gcse mathematics linear route map – foundation tier topic numberalgebra geometry & measures...
TRANSCRIPT
GCSE Mathematics Linear Route Map – Foundation Tier
Topic TopicTopic
Number Algebra Geometry & Measures
Topic
Statistics
Common content: Estimation
Optional content:Statistical
Techniques
Optional content:Graphical
Techniques
Optional content:Critical Path and
Risk Analysis
GCSE H Tier revision
Common content: maths for personal
finance
GCSE F Tier revisionICT skills
Common content: analysis of data
Common content: Critical analysis
Level 3 Mathematical Studies 2 year Route Map
OR OR
Wk1 Wk2 Wk3 Wk4 Wk5 Wk6 Wk7 Wk8 Wk9 Wk10
Wk11 Wk12 Wk13 Wk14 Wk15 Wk16 Wk17 Wk18 Wk19 Wk20
Wk21 Wk22 Wk23 Wk24 Wk25 Wk26 Wk27 Wk28 Wk29 Wk30
Wk31 Wk32 Wk33 Wk34 Wk35 Wk36 Wk37 Wk38 Wk39 Wk40
Wk41 Wk42 Wk43 Wk44 Wk45
SEPTEMBER OCTOBER NOVEMBER
NOVEMBER DECEMBER JANUARY
JANUARY FEBRUARY MARCH
APRIL MAY JUNE
JUNE JULY
Holiday Holiday
Holiday
Holiday
Holiday
Holiday
Holiday
Fermi Estimation
Introduction to spreadsheets
Collecting and Sampling Data
Types of Data
Year 12
Perimeter, Circumference and Area
Equation of a straight line
Year 13
Analyse Critically 1
Interest Rates
Collecting Data
Numerical Calculations
Representing data diagrammatically 1
Optional content Topic 1 – (select one from the right)
Project work: Analysis of Data or Personal Finance
Review and recap 1
Level 3 Mathematical Studies 2 year Route Map
Percentages Representing data numerically 1
Representing data numerically 1
REVISION AND END OF YEAR EXAMIANTIONS
Solution to financial problems
Similarity and Pythagoras Theorem
REVISION AND END OF YEAR EXAMS
Surface area and similarity
REVISION AND END OF YEAR EXAMS
Wk1 Wk2 Wk3 Wk4 Wk5 Wk6 Wk7 Wk8 Wk9 Wk10
Wk11 Wk12 Wk13 Wk14 Wk15 Wk16 Wk17 Wk18 Wk19 Wk20
Wk21 Wk22 Wk23 Wk24 Wk25 Wk26 Wk27 Wk28 Wk29 Wk30
Wk31 Wk32 Wk33 Wk34 Wk35 Wk36 Wk37 Wk38 Wk39 Wk40
Wk41 Wk42 Wk43 Wk44 Wk45
SEPTEMBER OCTOBER NOVEMBER
NOVEMBER DECEMBER JANUARY
JANUARY FEBRUARY MARCH
APRIL MAY JUNE
JUNE JULY
Holiday
Holiday
Holiday
Holiday
Holiday
Holiday
Holiday
Year 13
REVISION REVISION
Year 12
Taxation: Income tax and National Insurance
Graphical representation
Review and recap 2 Representing data diagrammatically 2
Representing data numerically 1
Optional content Topic 2 – (select one from the right)
Optional content Topic 3 – (select one from the right)
Option Topic 2
Analyse Critically 2
Graphical representation
Review and recap 3
Repayments and credit
Analyse Critically 3
Taxation: Value added tax (VAT)
Limits of accuracy
Review and recap 4
Level 3 Mathematical Studies 2 year Route Map
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Subject content: Online resources:
It is expected that spreadsheets and tables will be used throughout the teaching and learning of this Mathematical Studies specification.
