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Edexcel - Maths in context - PlannerHalf term

Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8

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AMSP Core Maths platform content: Drag and drop these shapes into the blank planner above. Stretch then to fit the number of weeks you require. The shapes contain links to an overview document which gives more details on the specification content covered and activities.

Representing data 1 – Teacher overview

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Representing data 1

Time series &Moving averages Sampling Finance

Recognising graphs

Representing data 2 Correlation Regression Probability

Exponential graphs

Sequences Spearman’s Rank

Linear programming

Understanding risk

Multi topic activities & projects

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Summary of content: This is the first of two sections on representing and interpreting data. The main focus of this section is interpreting statistical diagrams but it also covers quartiles and percentiles.

Pre-requisites: None but you may find you need to revise some of the statistics content of GCSE Maths.

Approximate guided learning hours: 8 - 10 GLH guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students. These skills should use in most of the other sections when working on problems.

Auto-marked online assessment: Section test - Representing and interpreting data 1

Teacher notes, solutions and any other support materials are contained in the teacher folders

Folder name: Interpreting data in bar chart and population pyramids

Document title Description Specification learning outcomes

Teacher ppt – multi bar charts A powerpoint presentation to support the teaching of this section.

Students sheet – UK babies 2016 This session is designed to encourage students to think more deeply about data presented in diagrams.

A good starting point would be a diagram which you suspect will get students talking and thinking about the data. The teacher’s powerpoint has two slides as an example.

Show the first slide and give the students some time to think. Ask them:

What do you notice?

What do you want to ask?

This sheet contains further diagrams and population pyramids to encourage students to think more deeply about data.

A3 construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and use them appropriately

A4 interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation, including box plots

A5 interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency, including quartiles, inter-quartile range, calculate and use variance and standard deviation

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Folder name: Mean and standard deviation


Teacher’s notes standard deviation Provides suggestions on how to get the most from the resource. Answers to the student’s sheet are included in this document.




Standard deviation pptx Powerpoint presentation provides an introductory problem and assists with the teaching of this content.

Teacher’s sheet – DigitalBreathTestdata2013 Answer to spreadsheet task related to Q5 on student sheet.

Student sheet standard deviation Students learn about the mean and standard deviation from the introductory problem on the ppt, then progress onto a number of examination style questions involving calculating and interpreting the mean and standard deviation in a variety of contexts.

The final task involves a large data set on digital breath tests in the form of an excel spreadsheet.

Students sheet – DigitalBreathTestData2013 Spreadsheet task related to Q5 on student sheet

Folder name: Dot plots – Box plots - Stem and leaf diagrams


Dot plots- Stem and leaf – is this a fair price ppx Teacher’s powerpoint to help with the teaching of this session

Student’s sheet – Dot plots- Stem and leaf - Bar charts

The students examine data from a variety of contexts.

A3 construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class

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(includes a matching task) The sheet provides guidance on how to calculate medians, Q1, Q3 and interquartile ranges. Students use these measures to compare samples.

intervals and cumulative frequency graphs, and use them appropriately



Folder name: Cleaning data and outliers


Student sheets

Cleaning data

Outliers

Outliers exam style questions

The first worksheet explores data cleaning and the second looks at investigating outliers, including thinking about whether to remove or keep them.

Finally, there is a sheet of examination style questions to aid preparation for the examination, this can be further enhanced by trying some examples from actual examinations.



Folder name: Interpreting data and using inzight online

This activity uses an online data tool called iNZight. The students are led through how to upload a sample data set, and then are shown how to get the tool to quickly produce diagrams. Using the data tool allows the students to explore the data, without the drudge of plotting and replotting diagrams.

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Skills acquired here can be used through this course and in project work other the subjects.


Teacher\student video– interpreting data A H5P video clip can be used to introduce this task.



Student sheet interpreting data Question shown at the end of the clip, plus another.

Student help sheet – using iNZight Instruction sheet about how to use the online data tool to obtain diagrams and summary statistics, plus interpretation questions

Data from CIA world factbook Data set as an excel file.

File name: Exam style questions – Bar Charts and Box plots


Exam style questions- Bar Charts and Box plots A selection of questions based on previous examination questions

Examinations practice/awareness

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Moving averages and time series – Teacher overview

Summary of content This section deals with moving averages and times series in context

Pre-requisites: GCSE work on mean average, graph plotting.

Approximate guided learning hours 2- 3 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.

Auto-marked online assessment:

(Solutions available in the teachers section only)


Folder name: Moving averages and time series

Activity title Description Specification learning outcomes

Student sheet (word and PDF) Activities for the students to try related to calculating and using moving averages

A2 interpret and construct tables and line graphs for time series data; calculate, interpret and use moving averagesData for students

House prices all regions

Average daily temperature

Births

Steps

Excel files – for using with activities plus answers.

Student interactive study packages

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Sampling – Teacher overview

Summary of content: This section investigates how to select samples using different sampling methods. This is basic to all statistical work and important in business, politics and journalism. The ideas of bias and variation are introduced and discussed.

Pre-requisites: It would be helpful for students to have done Representing Data 1 before this section.

