Download Foundation – Unit 1

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Foundation – Unit 1
OVERVIEW for Foundation Tier
Notes:
1 hour calculator exam
54 marks – 26.7%
Topic
Y10 AUTUMN TERM
Y9
SUMMER
TERM
1. Data collection
30 -40% Functional Elements
14 marks Number, 40 marks Statistics
Teaching
hours
6
2. Interpreting and
representing data
12
3. Range and
averages
4. Probability
6
5. Fractions,
decimals and
percentages
6. Ratio and
proportion
12
8
6
AQA Modular specification reference
The Data Handling Cycle: S1
Data Collection: S2.1, S2.2, S2.3, S2.4, S2.5
Data presentation and analysis: S3.1
Data presentation and analysis: S3.2
Data Interpretation: S4.2, S4.3
Data presentation and analysis: S3.3
Data Interpretation: S4.1
Data presentation and analysis: S3.1
Probability: S5.1, S5.2, S5.3, S5.4, S5.7, S5.8, S5.9
Working with numbers and the number system: N1.14
Fractions, Decimals and Percentages: N2.1, N2.5,N2.6, N2.7
Ratio and Proportion: N3.1, N3.3
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 1 Data collection
Time: 6 hours
S1 Understand and use the statistical problem solving process which involves

specifying the problem and planning

collecting data

processing and presenting the data

interpreting and discussing the results.
S2.1 Types of data: qualitative, discrete, continuous. Use of grouped and ungrouped data.
S2.2 Identify possible sources of bias.
S2.3 Design an experiment or survey.
S2.4 Design data collection sheets distinguishing between different types of data.
S2.5 Extract data from printed tables and lists.
S3.1 Design and use two-way tables for grouped and ungrouped data.
AQA
Spec
ref
S1
Learning objectives
Grade
Common mistakes and
misconceptions
Discuss all aspects of the data handling cycle within one situation
Know the meaning of the term hypothesis
Write a hypothesis to investigate a given situation
D
S2.3,
S2.4
Know where to look for information
Distinguish between primary and secondary data
D
S2.1
Decide whether data is qualitative, discrete or continuous – use this to choose
suitable diagrams
Understand the difference between grouped and ungrouped data including
advantages and disadvantages
D
S2.4
E
S2.4,
S2.5
Understand methods of observation, controlled experiment, questionnaire, survey,
data logging
Know where and why each might be used
Design and use data collection sheets.
Work out methods for gathering data that can take a wide range of values
Tabulate ungrouped data into grouped data.
Formulating a hypothesis that cannot be
tested.
Thinking that a hypothesis is not valuable
if it is eventually proved false.
Not realising that data collected by a third
party (even if the results of a survey or
experiment) is classed as secondary data.
Not appreciating that some data can be
treated as either discrete or continuous
depending on the context (e.g. age – this
is really continuous, but is often treated as
discrete, such as when buying child or
adult tickets).
Using shortcuts in the tallying process –
counting up the items in each class,
rather than tallying items one by one.
D
Using overlapping class intervals.
Recording data which is on the boundary
of a class interval in the wrong class.
S2.5
S3.1
Interrogate tables or lists
Design and use two-way tables
D
Not checking that the totals in two-way
tables add up.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
S2.3,
S2.4
S2.2,
S2.3,
S2.4
Write or criticise questions and response questions for a questionnaire
Suggest how a simple experiment may be carried out
Understand how to collect survey data
Know the techniques to use to get a reliable sample. Understand how bias may
arise and offer ways to minimise bias for a data collection method
Resources:
C
C
Giving an answer that is not requested.
Reading the data from the table
incorrectly
Using overlapping classes, or gaps
between classes, for response options.
Mistaking biased samples for random
samples.
AQA GCSE Maths Middle sets Book Sections 1.1 to 1.8, 5.3
AQA Modular GCSE Mathematics Foundation Tier
 Tally charts P1
 Two way tables P104
 Questionnaires & surveys P147
 Observation and data logging P151
Foundation Practice Book sections 1.1, 5.1, 7.1, 7.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Collecting Data/Teaching Resources
Questionnaire activity/powerpoint/worksheet
Body correlation lesson plan/teacher handout/worksheet
Collecting data homework sheet
2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Representing Data/Teaching Resources
Two way tables lesson plan/worksheet
Functional skills activities 2.1, 13.1
Notes:
Questions may be set that require candidates to go through the stages of the Data Handling cycle without individual prompts
Questions may explicitly test knowledge of the words discrete, continuous, qualitative, grouped etc but it is recognition of the type of data that will be more
important – e.g. ‘Draw a suitable diagram for the data’. An understanding of the terms ‘primary data’ and ‘secondary data’ is expected.