Spreadsheet formulae will include:“=A1+A2+A3” to sum values in cells“=2*B3” to multiply a value in a given cell“=SUM(A1:A10)”
Anthropometric Data - Nuffield Foundation
DISCUSS Regression and Correlation - Nuffield Foundation
Pay rates for men and women - Nuffield Foundation
Stature - Nuffield Foundation
Climate Prediction - Nuffield Foundation
Cup of Coffee - Nuffield Foundation
Test Run - Nuffield Foundation
Ozone Holes - Nuffield Foundation
Savings Growth - Nuffield Foundation
Election Results 2005 and 2010
Health Data - Nuffield Foundation
Mammals - Nuffield Foundation
Module Results - Nuffield Foundation
Pulse Rates - Nuffield Foundation
Exponential growth – MEI (Username: mei-imps Password:
imps)
Compound Interest – MEI (Username: mei-imps Username:
imps)
Student Loans 1 – MEI (Username: mei-imps Username: imps)
F1.1
substituting numerical values into
spreadsheets
Introduction to Spreadsheets (Slide 1 of 2)
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Subject content: Online resources:
It is expected that spreadsheets and tables will be used throughout the teaching and learning of this Mathematical Studies specification.
Spreadsheet formulae will include:“=A1+A2+A3” to sum values in cells“=2*B3” to multiply a value in a given cell“=SUM(A1:A10)”
Student Loans 2 – MEI
(Username: mei-imps
Username: imps)
Sport at School - TES
Guide to creating comparison c
harts in Excel – TES
Investigating y=mx+c
spreadsheet - TES
Intro to spreadsheets – TES
Modelling with spreadheets
- planning a festival - TES
An introduction to spreadsheets
2 - TES
F1.1
substituting numerical values into spreadsheets
Introduction to Spreadsheets (Slide 2 of 2)
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Subject content: Online resources:
D1.1
appreciating the difference between qualitative and quantitative
data;
Parking Permits - Nuffield Foun
dation
What Is Data? - Maths Is Fun
Types of data - discrete vs
continuous – TES
D1.2
appreciating the difference between primary and secondary
data (including the use of secondary data that has been
processed e.g. grouped)
Types of Data
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Subject content: Online resources:
D1.3
collecting quantitative and qualitative primary and secondary
data
Pulse Rates - Nuffield Foundation
Reaction Times - Nuffield Foundatio
n
What Is Data? - Maths Is Fun
E1.1
The modelling cycle:
- representing a situation mathematically, making assumptions
and simplifications
Parking Permits - Nuffield Foundatio
n
Runaway Train - Nuffield Foundatio
n
Pulse Rates - Nuffield Foundation
Modelling with spreadheets
- planning a festival - TES
E1.2
- selecting and using appropriate mathematical techniques for
problems and situations
E1.3
- interpreting results in the context of the given problem
E1.4
- evaluating methods and situations including how they may
have been affected by assumptions made
Collecting Data
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Subject content: Online resources:
F1.2
using conventional notation for priority of operations, including
brackets, powers, roots and reciprocals
BODMAS – MathsIsFun
BIDMAS – Transum
Order of Operation – CIMT
BODMAS Notes PPT - Mr Bart
on Maths
Order of Operation Jigsaw - Ma
ths With Graham
F1.1
substituting numerical values into formulaeClimate Prediction - Nuffield Fo
undation
Financial Calculations - Nuffield
Foundation
Tarsia Substitution - TES
Numerical calculations
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Subject content: Online resources:
F2.1
interpreting percentages and percentage
changes as a fraction or a decimal and
interpreting these multiplicatively
expressing one quantity as a percentage
of another
Percentages - Nuffield Foundation
Gas Guzzlers - Nuffield Foundation
Water Flow - Nuffield Foundation
Financial Calculations - Nuffield Foundation
Income Tax - Nuffield Foundation
Growth and Decay - Nuffield Foundations
Percentages - MEI Integral (Username: mei-iqm Password:
Guest1QM)
Student Loans 1 – MEI (Username: mei-imps Username: imps)
Student Loans 2 – MEI (Username: mei-imps Username: imps)
My Money Week 2014 - Inflation - Pfeg
My Money Week 2014 - Inflation - Pfeg
Percentages - Mathscentre
F2.3
comparing two quantities using
percentages
F2.4