Approximate guided learning hours: 6 – 7 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.




Folder name: Comparing sampling techniques


Student’s card sort – Statistical terms/definitions

Student’s card sort – Variance and bias

Two card sort activities have been provided. One which is designed to examine the difference between variance and bias and a second which looks at the definitions of some of the terms used in the section.

These card sorts could be used as a formative assessment/introductory task at the beginning of the session, or as a summative assessment/exit task, or one of each.

A1 infer properties of populations or distributions from a sample, while knowing the limitations of sampling

Sampling – Students sheet 1 Excel sheet (data file for use in the task)

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Instruction sheets

Random sample Stratified sample Systematic sample

These sheets are intended for students. They provide guidance on how to use Excel to take a sample from a large data set.

The intention is that students then analyse the distribution of the sample means and examine the variation of the samples obtained using each technique.

Further guidance on using the sheets can be found in 1.1 Teacher’s notes sampling

A1

infer properties of populations or distributions from a sample, while knowing the limitations of sampling

Students sheet – Personal research task Students are encouraged to do some personal research. Some structure is provided in order to guide the project and summarise their findings.

This could be done either after the spreadsheet tasks detailed above or a pre-session task.

A1


Folder name: Setting a pass mark


Setting a pass mark – sample generator A spreadsheet tool which generates random samples of different sizes. Can be used with students to demonstrate variability of samples.

A1


Student sheet – setting a pass mark Student’s worksheets to accompany the session.

This resource starts with the context of a multiple-choice test and asks students to consider the problem of setting a pass mark which will not allow guessers to pass easily. This context leads students into exploration of ideas related to probability distributions, including the Normal distribution, mean, spread and gives them an informal, intuitive idea of the principles

The Normal distribution is not in the specification but it is a common theoretical distribution which many students will have met; although this resource is an extension resource, you can use it to address the following specification statement:

P1 understand and demonstrate that empirical unbiased samples tend towards

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underlying statistical hypothesis testing. Students look at multiple choice tests with two answers per question.

theoretical probability distributions, as sample size increases

Supplied samples – setting a pass mark For use with student sheet


Population and sampling

Census and sampling

Quantitative and qualitative data

Auto-marked online activities with video clips to support the learning in this section.

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Percentages revision (optional)– Teacher overview

This section aims to provide a recap on percentages work from GCSE in preparation for work in the finance section. It is unlikely that all of the content will be used with all students, this will depend on the needs of individual studentsSummary of content

This section reviews percentages starting from the context of finance and extending to other contexts. Some students will already have a good understanding of percentages from GCSE and will need to spend very little time on this section.

In the context of finance, linking percentage to number of pence per pound may help students. Students may be quite good at working out simple percentages of an amount, such as 10% and 50% of £25, but find it much more difficult to work out what

percentage something has changed by; e.g. a leaf grows from 2.8 cm to 3.1 cm, what is the percentage change? Using a spreadsheet will require them to think about what steps the calculation needs and so help them work with harder numbers.

Some students may not have used multipliers for percentages at GCSE; they will need to do so in order to work with interest rates for loans and savings. A good understanding of percentages is important for everyday life, understanding the news and in business, science and social science. Many careers will include the use of spreadsheets; this section is an opportunity to use basic formulas and graphs in a spreadsheet to work with and compare

percentage change.

Pre-requisites: GCSE percentage workApproximate guided learning hours: 6-7 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.Auto-marked online assessment: (Solutions available in the teachers section only)Teacher notes, solutions and any other support materials are contained in the teacher folders

Folder name: Percentage for comparison Note: This resource has two supporting video clips


Percent starter A question to start students thinking about how to compare quantities – see below.

Preparation for later work on finance

Using percentages for comparison A powerpoint to introduce the idea of using percentages for comparison – some students will already be familiar with these ideas.

Questions percent for comparison Questions to practise using percentages for comparison

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Driver data A spreadsheet with the data for question 5Folder name: Percentage Change


Percentage change A powerpoint to introduce students to percentage increase and decrease mentally and on a calculator. Notice the suggested spreadsheet exercise below.

Preparation for later work on finance

Multipliers A simple spreadsheet to let students practise getting the correct multiplier for a percentage change.

Percentage change questions Questions to practice percentage change.

Discussion better offer A question to promote discussion and problem solving – students should be able to justify their solutions to convince other

Reverse percentages A powerpoint to introduce students to the idea of using multipliers to find a quantity before a percentage change.

Multipliers for percentages This powerpoint can be used to show students how to use multipliers to find what the percentage is – some students will prefer to use the methods they are already familiar with and you may choose not to use this.

Mixed percent questions These mixed questions include forward and reverse percentage change as well as finding the percentage

Folder name: Repeated percentage change. Note: This resource has a supporting video clip


Depreciation worksheet A simple worksheet to promote discussion SG1 set up, solve and interpret the answers to

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comparing constant percentage decrease in value with the way car values actually decrease.

growth and decay problems, including compound interest

SG2 calculate simple interest and compound interest; use and interpret graphical representation of simple and compound interest

Depreciation spreadsheet A spreadsheet which allows students to compare a constant annual percentage decrease with decreasing values from a website.