Causes of bias will be clear for candidates to identify
Real data may be used in examination questions. Including knowing and using the term ‘hypothesis’ for a general prediction which is to be tested.
Closely related -
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations
S5.9 Understand that increasing sample size generally leads to better estimates of probability and population
characteristics
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 2 Interpreting and representing data
Time: 12 hours
S3.2 Produce charts and diagrams for various data types. Scatter graphs, stem-and-leaf, tally charts, pictograms, bar charts, dual bar charts, pie charts, line
graphs, frequency polygons, histograms with equal class intervals.
S4.2 Look at data to find patterns and exceptions.
S4.3 Recognise correlation and draw and/or use lines of best fit by eye, understanding what they represent.
AQA
Mod
spec
ref
S3.2
Learning objectives
Grade
Common mistakes and misconceptions
Draw bar charts, dual bar charts and composite bar charts
E, F, G
Bar widths or gaps between bars not equal.
Incorrect scale
S3.2
S3.2
S3.2
Produce a tally chart
Draw or complete a pictogram
Draw a pie chart.
F
S3.2
Complete an ordered stem-and-leaf diagram
D
S3.2,
S4.2
Draw a scatter diagram on a given grid
Find patterns in data that may lead to a conclusion being drawn e.g. Interpret points
on a scatter diagram
Look for unusual data values (outliers/anomalies)
D
S4.3
D, C
Trying to make the line of best fit go through
the origin, rather than drawing it appropriately.
Not appreciating correlation in terms of
‘positive’ and ‘negative’.
S3.2
Draw a line of best fit on a scatter diagram or know that a line of best fit is not
justified due to lack of correlation
Recognise and name types of correlation and strength of correlation – none,
positive, negative, weak, strong, moderate
Understand that if correlation exists, this does not mean causality exists
Use the line of best fit to estimate unknown values when appropriate
Produce histograms with equal class intervals
D
S3.2
Draw frequency polygons for grouped data
C
Using grouped labels on the data axes (e.g.
15–20, rather than the ends of the bar being
clearly marked with a 15 at one end and a 20
at the other end).
Using a grouped label on the horizontal axis
rather than a continuous scale.
E
Not drawing the angles in the pie chart
accurately or using the appropriate scale on
the protractor.
Measuring each angle from the same starting
point
Forgetting to put a key and order the leaves.
Forgetting to recombine the stem and leaf and
just giving the leaf as the value.
Assuming that all the plotted points must be
joined with a line.
Drawing the diagram without spending time
working out the best scale.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Plotting the upper bound instead of the midpoint.
S3.2
Produce line graphs
Resources:
AQA GCSE Maths Middle sets Book Sections 3.1 to 3.6
AQA Modular GCSE Mathematics Foundation Tier
 Tally charts P1
 Pictograms P8
 Bar charts P13
 Pie charts P75
 Stem and leaf diagrams P81
 Scattergraphs P86
 Time series (line graphs) P93
 Frequency polygons P173
 Histograms P178
Foundation Practice Book 1.1, 1.2, 1.3, 4.1, 4.2, 4.3, 4.4, 8.3, 8.4
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Representing Data/Teaching Resources
Stem and leaf lesson plan/worksheet/homework sheet
2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Scattergraphs/Teaching Resources
Scattergraphs lesson plans/homeworksheet/powerpoint
Functional skills activities 2.2, 2.3, 2.4, 5.1, 13.1, 13.2, 13.3, 16.1, 16.2, 16.3
Notes:
Candidates may be asked to draw a suitable diagram for data. An understanding of the type and nature of the data is expected from the candidate in order to
make a choice. Axes and scales may or may not be given.
Though the words interpolation and extrapolation will not be used in the examination, the idea that finding estimates outside of the data range is less reliable
than finding estimates from within the data range is expected to be understood by candidates.