working with percentages over 100%
Percentages (Slide 1 of 2)
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F2.5
solving problems involving
percentage change - including percentage increase/decrease and original value problems - including simple and compound interest
Percentages - Nuffield Foundation
Income Tax - Nuffield Foundation (rules may need updating)
National Insurance - Nuffield Foundation (rules may need updating)
Savings Growth - Nuffield Foundation
Savings Facts and Formulae - Nuffield Foundation
Growth and Decay - Nuffield Foundations
Percentages - MEI Integral (Username: mei-iqm Password: Guest1QM)
Compound Interest – MEI (Username: mei-imps Username: imps)
Student Loans 1 – MEI (Username: mei-imps Username: imps)
Student Loans 2 – MEI (Username: mei-imps Username: imps)
Percentages - Mathscentre E1.2
selecting and using appropriate mathematical techniques for problems and situations
Percentages (Slide 2 of 2)
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Subject content: Online resources:
E2.1
Fermi estimation - making fast,
rough estimates using quantities
which are either difficult or
impossible to measure directly
How should mathematics be taught to non-mathematicians? - Tim Gower's Blog
Classic Fermi Questions – Mathsforum
Fermi Maths Problems – Kidsjig
Estimation - MathsIsFun
How many piano tuners are there in Chicago? – TES
Fermi Problems - TES
F1.1
substituting numerical values
into financial expressions
(including bank accounts)
Income Tax - Nuffield Foundation (rules may need updating)
Savings Growth - Nuffield Foundation
Savings Facts and Formulae - Nuffield Foundation
Growth and Decay - Nuffield Foundations
F1.4
finding approximate solutions to
problems in financial contexts
Fermi Estimation
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Subject content: Online resources:
D3.1
calculating/identifying mean, median, mode from raw dataHE Applications - Nuffield Foun
dation
Stature - Nuffield Foundation
Mammals - Nuffield Foundation
Module Results - Nuffield Foun
dation
Pulse Rates - Nuffield Foundati
on
Averages and Spread - Standar
d Deviation -
TeachIt Maths (PDF File is free
access)
Data Summaries - Statstutor
D3.1
calculating/identifying quartiles, percentiles, range, interquartile
range, standard deviation from raw data
D3.2
interpreting these numerical measures and reaching
conclusions based on these measures
Representing Data Numerically 1
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Subject content: Online resources:
D4.1
constructing and interpreting diagrams for grouped discrete data and continuous data and know their appropriate use - box and whisker plots - stem-and-leaf diagrams (including back-to-back)
HE Applications - Nuffield Foundation
Mammals - Nuffield Foundation
Module Results - Nuffield Foundation
Pulse Rates - Nuffield Foundation
Box and Whisker Plots - Statstutor
Stem and Leaf Diagrams - Maths is Fun
Representing Data Diagrammatically 1
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Subject content: Online resources:
F3.1
simple and compound interest Annual Equivalent Rate (AER)
Financial Calculations - Nuffield Foundation
Income Tax - Nuffield Foundation (rules may need updating)
National Insurance - Nuffield Foundation (rules may need updating)
Savings Growth - Nuffield Foundation
Savings Facts and Formulae - Nuffield Foundation
Growth and Decay - Nuffield Foundations
Compound Interest – MEI (Username: mei-imps Username: imps)
My Money Week 2014 - Inflation - Pfeg
F3.2
savings and investments
E1.2
selecting and using appropriate mathematical techniques for problems and situations
Interest Rates
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Subject content: Online resources:
find the gradient of a line connecting
two different points.
Gas Guzzlers - Nuffield Foundation
How Frequent are Earthquakes? - Nuffield Foundation
Smoke Strata - Nuffield Foundation
Water Flow - Nuffield Foundation
Test Run - Nuffield Foundation
Match Linear Functions and Graphs - Nuffield Foundation
Exponential growth – MEI (Username: mei-imps Password: imps)
Equation of a Straight Line - Mathscentre
The Gradient of a Straight Line Segment - Mathscentre
Investigating y=mx+c spreadsheet - TES
knowledge and use of the formula .