Repeated percentage change A powerpoint introducing repeated percentage change with a spreadsheet and with a calculator – the latter using powers of multipliers.

Rising prices questions An introduction to the effects of inflation over time and the idea of an average annual percentage increase.

Growing money spreadsheet A spreadsheet showing the effect of a repeated percentage increase on money – it can be used for inflation or interest calculations.

Rising prices solutions Full written solutions to the rising prices questions

Average percentage change A powerpoint showing how to find the average annual percentage change over a period of time.

AER and APR questions Information and questions about interest on savings and loans

Repaying loans spreadsheet A spreadsheet which allows students to explore loan repayments; amount borrowed, interest rate and repayment can all be varied.

Rule of 72 A spreadsheet exploration of an approximating rule used in finance calculations. Students should write their own spreadsheet to explore this.

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Compare House Price A starter question to encourage students to think about the need for index numbers – available in pdf or powerpoint format.

Index powerpoint A powerpoint which goes through the process of calculating an index.

Average House Index spreadsheet This allows students to practice calculating an index and gives feedback on whether they are right. Answers are also available.

Index Compare questions Questions for students about using an index to make comparisons.

UK House price spreadsheet Data for students to use when comparing house prices (see last question of Index Compare).

Index percent change powerpoint A powerpoint which goes through the process of finding a percentage change from an index number.

House building spreadsheet Data used in the powerpoint.

Index percent change questions Questions about finding percentage change from an index number.

Calculating Inflation spreadsheet Data needed for the final Index percent change question.

Index percent change solutions Full written solutions to the questions.

Questions: repeated change Mixed questions about repeated percentage change, includes questions about the average percentage change over a period of years.


H5P Proportions and amounts Auto-marked online activity with video clips. Looks at the how change can be described using a proportion (%) or an actual amount.

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H5P Using proportions to compare risks This activity links to H5P proportion and amounts by looking at relative and absolute risk.

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Finance – Teacher overview

Summary of content: This section covers compound interest and inflation. It can be linked to later work on sequences and exponentials.

Pre-requisites: A knowledge of percentages and multipliers.

Approximate guided learning hours: 10-12 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students. These skills should use in most of the other sections when working on problems.

Auto-marked online assessment: Section test


Folder name: Football tickets - Inflation


Spreadsheet Football tickets Spreadsheet for student tasks SG1 set up, solve and interpret the answers to growth and decay problems, including compound interest


Students sheet - Football tickets This two-part lesson compares prices now and in the past. Students work on an initial task comparing football ticket prices now and in 1984. It turns out ticket prices for Manchester Utd have increased way above inflation! Students will be guided to investigate a real-world situation. The autonomous task will consolidate and support learners with fluency in key mathematical skills and competencies needed in level 3 Core Maths and life. Worksheets containing tasks and information

Folder name: Student loans

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Student sheet – Initial questions Starter activity – questions

Students question sheet Follow on questions SG2 calculate simple interest and compound interest; use and interpret graphical representation of simple and compound interestSpreadsheet for last question To support the final task on the spreadsheet

Folder name: Exam style questions


Saving and Borrowing exam style Two exam style questions which can be used either in class or as homework.

SG1 set up, solve and interpret the answers to growth and decay problems, including compound interest



Interest rates

Loans and interest rates

This interactive package provides a useful interactive self-study package covering interest on saving, compounding, and AER.

This interactive package provides a useful interactive self-study package covering interest on loans, compounding, and APR.



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Representing data 2 – Teacher overview

Summary of content: This is the second section devoted to representing and interpreting data, in this section students look at the mean and standard deviation, as well as histograms. There is also scope to do some individual project work.

Pre-requisites: Covering representing and interpreting a data 1 would be an advantage.

Approximate guided learning hours: 8 – 10 GLH guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students. These skills should use in most of the other sections when working on problems.

Auto-marked online assessment: Section test – representing data.


Folder name: Social media influencers (an introductory task)


Student sheet – influencers V5 Students explore data on social media influences.

Includes interpreting data displayed in tables and considering how to measure the effectiveness of influencer advertising.


Folder name: Percentiles and cumulative frequency


Percentiles

Teacher notes – Percentiles

Teacher presentation(ppt) Percentiles

Introduces the idea of percentiles using baby/child growth curves. Leads into work on cumulative frequency curves

A3 construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and use them appropriatelyStudent worksheet Introduces the idea of percentiles using

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baby/child growth curves. Leads into work on cumulative frequency curves



Cumulative frequency

Teacher notes – Cumulative frequency

Teacher presentation(ppt) - Cumulative frequency

Demo video – Autograph cumulative frequency

Demo video – GeoGebra cumulative frequency

Using GeoGebra to draw cumulative graphs (instruction sheet)

GeoGebra applet – Cumulative frequency practice

This work follows on from percentiles.

Cumulative frequency curves, q1, q2 and q3 are introduced and interquartile range.

A range of context are used.