Closely related –
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations
S4.1 Interpret a wide range of graphs and diagrams and draw conclusions.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 3 Range and averages
Time: 6 hours
S3.3 Calculate median, mean, range, mode and modal class.
S4.1 Interpret a wide range of graphs and diagrams and draw conclusions.
AQA
Mod
spec ref
S3.3,
S4.1
Learning objectives
Grade
Common mistakes and
misconceptions
Find the mean, median and range from a set of data, including data given in a stem
and leaf diagram
E, D
S3.3,
S4.1
Calculate the mode, median and range from an ungrouped frequency table
Use lists, tables or diagrams to find values for the above measures
Find the median for a discrete frequency distribution
Find the mode for frequency distributions
Find the interval containing the median for a grouped frequency distribution
Choose an appropriate measure according to the nature of the data to be the
‘average’
Calculate the mean from an ungrouped frequency table
Find the mean for a discrete frequency distribution
Omitting units when writing averages or
range.
Forgetting to include the stem when
reading the median from a stem and
leaf diagram.
Confusing the frequencies and the data
values.
D, C
Dividing by the number of rows in the
frequency table (i.e. the number of
different data values), not by the sum of
the frequencies.
Not appreciating that the statistics
calculated from grouped frequency
tables are estimates.
Not understanding that the estimate for
the range is an upper limit.
Incorrectly calculating the mid-points of
class intervals for grouped discrete data
(e.g. the mid-point of the class interval
10–19 is 14.5, not 15).
Interpreting ‘find an estimate for the
mean’ as ‘guess the mean’.
S3.3,
S4.1
S3.3,
S4.1
Find the modal class from a grouped frequency table
Estimate the range from a grouped frequency table
Work out the class interval which contains the median from data given in a grouped
frequency table
D, C
S3.3,
S4.1
Estimate the mean of data given in a grouped frequency table, knowing why it is an
estimate
C
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 4.1 to 4.5
AQA Modular GCSE Mathematics Foundation Tier
 Mode P25
 Mean P 29
 Median P34
 Range P39
 Mean of a discrete frequency distribution P109
 Comparing distributions P117
 Mean for grouped data P162
 Finding the median for frequency distributions P168
Foundation Practice Book 2.1 – 2.4, 5.2, 5.3, 8.1, 8.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Statistical measures/Teaching Resources
lesson plans/worksheets/homework sheet/problem sheet
Functional skills activities 6.1, 6.2, 17.1 – 17.3
Notes:
Candidates may be asked to draw a suitable diagram for data. An understanding of the type and nature of the data is expected from the candidate in order to
make a choice,
Axes and scales may or may not be given.
Closely related –
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations
S4.4 Compare distributions and make inferences – includes comparisons of average and range at tier F
S3.2 Produce charts and diagrams for various data types
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 4 Probability
Time: 8 hours
S5.1 Understand and use the vocabulary of probability and the probability scale.
S5.2 Understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency.
S5.3 List all outcomes for single events, and for two successive events, in a systematic way and derive related probabilities.
S5.4 Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1.
S5.7 Compare experimental data and theoretical probabilities.
S5.8 Understand that if an experiment is repeated, this may – and usually will – result in different outcomes.
S5.9 Understand that increasing sample size generally leads to better estimates of probability and population characteristics.
AQA
Mod
spec ref
S5.1,
S5.4
S5.4
S5.2
S5.2,
S5.7,
S5.8,
S5.9
5.3
Learning objectives
Grade
Common mistakes and misconceptions
Use words to indicate the chances for an outcome of an event
Use fractions, decimals or percentages to put values to probabilities
Place probabilties or outcomes to events on a probability scale
Work out the probability of an event not happening when you know the probability
that it does happen
Understand when outcomes can or cannot happen at the same time. Use this
understanding to calculate probabilities
Understand and use the fact that the sum of the probabilities of all mutually
exclusive outcomes is 1
Find the probability of a single outcome from knowing the probabilities of all other
outcomes
Work out probabilities by counting or listing equally likely outcomes
Estimate probabilities by considering relative frequency
Predict the likely number of successful events given the probability of any outcome
and the number of trials or experiments
Estimate probabilities from experimental data
Understand and use the term relative frequency
Consider the differences between theoretical probability and relative frequency
from a practical situation
Understand that experiments rarely give the same results when a random process
is involved
Appreciate the lack of memory in a random situation e.g. tails or heads are equally
likely even after 5 heads in a row
Understand the greater the number of trials the more the reliable the results
Understand how relative frequency diagram may settle as sample size increases
List all outcomes for a single event in a systematic way
List all outcomes for two events in a systematic way
G
F
Not remembering that probabilities can be
written as fractions, decimals and
percentages.