Equation of a straight line
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Subject content: Online resources:
D2.2
appreciating the strengths and limitations of random,
cluster, stratified and quota sampling methods and applying
this understanding when designing sampling strategies
Parking Permits - Nuffield Foundatio
n
Reaction Times - Nuffield Foundation
D2.2
appreciating that improving accuracy by removing bias and
increasing sample size may cost/save both time and money
Parking Permits - Nuffield Foundatio
n
D2.1
inferring properties of populations or distributions from a
sample, whilst knowing the limitations of sampling
HE Applications - Nuffield Foundatio
n
Pulse Rates - Nuffield Foundation
Reaction Times - Nuffield Foundation
Collecting and Sampling Data
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Subject content: Online resources:
S1.1
knowledge that this is a symmetrical distribution and that the
area underneath the normal ‘bell’ shaped curve represents
probability
Normal Distribution - Maths Is F
un
The Normal Distribution - S-Co
ol
The Normal Distribution - CIM
T
The Normal Distribution - Unive
rsity of Oxford
Stature - Nuffield Foundation
Normal Distribution Tarsia
– TES
Autograph Activity - Normal Dis
tribution Calculator - TES
S1.1
knowledge that approximately rds of observations lie within 1
standard deviation of the mean and that approximately of
observations lie within 2 standard deviations of the mean
S2.1
use of the notation for the standardised normal distribution with
mean = 0 and standard deviation = 1
The Normal Distribution (Slide 1 of 2)
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S3.1
using a calculator or tables to find probabilities for normally distributed data with mean = 0 and standard deviation = 1
Normal Distribution - Maths Is F
un
The Normal Distribution - S-Co
ol
The Normal Distribution - CIM
T
The Normal Distribution - Unive
rsity of Oxford
Stature - Nuffield Foundation
S3.1
using a calculator or tables to find probabilities for normally distributed data with known mean and standard deviation(the finding of an unknown mean or standard deviation by making use of percentage points will not be required)
C1.1
presenting logical and reasoned arguments in context criticising the arguments of others
C2.1
communicating mathematical approaches and solutions
The Normal Distribution (Slide 2 of 2)
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R1.1
representing compound projects by activity networks Refurbishing a Room - Nuffield Foundat
ion
Critical Path Analysis – CIMT
Critical Path Analysis - Learn About OR
Critical path analysis – TES
Earliest and Latest Event Times – TES
Gantt charts and resource histrograms
– TES
Thinking Skills Activities Lesson Decisio
n Maths - TES
R1.2
activity-on-node representation will be used
R2.1
using early time and late time algorithms to identify critical
activities and find the critical path(s)
R3.1
using Gantt charts (cascade diagrams) to present project
activities
C1.1
presenting logical and reasoned arguments in context
criticising the arguments of others
C2
communicating mathematical approaches and solutions
Critical Path Analysis
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Subject content: Online resources:
G1.1
sketching and plotting curves defined by
simple equations (a knowledge of the shapes of
the graphs of linear, quadratic, cubic and
exponential functions will be expected)
Minimum and Maximum Problems - Nuffield Foundation
Gas Guzzlers - Nuffield Foundation
Coughs and Sneezes - Nuffield Foundation
Cup of Coffee - Nuffield Foundation
Climate Prediction - Nuffield Foundation
How Frequent are Earthquakes? - Nuffield Foundation
How Frequent are Earthquakes? - Nuffield Foundation
Smoke Strata - Nuffield Foundation
Water Flow - Nuffield Foundation
Test Run - Nuffield Foundation
Ozone Holes - Nuffield Foundation
Runaway Train - Nuffield Foundation
G2.1
plotting and interpreting graphs in real
contexts, to find approximate solutions to
problems
Graphical Methods (Slide 1 of 2)
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G2.2
interpreting the solutions of equations as the
intersection points of graphs and vice versa
Liner quadratic cubic graph match – TES
Solving linear equations graphically – TES
Quadratic sketch treasure hunt – TES
Solving equations graphically lesson – TES (ignore
first three slides of the powerpoint)
C1
presenting logical and reasoned arguments in
context
Minimum and Maximum Problems - Nuffield Foundat
ion
Gas Guzzlers - Nuffield Foundation
Coughs and Sneezes - Nuffield Foundation
Climate Prediction - Nuffield Foundation
Smoke Strata - Nuffield Foundation
Test Run - Nuffield Foundation
