using tree diagrams to calculate conditional probabilities for events that are not independent
HD2a/4d/g/h
PRIOR KNOWLEDGE
Chapter 5: Probability
OBJECTIVES
– Solve problems involving non-replacement
– Solve simple problems involving conditional probability
DIFFERENTIATION AND EXTENSION
More complicated examples of conditional probability involving several stages
Find conditional probabilities from two-way tables
RESOURCES
Heinemann GCSE Modular Mathematics Unit 1 (old Unit 2) Higher
See the Teaching and Learning Software for the activities linking to this chapter.
Chapter/section: 6.1
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
– Students may be expected to draw a tree diagram in the examination.
– Tree diagrams should be drawn carefully.
– Use Exercise 6A for practice. Use Mixed Exercise 6 for consolidation.