Incorrectly subtracting decimals from 1.
E
D
Adding or subtracting the incorrect values
due to misreading the question.
G, F
E
D
Incorrectly finding fractions of an amount.
Not cancelling a fraction to its simplest form.
C
Trying to plot decimals worked out to three
decimal places or more.
Comparing theoretical probability with
relative frequency without taking into
account the number of trials carried out.
G,F
E
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Use two-way tables to list outcomes
Use lists or tables to find probabilities
Resources:
D
AQA GCSE Maths Middle sets Book Sections 5.1 to 5.6
AQA Modular GCSE Mathematics Foundation Tier
 Chance P48
 Probability scales and calculations P51
 Listing outcomes P56
 Calculating probabilities P61
 Probability for mutually exclusive outcomes P66
 Relative frequency P128
 Using relative frequency P135
Foundation Practice Book 3.1 – 3.5, 6.1, 6.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Probability/Teaching Resources
lesson plans & starters/worksheets/homework sheets/problem sheets/powerpoints/interactive activities
Functional skills activities 7.1, 7.2, 18.1, 18.2
Notes:
The words candidates should be familiar with will be limited to impossible, (very) unlikely, evens or even chance, (very) likely and certain.
Candidates should not use word forms or ratio for numerical probabilities such as 1 out of 2 or 1 : 2.
Situations will be familiar, such as dice or bags containing numbered counters.
Probabilities and relative frequencies should be written using fractions, decimals or percentages. Cancelling a fraction to its simplest form may be required.
If not directed, listing can be done using lists, tables or sample space diagrams.
The term sample space will not be tested.
The term mutually exclusive will not be tested though the principle will.
Closely related
S3.1 Design and use two-way tables for grouped and ungrouped data.
Work from N2.1 may be assessed with this specification reference.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 5 Fractions, decimals and percentages
Time: 12 hours
N1.14 Use calculators effectively and efficiently, including statistical functions.
N2.1 Understand equivalent fractions, simplify by cancelling all common factors
N2.5 Understand that percentage means parts per hundred and use this to compare proportions
N2.6 Interpret fractions, decimals and percentages as operators.
N2.7 Calculate with fractions, decimals and percentages.
AQA
Mod
spec ref
N2.7
Learning objectives
Grade
Common mistakes and
misconceptions
Find a fraction of a quantity with a calculator
Find a fraction of an amount with a calculator in more complex situations
Use a calculator for the four rules for fractions
Calculate with fractions, decimals or percentages in a variety of contexts including
statistics and probability
Write one quantity as a fraction of another
E, D
Incorrectly inputting numbers on the
calculator.
Being unsure of what to work out when
a fraction calculation is set in context.
D
N1.14
Use the fraction key on a calculator
Use the fraction key on a calculator with mixed numbers
E, D
N2.7
Find a percentage of a quantity with a calculator
Find percentages of amounts in more complex situations - Perform calculations
involving repeated percentage changes
E, D
Not making the denominator the total in
questions involving a number of
quantities.
Working with quantities in different
units.
Incorrectly cancelling down.
Not recognising or know how to use the
fraction key on a calculator.
Misinterpreting a mixed number on a
calculator display.
Thinking that percentages over 100%
cannot exist.
Treating a percentage such as 0.05%
as though it were 5%.
Adding the percentage to the cost when
finding a percentage increase (e.g.
£315 + 15% VAT = £330).
Leaving the multiplier as a percentage,
instead of converting to a decimal.
Inaccurately converting to a decimal.
Not understanding compounding (e.g.
treating compound interest as simple).