Ozone Holes - Nuffield Foundation
Runaway Train - Nuffield Foundation
C1.1
criticising the arguments of others
C2
communicating mathematical approaches and
solutions
Graphical Methods (Slide 2 of 2)
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Review and recap 1
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Subject content: Online resources:
F7.1
the effect of inflation
Retail Price Index (RPI), Consumer Price
Index (CPI)
Financial Graphs and Charts - Nuffield Foundation
Inflation Indices - Nuffield Foundation
My Money Week 2014 - Inflation - Pfeg
F7.2
setting up, solving and interpreting the
solutions to financial problems, including
those that involve compound interest using
iterative methods
Financial Calculations - Nuffield Foundation
Savings Growth - Nuffield Foundation
Savings Facts and Formulae - Nuffield Foundation
F7.3
currency exchange rates including commission
Changing to a Foreign Currency - BBC Bitesize
Currency Conversion - Maths is Fun
Currency exchange Mathsopoly – TES
Currency Conversion Exchange - World Travelling - TES
Solution to financial problems (Slide 1 of 2)
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F7.4
budgeting Income Tax - Nuffield Foundatio
n
(rules may need updating)
National Insurance - Nuffield Fo
undation
(rules may need updating)
Savings Growth - Nuffield Foun
dation
Savings Facts and Formulae -
Nuffield Foundation
Student Loans 1 – MEI
(Username: mei-imps
Username: imps)
E1.2
selecting and using appropriate mathematical techniques for
problems and situations
Solution to financial problems (Slide 2 of 2)
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Subject content: Online resources:
Knowledge and use of the perimeter of 2D shapes and their
areas
Area and Perimeter match up -
TES
Compound Rectangles - TES
Maths Functional Skills: A New
Floor - TES
knowledge and use of the formulae for the circumference and
the area of circle
Circumference of a circle works
heet - TES
Area and Perimeter of sectors
worksheet - TES
Arcs and sectors worksheet - T
ES
Maths Valentines Card - Area a
nd Perimeter – TES
Perimeter of circles and semicir
cles - TES
Knowledge and use of the formulae for calculating fractional
areas of circles and composite shapes
Perimeter, Circumference and Area
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the application of the concepts of similarity
including lengths in similar figures
Pythagoras’ theorem applied to 2-D and 3-D
figures.
Similar Shapes Worksheet – TES
GCSE Similar Triangles Geometry Activity - TES
GCSE Introducing Pythagoras Theorem lesson – TES
Pythagoras Theorem in 3D – TES
Pythagoras Theorem Lesson – TES – incudes an
algebraic proof of the theorem
Pythagoras Theorem and coordinates – TES
KS4 worksheet - using Pythagoras in 3D - TES
Pythagoras worded question worksheet - TES Pythagoras’ theorem applied to 3-D figures.
Similarity and Pythagoras’ Theorem
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Subject content: Online resources:
C3.2
critical analysis of data quoted in media, political campaigns, marketing etc - questions will concentrate on the analysis of numerical and graphical data - numerical data will normally be given in tabular or spreadsheet form
E1.1
The modelling cycle:
- representing a situation mathematically, making assumptions and simplifications
Parking Permits - Nuffield
Foundation
Runaway Train - Nuffiel
d Foundation
Pulse Rates - Nuffield
Foundation
Sport at School - TES
E1.2
- selecting and using appropriate mathematical techniques for problems and
situations
E1.3
- interpreting results in the context of the given problem
E1.4
- evaluating methods and situations including how they may have been affected
by assumptions made
Analyse Critically 1
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Subject content: Online resources:
calculate surface areas of spheres, cones, pyramids and composite solids, including the application of the concepts of similarity including lengths in similar figures
Area and Volume of similar sha
pes / solids – TES
Ratio of lengths, areas, volume
s of similar
shpes – TES
Activity for 3D shapes - TES
Surface area and volume of pri
sms – TES
Surface area and volume of bui
ldings - TES
Volume and surface area of a sp
here
Surface Area Worksheets - TE
S
Surface area and similarity
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Subject content: Online resources:
Analysis of DataMammals - Nuffield Foundation
Reaction Times - Nuffield Foun
dation
Sport at School - TES
Personal FinanceMathematical Applications of Fi
nance - Nuffield Foundation
C1.1
presenting logical and reasoned arguments in context
criticising the arguments of others