Students learn how to use GeoGebra and/or Autograph




Student worksheet – Cumulative Frequency

Plus

Demo video – Autograph cumulative frequency

Demo video – GeoGebra cumulative frequency


GeoGebra applet – Cumulative frequency

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practice

GeoGebra applet – Cumulative frequency practice


Folder name: Histograms


Teacher’s – Histogram resourceV2 Provides suggestions on how to get the most from the resource. Answers to the student sheet are included in this document.




Histogram2 pptx Powerpoint presentation to assist with the teaching of this content.

Teachers answer sheet Q1V2 xlsx

Teachers answer sheet Q2aV2 xlsx



Excel spreadsheets with the data files which show the answers to questions from the student sheets

Students- Histograms resourceV2 Students interpret and construct histograms from data covering a variety of contexts including real data on road traffic accidents, and roadside breath tests.

Folder name: Which diagram

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5 Students sheet – which diagram activity Students are asked to look at several data sets and associated diagrams. For each pairing, the students are asked:a) Is this most the suitable way of displaying the

data? (explain why)b) If not, then what way would you have

chosen? (explain why)


6 Student sheet – Which diagram data set sheetStudents are given four data sets and asked to choose an appropriate method of presenting them. This can be done by hand or using a spreadsheet – see the Excel file - 7 which diagram data sets

7 Which diagram - data setsExcel file of data sets to support the activity

6 Student sheet – Which diagram data set sheet

Folder name: Autonomous Learning Task

This task is designed to give students the opportunity to bring together the knowledge, skills and understanding they have developed in this section, in a realistic, work related context.


ALT – Student’s task sheet Encourages the students to think of three questions they would like to answer using the data set. Then think about how they will display the data and what calculations to use.

Students are asked to produce a poster or a powerpoint and present their findings.



A5 interpret, analyse and compare the

ALT – Student’s sheet – DigitalBreathTest2013.xlx

Large data set on Excel spreadsheet

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distributions of data sets from univariate empirical distributions through appropriate measures of central tendency, including quartiles, inter-quartile range, calculate and use variance and standard deviation

File name: Exam style questions – Histograms


Exam style questions- Histograms A selection of questions based on previous examination questions

Examinations practice/awareness

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Correlation – Teacher overview

Summary of content: This section aims to build an understanding of correlation by examining and interpreting real data on countries. The term association is used to refer any potential relationship between variables and correlation is used when referring to a linear relationship. The students are introduced to the product moment correlation coefficient and encouraged to explore the value and limitation of using this figure as a measure of the strength of a correlation. Causation and outliers are also covered in this section.

Pre-requisites: GCSE level understanding of scatter diagrams

Approximate guided learning hours: 12-15 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students. These skills should use in most of the other sections when working on problems.

Auto-marked online assessment: Section test


Folder name: Scatter diagrams, outliers and product moment


2 Students sheet Correlation WS Uses data from the CIA world fact-book to develop students’ understanding of correlation and their skills in reading and interpreting data.

The term outlier is introduced, and students are encouraged to use a reasoned approach when deciding if a point is an outlier.

After reasoning using the general shape and direction of the scatter, the students are introduced to the product moment correlation coefficient.

The students are walked through calculating PMCC for a large data set with Microsoft Excel.

A6 (part)recognise correlation

A8 (part)use and interpret the product moment correlation coefficient, recognising its limitations

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(see 2c for student’s spreadsheet, or 2b for a printable hard copy)

A card matching activity where students match scatter diagrams to a PMCC is provided as consolidation. (see 2a below)

2a Correlation Vs world matching cards A card matching activity where students match scatter diagrams to a PMCC.


A8 (part) use and interpret the product moment correlation coefficient, recognising its limitations2b Students sheet – Correlation WS world data

sheet V3A PDF hard copy of the data contained in the Excel spreadsheet 2c

2c Students – Correlation tasks An Excel spreadsheet containing data, to be used alongside Q10 on 2 Students sheet Correlation WS

Folder name: Using a calculator to find PMCC These resources have been included as it could be useful for questions where students have a small data set and are not required to use the summary data, however, examination questions have tended to focus on using the summary data and the formula.


Students sheet - using a calc A set of student friendly instructions showing how to calculate the PMCC using a Classwiz calculator are provided to enable students to work through the sheet. Two data sets with follow up questions have been provided.


A8 (part)use and interpret the product moment correlation coefficient, recognising its limitations

Folder name: Using the formula and summary statistics to find r folder


Students sheet - Using summary data to calculate PMCCv2

This activity is designed to get students familiar with the formula for calculating r and to recap on ideas previously used in the world data activity.


A8 (part)

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The introductory passage of the student sheet explains how sometimes summary figures are used to calculate the value of r. You may wish to have a source booklet from a previous examination so students can see how the formula is presented.

The questions show a steady progression starting with three components Sxx , Syy and Sxy. Then using different letters to represent variables; t, p and w in place of x and y. Finally moving onto Σxi, Σyi , Σxiyi , Σxi

2 Σyi2 . At this

point it’s worth emphasising the difference between Σxi

2 the total of x2 values and ¿ (the total of x values)2

Question 3 aims to illustrate that using the scatter diagram and the correlation coefficient together is probably a better indicator of the difference in the strength of correlations than using one of these in isolation.

use and interpret the product moment correlation coefficient, recognising its limitations

Folder name: Correlation and causation


Students sheet - Correlation sort Activity linked to the video clip. A6 recognise correlation and know that it does not indicate causation.