N2.7
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
N2.7
Write one quantity as a percentage of another
Write one quantity as a percentage of another in more complex situations – work
what percentage one is of another
D, C
N2.6,
N2.7
Calculate a percentage increase or decrease
Use fractions, decimals or percentages to compare or interpret data sets or statistical
diagrams
Interpret a fraction, decimal or percentage as a multiplier when solving problems
Convert between fractions, decimals and percentages
Understand and use a retail prices index
Understand and use a retail prices index in more complex situations
Identify equivalent fractions
Simplify a fraction using a calculator
Understand whether a value is a percentage, decimal or fraction
Convert values between fractions, decimals or percentages in order to compare
them
D
C
N2.7
N2.1
N2.5
D, C
E, D
G, F
E
Not using the original amount as the
denominator, when finding a
percentage difference.
Working with quantities in different
units.
Giving the actual increase/decrease as
the answer when the amount after the
increase/decrease is what is required.
Using the multiplier as 1.5 rather than
1.05 for an increase of 5%.
Using a previously found price instead
of the base year price.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 2.1 to 2.7
AQA Modular GCSE Mathematics Foundation Tier
 Social Statistics P156
 Conversions of fractions, decimals and percentages P253
 Fraction of a quantity P258
 Percentage of a quantity P261
 Ordering decimals, fractions and percentages P264
 Expressing one quantity as a fraction of another P268
 Addition and subtraction of fractions P273
 Multiplication and division of fractions P279
 Addition and subtraction of decimals P285
 Multiplication and division of decimals P288
 Expressing one quantity as a percentage of another P314
 Increasing and decreasing by a percentage P318
 Finding a percentage change P321
 Percentages in real life P324
Foundation Practice Book 7.3, 13.1 – 13.5, 14.1 – 14.4, 16.1 – 16.4
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Fractions/Teaching Resources
lesson plans/worksheets/homework sheets
2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Decimals/Teaching Resources
Lesson plans & starters/worksheets/homework sheets
2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Percentages/Teaching Resources
Lesson plans/matching cards/powerpoints/homework sheets/plenary questions
Functional skills activities 3.1 – 3.4, 14.1 -14.4
Notes: This is part of the core number work required across all units. The term common denominator will not be used. Candidates should be able to
interpret percentage problems using a multiplier.
Closely related
N1.3 Understand and use number operations and the relationships between them, including inverse operations and the hierarchy of
operations
N1.4 Approximate to a given power of 10 (nearest 10,100, 1000), up to 3 decimal places and 1 significant figure
N1.14 Use a calculator effectively and efficiently, including statistical functions
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 6 Ratio and proportion
Time: 6 hours
N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation.
N3.3 Solve problems involving ratio and proportion, including the unitary method of solution.
AQA Mod
spec ref
N3.1
Learning objectives
Grade
Common mistakes and misconceptions
Understand the meaning of ratio notation
Simplify a ratio to its lowest terms a:b where a and b integers
Use a ratio in practical situations
F, E, D
N3.1, N3.3
Write a ratio as a fraction
Use a ratio to find one quantity when the other is known
Use a ratio and proportion to solve statistical and number problems
E, D, C
Swapping over the numbers in the ratio
(e.g. 2 : 5 becomes 5 : 2).
Simplifying ratios without ensuring the
quantities are in the same units.
Turning a ratio into a fraction (e.g. the ratio
4
4 : 5 becomes 5).
Failing to find the value of the unit fraction in
more complex problems.
N3.3
Write a ratio in the form 1 : n or n : 1
C
N3.3
Solve word problems involving ratio
C
N3.3
Understand direct proportion
Solve proportion problems, including using the unitary method
D
N3.3
Work out which product is the better buy
D
Ignoring different units in a ratio (e.g.
simplifying 2 days : 15 hours to 1 : 7½) .
Not multiplying both sides of the ratio by the
same number.
Giving an answer without considering the
context.
Not always seeing the relationships
between numbers (e.g. if the cost of 4 items
is given, and the price of 8 is asked for).
Not making the units the same for each
item.
Comparing unlike unit rates (e.g. price per
gram for one item but amount for 1p for the
other).
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 7.1 to 7.8 (7.8 higher)
AQA Modular GCSE Mathematics Foundation Tier
 Ratio P331
 Proportion and best value P336
Foundation Practice Book 17.1, 17.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Foundation Tier/Unit 1/Ratio/Teaching Resources
lesson plans & starters/sorting activity/problem sheets/homework sheets
Functional skills activities 4.1, 4.2, 15.1 – 15.3
Notes: This is part of the core number work required across all units. Ratio may be linked to a probability. Division in a given ratio is only tested in Unit 2.