Mathematical Applications of Fi
nance - Nuffield Foundation
Mammals - Nuffield Foundation
C2.1
communicating mathematical approaches and solutions
Summarising and report writing
Project work: Analysis of data or Personal Finance
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Subject content: Online resources:
Review and recap 2
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Subject content: Online resources:
D4.1
constructing and interpreting diagrams for grouped discrete data and continuous data and know their appropriate use - histograms with equal and unequal class intervals - cumulative frequency graphs
Pay rates for men and women - Nuffield Foundation
Stature - Nuffield Foundation
Mammals - Nuffield Foundation
Module Results - Nuffield Foundation
Pareto Charts - Nuffield Foundation
Pulse Rates - Nuffield Foundation
Cumulative Tables and Graphs - Maths is Fun
Drawing Histograms - TES
GCSE Histograms Worksheet – TES
Cumulative frequency Collective Memory – TES
Plotting cumulative frequency curves video tutorial – TES
Elephants Cumulative frequency - TES
Representing Data Diagrammatically 2
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Subject content: Online resources:
D3.1
calculating/identifying mean, median, mode from cumulative
frequency diagrams, stem and leaf diagrams or boxplots
Stature - Nuffield Foundation
Mammals - Nuffield Foundation
Module Results - Nuffield Foun
dation
Pareto Charts - Nuffield Found
ation
Cumulative Tables and Graphs
- Maths is Fun
Standard Deviation Worksheet
– TES
Cumulative frequency and boxp
lots lessons – TES
Median, quartiles and boxplots
worksheet - TES
Find ht
quartiles and interquartile range
- TES
D3.1
calculating/identifying quartiles, percentiles, range, interquartile
range, standard deviation from cumulative frequency diagrams,
stem and leaf diagrams or boxplots
D3.2
interpreting these numerical measures and reaching
conclusions based on these measures
E1.2
selecting and using appropriate mathematical techniques for
problems and situations
Representing Data Numerically 2
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Subject content: Online resources:
F5.1
plotting points to create graphs and interpreting results from
graphs in financial contexts
Financial Graphs and Charts -
Nuffield Foundation
Pareto Charts - Nuffield Found
ation
Match Linear Functions and Gr
aphs - Nuffield Foundation
E1.1
representing a situation mathematically, making assumptions
and simplifications (students will engage in the tackling of
'open' mathematical problem-solving where there may not be a
clear single approach or 'correct' answer)
Graphical representation
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S7.1
recognising when pairs of data are uncorrelated, correlated, strongly
correlated, positively correlated and negatively correlated
DISCUSS Regression and Corr
elation - Nuffield Foundation
Anthropometric Data - Nuffield F
oundation
Mammals - Nuffield Foundation
Pearson’s Correlation Coefficien
t -
Statstutor
Scatter Diagrams - Maths Is Fu
n
Interactive correlation activity -
TES
Statistics 1 Correlation – TES
Ten point PMCC - TES
S7.2
appreciating that correlation does not necessarily imply causation
understanding the idea of an outlier
S8.1
understanding that the strength of correlation is given by the pmcc
S8.2
understanding that pmcc always has a value in the range from – 1 to
+ 1
S8.3
appreciating the significance of a positive, zero or negative value of
pmcc in terms of correlation of data
Correlation and regression (Slide 1 of 3)
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S9.1
the plotting of data pairs on scatter diagrams and the drawing, by eye, of
a line of best fit through the mean point (the idea of residuals will not be
required)
DISCUSS Regression and Corr
elation - Nuffield Foundation
Anthropometric Data - Nuffield F
oundation
Mammals - Nuffield Foundation
Correlation and Regression - TE
S
S9.2
understanding the concept of a regression line
S9.3
plotting a regression line from its equation
S9.4
using interpolation with regression lines to make predictions
S9.5
understanding that there are problems concerning extrapolation
S10.1
where raw data is given, candidates will be expected to use a calculator
to calculate the pmcc and the equation of the regression line (calculations
from grouped data will not be required)
DISCUSS Regression and Corr
elation - Nuffield Foundation
Anthropometric Data - Nuffield F
oundation
Pearson’s Correlation Coefficien
t -
Statstutor
Correlation and regression (Slide 2 of 3)
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page
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Subject content: Online resources:
C1.1
presenting logical and reasoned arguments in context
criticising the arguments of others
communicating mathematical approaches and solutions
DISCUSS Regression and Corr
elation - Nuffield Foundation
Anthropometric Data - Nuffield
Foundation
Mammals - Nuffield Foundation
Correlation and regression (Slide 3 of 3)
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R4.1
understanding that uncertain outcomes can be modelled as random
events with estimated probabilities
knowing that the probabilities of an exhaustive set of outcomes sum
to one
Probability - Nuffield Foundatio
n
Laws of Probability - Nuffield F
oundation
Crack the code - 5 lock proble
ms - TES
R4.2
applying ideas of randomness, fairness and equally likely events to
calculate expected outcomes
R5.1
understanding and applying Venn diagrams and simple tree diagramsProbability - Nuffield Foundatio
n
Laws of Probability - Nuffield F
oundation
Three Dice - Nuffield Foundatio
n
Basic introduction to probability
tree diagrams – TES
Venn diagram lesson - TES
R6.1
calculating the probability of combined events: both A and B; neither A nor B; either A or B (or both)to include independent and dependent events
Expectation (Slide 1 of 2)
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R7.1
calculating the expected value of quantities such as financial
loss or gain
C1
presenting logical and reasoned arguments in context
criticising the arguments of others
communicating mathematical approaches and solutions
Expectation (Slide 2 of 2)
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G3.1
interpreting the gradient of a straight line graph as a rate of
change
Test Run - Nuffield Foundation
Gradients - Nuffield Foundation
(rules for differentiation could be
used as an extension activity)
Model the Motion - Nuffield Fou
ndation
G3.2
interpreting the gradient at a point on a curve as an
instantaneous rate of change
G3.3
estimating rates of change for functions from their graphs
G4.1
knowing that the average speed of an object during a
particular period of time is given by
Model the Motion - Nuffield Fou
ndation
Tour de France problem
solving – TES
Speed time graphs - TES
Rates of change (slide 1 of 2)
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G5.1
knowing that the gradient of a distance–time graph represents speed and that the gradient of a velocity–time graph represents acceleration
Test Run - Nuffield Foundation
Model the Motion - Nuffield Fou
ndation
C1
presenting logical and reasoned arguments in context criticising the arguments of others communicating mathematical approaches and solutions
Test Run - Nuffield Foundation
Rates of change (slide 2 of 2)
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C3.2
critical analysis of data quoted in media, political campaigns, marketing etc - questions will concentrate on the analysis of numerical and graphical data - numerical data will normally be given in tabular or spreadsheet form
E1.1
The modelling cycle:
- representing a situation mathematically, making assumptions and
simplifications
Parking Permits - Nuffield Foun
dation
Runaway Train - Nuffield Fou
ndation
Pulse Rates - Nuffield Found
ation
Sport at School - TES
E1.2
- selecting and using appropriate mathematical techniques for problems and
situations
E1.3
- interpreting results in the context of the given problem
E1.4
- evaluating methods and situations including how they may have been
affected by assumptions made
Analyse Critically 2
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Review and recap 3
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Subject content: Online resources:
F4.1
student loans and mortgagesAnnual Percentage Rate (APR)
Credit Cards - Nuffield Foundation
APR - Nuffield Foundation
Financial Calculations - Nuffield Foundation
Inflation Indices - Nuffield Foundation
Compound Interest – MEI (Username: mei-imps
Username: imps)
Student Loans 1 – MEI (Username: mei-imps
Username: imps)
Student Loans 2 – MEI (Username: mei-imps
Username: imps)
E1.2 selecting and using appropriate mathematical techniques
for problems and situations
Repayments and credit
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F6.1
Taxation: Value Added Tax (VAT) Government Spending and VAT
- TES
E1.2
selecting and using appropriate mathematical techniques for problems and situations
Taxation: Value Added Tax (VAT)
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F1.3
applying and interpreting limits of accuracy, specifying simple
error intervals due to truncation or rounding
Error Bounds, Limits of Accurac
y in Measurement – TES
Limits of Accuracy homework –
TES
Limits of accuracy powerpoint