A7 apply and interpret explanatory (independent) and response (dependent) variables, interpolate and extrapolate apparent trends while knowing the dangers of doing so

Students sheet – independent and dependent variables

Activity linked to the video clip

Students sheet – Is this a valid argument? Activity investigating false/spurious correlations


Understanding and using scatter diagrams An online lesson activity with video explanations.

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Students explore a scenario involving a project with real data. As the activity progresses the students look at the anomalies such as outliers and think through how to deal with them.

Product moment correlation coefficient (r) The activity looks at using a spreadsheet to find the product moment correlation coefficient.

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Regression – Teacher overview

Summary of content: The matching puzzle provides an opportunity to recap on work from GCSE, including the general equation of a straight line y=mx+cand the significance of the gradient (m) and intercept on the y axis (c). The averages cards, containing x and y , can be matched to the diagrams by using the fact that the line should pass through (x , y ). The regression worksheets involve use of data from the world happiness report. Students learn to calculate, use and interpret a regression line. R2 values are shown on the plots providing the opportunity, should you wish, to extend the student’s knowledge to include the use/misuse of this figure.

Pre-requisites: GCSE knowledge of scatter diagrams. GCSE knowledge of equation of a straight line.

Approximate guided learning hours: 6 - 8 GLH guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.

Auto-marked online assessment: Section test - Regression


Folder name: Regression


Scatter plot matching Students are asked to match four scatterplots with their equations and summary statistics.

This activity provides an opportunity to correct misunderstandings and emphasise some key points like, the general equation of a straight line y=mx+c and the significance of the gradient (m) and intercept on the y axis (c) Two of the regression lines have positive gradients and two have negative gradients, so matching equations to diagrams is possible using the gradient and intercept. There is also an opportunity here to recap word descriptions of correlations and assessing the strength of a correlation from the appearance of the graph, (skills covered in

A9 (part) Calculate the equation of a linear regression line using the method of least squares (candidates may be asked to draw this regression line on a scatter diagram)

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greater depth in the section on correlation).

The averages cards, containing and , can be matched to the diagrams by using the fact that the line should pass through ( , )

The tables containing values of x and y, could be matched to the summary data by calculating and , or alternatively the students can use an appropriate function on their calculator to find the regression line.

As well as giving practice in key skills, the matching exercise provides an opportunity to assess whether any further support is required before tackling the student sheet.

Students sheet – RegressionV2.2 This sheet uses world data to encourage the students to think about the meaning of the trend shown by the regression line.

Students are then asked to calculate the equation of regression lines using the function on their calculator. (It may be a good idea to have a copy of the user manual or some instructions for the popular brand of calculators)

(Note : In the activity, students are not asked to draw a line of best fit however should you wish to you could ask them to draw a scatter diagram for the data in Q6. You should also ensure that students are able to calculate the equation of the regression line using the formula rather than calculator functions.)

In later questions students are asked to interpret

A8 Draw estimated lines of best fit and make predictions; use and interpret the product moment correlation coefficient, recognising its limitations.

A7 Apply and interpret explanatory (independent) and response (dependent) variables, interpolate and extrapolate apparent trends while knowing the dangers of doing so.

(Note the terms shown in bold are not used explicitly on the student sheet, but you may wish to introduce them when discussing the work.)

A9 Use, apply and interpret linear regression; calculate the equation of a linear regression line using the method of least squares (candidates

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the meaning of the gradient of the regression line and substitute values into the equation of the regression line to obtain predictions.

The dangers of extrapolation are covered in the last question of this sheet and in the interactive student packages.

may be asked to draw this regression line on a scatter diagram)


Introducing regression This online activity starts by examining linear relationships and using them to predict costs. Skills such as reading from graphs are practiced. In the later pages of the activity students are shown how to find the equation of a line of best fit by using a calculator.

A9 Use, apply and interpret linear regression; calculate the equation of a linear regression line using the method of least squares (candidates may be asked to draw this regression line on a scatter diagram)

Using regression This activity builds on work covered in the introducing regression by using regression to model different scenarios. The activity also examines the dangers of extrapolation.

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Recognising graphs – Teacher overview

Summary of content: This section covers quadratic, reciprocal, polynomial and exponential graphs. Students will have met these at GCSE but here they are also considering how the graphs can be used to represent real situations. Graphical modelling is used in many situations – you may find examples in the news that you want to share with students.

Pre-requisites: It will be helpful if students understand standard algebraic notation and can read and plot points on a graph. This section may highlight the need to revise some of the work on graphs and gradients from GCSE.

Approximate guided learning hours: 10 -12 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.