and worksheet - TES
Limits of accuracy
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Review and recap 4
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S4.1
understand what is meant by the term ‘population’ in statistical
terms
S4.2
developing ideas of sampling to include the concept of a simple
random sample from a population
S5.1
knowing that the mean of a sample is called a ‘point estimate’ for
the mean of the population appreciating that accuracy is likely to be
improved by increasing the sample size
Probabilities and estimation (Slide 1 of 2)
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S6.1
confidence intervals for the mean of a normally distributed population of known variance using
(confidence intervals will always be symmetrical; the confidence level required and the sample size will always be stated)
C1
presenting logical and reasoned arguments in context criticising the arguments of others communicating mathematical approaches and solutions
Probabilities and estimation (Slide 2 of 2)
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R8.1
understanding that many decisions have to be made when
outcomes cannot be predicted with certainty
R9.1
Control measures: understanding that the actions that can be taken
to reduce or prevent specific risks may have their own costs (to
include the costs and benefits of insurance)
R10.1
using probabilities to calculate expected values of costs and benefits
of decisions other factors must be considered, for example - the regulatory framework (eg compulsory insurance) - minimising the maximum possible loss
Cost benefit analysis (Slide 1 of 2)
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R10.2
understanding that calculating an expected value is an important part of such decision making
C1 presenting logical and reasoned arguments in context criticising the arguments of others communicating mathematical approaches and solutions
Cost benefit analysis (Slide 2 of 2)
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G6.1
using a calculator to find values of the function (the laws of
logarithms will not be required)
Climate Prediction - Nuffield Foundation
Gas Guzzlers - Nuffield Foundation
Cup of Coffee - Nuffield Foundation
How Frequent are Earthquakes? - Nuffield
Foundation
Smoke Strata - Nuffield Foundation
Growth and Decay - Nuffield Foundations
Matching Graph Sketches - TeachIt Maths
(Includes some extension graphs beyond the
specification: PDF File has free access)
Exponential growth – MEI (Username: mei-
imps Password: imps)
G6.2
using a calculator log function to solve equations of the
form and
G7.1
understanding that has been chosen as the standard base
for exponential functions
knowing that the gradient at any point on the graph of is
equal to the value of that point
Exponential Functions (Slide 1 of 2)
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G8.2
using exponential functions to model growth and decay in
various contexts
Climate Prediction - Nuffield Foundation
Gas Guzzlers - Nuffield Foundation
Cup of Coffee - Nuffield Foundation
How Frequent are Earthquakes? - Nuffie
ld Foundation
Smoke Strata - Nuffield Foundation
Growth and Decay - Nuffield Foundation
s
Exponential growth – MEI (Username:
mei-imps Password: imps)
G8.1
formulating and using equations of the form and
C1
presenting logical and reasoned arguments in context
criticising the arguments of others
communicating mathematical approaches and solutions
Exponential Functions (Slide 2 of 2)
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F6.1
Taxation: income tax, National Insurance, Income Tax - Nuffield Foundatio
n
(rules may need updating)
National Insurance - Nuffield Fo
undation
(rules may need updating)
E1.2
selecting and using appropriate mathematical techniques for problems and situations
Taxation: Income Tax and National Insurance
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Subject content: Online resources:
C3.2
critical analysis of data quoted in media, political campaigns, marketing etc - questions will concentrate on the analysis of numerical and graphical data - numerical data will normally be given in tabular or spreadsheet form
E1.1
The modelling cycle:
- representing a situation mathematically, making assumptions and simplifications
Parking Permits - Nuffield F
oundation
Runaway Train - Nuffield
Foundation
Pulse Rates - Nuffield Fo
undation
Sport at School - TES
E1.2
- selecting and using appropriate mathematical techniques for problems and situations
E1.3
- interpreting results in the context of the given problem
E1.4
- evaluating methods and situations including how they may have been affected
by assumptions made
Analyse Critically 3