Auto-marked online assessment: (To be added when available)



Folder name: Recognising and interpreting graphs


1.a Graph matching puzzle

(also PDF version)

Students sheet. SG3 recognise, sketch and interpret graphs of quadratic functions, reciprocal functions, polynomial functions of the form y = xn and exponential functions y = kx for positive values of k

2 Finding the gradient 1

2 Finding the gradient 2GeoGebra files to assist with teaching & learning SG4 interpret the gradient at a point on a curve

as the instantaneous rate of change and apply the concepts of average and instantaneous rates of change (gradients of chords and tangents) in numerical and graphical contexts

2a. Students sheet – The gradient of a curve

(also PDF version)

Students task sheet

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3 Answer bacteria question

3 Answer youtube question

3 Finding a gradient 3

GeoGebra files to help demonstrate answers

3a Students sheet – Using tangent

(also PDF version)

Student worksheet

4. Exploring y=a^x

4. Investigating y=a^x

GeoGebra files for students to use with the task sheet.

SG3 recognise, sketch and interpret graphs of quadratic functions, reciprocal functions, polynomial functions of the form y = xn and exponential functions y = kx for positive values of k

SG4 interpret the gradient at a point on a curve as the instantaneous rate of change and apply the concepts of average and instantaneous rates of change (gradients of chords and tangents) in numerical and graphical contexts

SG5 calculate with roots, and with integer and fractional indices

4a Students sheet – investigating y=a^x

(also PDF version)

Student task sheet


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Probability– Teacher overview

Summary of content: Understanding probability related to realistic contexts is important for all citizens when thinking about the risks they may face in everyday life. When working with conditional probabilities, either in a two way table or in a tree diagram, students may find that they are better able to understand the situation if they work with representative frequencies than if they work with probabilities.

Introduce the following formulae where appropriate:

P6 understand, interpret and use appropriately the following formulae: P(A’) = 1 – P(A); P(A ∪ B) = P(A) + P(B) – P(A ∩ B); P(A ∩ B) = P(A)P(B|A); P(B|A) = P(B) and P(A|B) = P(A); P(A ∩ B) = P(A)P(B)

Pre-requisites: GCSE probability – there is an interactive study package to help students revise these concepts.

Approximate guided learning hours: 8 – 10 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.




Folder name: Frequency trees


Student’s sheet Frequency trees This resource is aimed at demonstrating how mathematics can help when making an informed choice. To do this, it uses situations which are counter intuitive, predominantly medical screening. It is important to ensure that students understand that medical screening serves an important purpose and the tests are very good, just not perfect. The situation regarding the number of false positives being larger than the

P2 enumerate sets and combinations of sets systematically using tree diagrams

P3 (part) calculate the probability of independent and dependent combined events, including sampling with and without replacement, using tree diagrams

P4 (part) calculate and interpret conditional probabilities through representation using

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number of true positives arises because of a combination of large numbers tested and very low the prevalence of the medical condition. In effect a very small percentage of a very large number is larger than a very large percentage of a very small number. In practice, the results of any positive test are checked again to reduce the probability of a false positive – understanding the probabilities has led to this becoming common practice. It is important that students are not put off screening tests, against NHS guidance.

expected frequencies with tree diagrams

Folder name: Two-way table card sort


Spinners card sort – Student sheet This card sort is designed to encourage students to think about a number of aspects connected to probability whilst tackling a problem. Aim to discuss:

That with practical experiments such as these, it is very unlikely that the results of two experiments will be exactly the same. There will be some variation due to random chance. You may be able to add that doing a greater number of trials generally leads a result closer to the theoretical probability.

The advantages and disadvantages of the methods chosen by the students to find the probabilities of the scores.

P3 (part) calculate the probability of independent combined events, using other representations,

Folder name: Using Venn diagrams

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Student sheet Probability Venn diagrams This activity introduces the students to Venn diagrams and some notation. Venn diagrams are used to answer questions in context.

P2 enumerate sets and combinations of sets systematically using tree diagrams

P3 calculate the probability of independent and dependent combined events, including sampling with and without replacement, using tree diagrams and other representations, Venn diagrams, sum and product laws

P5 understand, use and interpret probability notation, its application to Venn diagrams, exclusive and complementary events, independence of two events

Folder name: Conditional probability


Student sheet conditional probability

and

Student sheet card sort conditional probability

This activity uses a number of contexts to introduce conditional probability.

The card sort is included as part of this sheet

P4 calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

P5 understand, use and interpret probability notation, its application to Venn diagrams, exclusive and complementary events, independence of two events and conditional probability


Basic probability A recap on GCSE probability but involving the sort of contexts applicable to Core Maths

P3 (part) calculate the probability of independent and dependent combined events,

Setting up and using frequency trees Starts by introducing frequency trees and leads students towards conditional probability.

P4 (part) calculate and interpret conditional probabilities through representation using

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expected frequencies with tree diagrams

Conditional probability A look at probability in context such as lie detectors and drug tests, using frequency trees.

P4 calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

Understanding risk – Teacher overview

Summary of content The students examine a variety of scenarios involving product insurance, linked to expected losses.

Pre-requisites: It may be better to do this section after the one on probability.

Approximate guided learning hours: 4 - 5 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.




Folder name: Hazard and risk

Activity title Activity title Activity title

Student spreadsheet – financial risk Student spreadsheet – financial risk Student spreadsheet – financial risk

Note there is a teachers ppt with discussion questions which introduces hazard and risk


P7 understand and interpret risk as the probability of something happening multiplied by

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Students help sheet (word and PDF) Students help sheet (word and PDF) the resulting cost or benefit if it does; comparison of levels of risk; application of risk to real-life contexts such as finance, insurance and trading


Students help sheet (word and PDF)

Folder name: Product insurance


Students sheet product insurance The students examine a variety of scenarios involving product insurance, linked to expected losses

P7 understand and interpret risk as the probability of something happening multiplied by the resulting cost or benefit if it does; comparison of levels of risk; application of risk to real-life contexts such as finance, insurance and trading


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Spearman’s rank – Teacher overview

Summary of content: This section introduces students to calculating Spearman’s rank correlation coefficient; it contains an activity from the Core Maths Support Program (CMSP). The activity is described in the overview as follows:

“This activity is based on the idea of finding the best songs ever. Clearly personal choice will vary, but this resource is aimed at finding what agreement there is between individual choices. Spearman’s rank correlation coefficient is used to measure the agreement between individual choices.”

Pre-requisites: Some knowledge of correlation is useful

Approximate guided learning hours: 5-7 for the whole section including student interactive packages. Guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students. These skills should be of use in most of the other sections when working on problems.


File Name – Reaction time investigation


Reaction time investigation – Edexcel version Idea for a teacher led project Specification content statements A4 – A10

Folder name: Spearman’s rank activity from CMSP


Best songs ever ppt Activity involving ranking and comparing 10 songs.

A 10 use, apply and interpret Spearman’s rank; calculate Spearman’s rank correlation coefficient and use it as a measure of agreement or for comparisons of the degree of correlation (tied ranks may be tested in the examination papers)


Lesson 1 Understanding and calculating In this lesson students are introduced to some of A10 use, apply and interpret Spearman’s rank;

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Spearman’s rank correlation the different types of data. There is particular emphasis on recognising and understanding ordinal data such as ranks. By using a spreadsheet tool, students observe how using ranks changes a non-linear association to a linear correlation. Students learn why it is important to rank both variables in the same way, either both ascending, or descending, to enable then to use word descriptions of correlations correctly. The section ends by showing students how to calculate rs using the Spearman’s formula, and using the =correl function in Excel (a PMCC using the ranks).

calculate Spearman’s rank correlation coefficient and use it as a measure of agreement or for comparisons of the degree of correlation

Lesson 2 Spearman rank correlation with tied ranks

In this lesson, students find out how to assign and work with tied ranks. This section highlights how having tied ranks results in the Spearman formula giving a different answer to using PMCC for the ranks. It is more correct to use PMCC for the ranks in this case but students may see the Spearman formula being used in other subjects.

A10 as above (tied ranks may be tested in the examination papers).

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Exponential graphs – Teacher overview

Summary of content The students learn about exponential growth and decay in a variety of contexts.

Pre-requisites: GCSE graphs. Using multipliers for percentage change.

Approximate guided learning hours: 3-4 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.




Folder name: Exponential graphs


Bacteria graph

Depreciation graph

Half life

Savings

GeoGebra files to support the session – see teachers’ notes for further guidance


SG2 (part) calculate simple interest and compound interest; use and interpret graphical representation of simple and compound interestSimulating dice to use

Simulating dice example

Excel files to support the session – see teachers’ notes for further guidance

Student worksheets Materials for students.


H5P Exponential growth and decay

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Sequences – Teacher overview

Summary of content This section covers the bulk of the content on sequences. Teachers may wish to use individual activities at different times rather than doing the whole of the section in one block. The inflation could be linked to the section on finance, and going viral links to exponential growth.

When teaching sequences, show how term to term rules (which students often express in words) can be expressed algebraically by a simple relation of the form xn+1 =f (xn )Pre-requisites: This section builds on GCSE work on algebra, whilst introducing new mathematics.

Approximate guided learning hours: 18 -20 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.




Folder name: Inflation


Student sheets - Inflation The activity uses the website “back in my day” to introduce students to the concept of inflation.

This is then developed into using multipliers to calculate percentage changes, leading on to geometric sequences.

The work introduces the notation of a and r for the first term and common ratio respectively.

SG1 set up, solve and interpret the answers to growth and decay problems, including compound interest.

SG7 recognise, use and interpret sequences, including those given by a formula for the nth term, those generated by a simple relation of the

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The students then use a geometric sequence as a model and finally look at summing the terms of a sequence. Ensure that students can understand and use sigma notation. You can extend this to cover the following learning outcome:

SG10 (part) the sum to infinity of a convergent geometric series including the use of |r| < 1.

The formula Sn=a (1−r n)1−r

is presented, but the

proof of formula is not part of this activity.

A GeoGebra app is provided for teachers wishing to demonstrate the proof.

form

SG8 understand and use sigma notation

SG10 recognise, use and interpret geometric series, including the general term of a geometric series, the sum to n terms of a geometric series and the sum to infinity of a convergent geometric series including the use of |r| < 1.

Student sheet – sequences matching puzzle Students are asked to place a set of numbers into a grid to make sequences for given values of a and r


Folder name: Going viral


Student sheet This activity guides the students through the process of modelling a scenario with a geometric series.

The students build a spreadsheet from a template and use this to investigate how changing the parameters of the model affect the results.

Standard notation is used, describing terms ie a, ar …

SG3 recognise, sketch and interpret graphs of quadratic functions, reciprocal functions, polynomial functions of the form y = xn and exponential functions y = kx for positive values of k


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Folder name: Patterns of growth and decay


Student sheet This activity is intended to introduce the students to arithmetic sequences in preparation for the autonomous learning task.

The students meet arithmetic sequences and series. The formulas for calculating a term and the sum are introduced. And some scenarios are modelled.

SG9 recognise, use and interpret arithmetic series, including the general term of an arithmetic series and the sum to n terms of an arithmetic series

Folder name: Autonomous learning task


Student sheet Students are asked to build a model using an arithmetic and a geometric sequence. The students are then asked to compare, contrast and evaluate the models.


SG9 recognise, use and interpret arithmetic series, including the general term of an arithmetic series and the sum to n terms of an arithmetic series

SG10 recognise, use and interpret geometric series, including the general term of

a geometric series, the sum to n terms of a geometric series and the sum to

infinity of a convergent geometric series including the use of |r| < 1.

Student sheet – workforce data An Excel spreadsheet with data from NOMIS about the UK workforce.

Folder name: Investigating the sum of a geometric series using GeoGebra. (Extension activity – beyond specification content)

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GeoGebra applet Applet, for teacher and students SG6 recognise and interpret linear and quadratic sequences; deduce expressions to calculate the nth term of linear and quadratic sequences

Folder name: Quadratic sequences


Quadratic sequences

Finding a quadratic sequence formula

GeoGebra demonstration files, links are contained in student and teacher sheets

SG6 recognise and interpret linear and quadratic sequences; deduce expressions to calculate the nth term of linear and quadratic sequences

Students sheet sequences– (word and PDF) Student activities

Match the sequences – (word and PDF) Matching puzzles

Folder name: Fibonacci sequences and Golden ratio


Student sheet (word and PDF versions) Activities and questions for students SG7 recognise, use and interpret sequences, including those given by a formula for the nth term, those generated by a simple relation of the form

Xn+1 = f(xn)

Fibonacci sequences and the golden ratio


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Linear programming – Teacher overview

Summary of content This section introduces the students to linear programming and works towards examination style questions. It would be useful to recap on some linked GCSE work before starting this section, including revision of simultaneous equations as in the following specification learning outcomes:

LP1 translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution

LP2 (part) use the form y = mx + c to identify parallel lines; find the equation of the line through two given points, or through one point with a given gradient

LP4 solve algebraically linear equations in one unknown with the unknown on both sides of the equation

LP6 solve linear inequalities in one variable, representing the solution on a number line using set notation

Extend formulation of linear programming problems to those including three variables – there is an opportunity here to show how these can be solved using software as it will no longer be possible to represent them on graph paper.

Pre-requisites: This section builds on GCSE work on algebra and functions. Some recap work on equations and inequalities is provided in the interactive packages.

Approximate guided learning hours: 7 - 8 guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students.

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Folder name: Section 1 Introducing linear programming


1.2 Student – Using a graph to solve the starter problem.

Students need the GeoGebra Files:

Exploring inequalities

Linear program t-shirts

This extends the students initial experience of the problem and introduces the more formal idea of linear programming

LP2 plot graphs of equations that correspond to straight line graphs in the coordinate plane; use the form y = mx + c to identify parallel lines; find the equation of the line through two given points, or through one point with a given gradient

LP3 recognise, interpret graphs of linear functions

LP7 solve linear inequalities in two variables, representing the solution on a graph

LP8 use algebra to support and construct arguments

LP11 consider problems where solutions must have integer values

1.3 Students linear programming card matching This card matching activity is provided to consolidate the learning in 1.2


LP9 formulate problems as linear programs with up to three variables

1.4 Students intersecting lines matching puzzles Introduces the students to finding the LP5 solve two simultaneous equations in two variables (linear/linear) algebraically; find

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intersection of lines, by inspection and more formal algebraic methods

approximate solutions using a graph

Folder name: Section 2 – Starting exam style questions


2.1 Student sheet - exam style questions, starter questions

Two questions to be used alongside the teacher’s notes and ppt to introduce students to exam style questions.

LP2 plot graphs of equations that correspond to straight line graphs in the coordinate plane; use the form y = mx + c to identify parallel lines; find the equation of the line through two given points, or through one point with a given gradient

LP3 recognise, interpret graphs of linear functions





2.2 Student sheet Further linear programming questions

Further exam style questions for consolidation. LP2 plot graphs of equations that correspond to straight line graphs in the coordinate plane; use the form y = mx + c to identify parallel lines; find the equation of the line through two given points, or through one point with a given gradient

LP3 recognise, interpret graphs of linear

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functions


LP10 solve and interpret two-variable problems graphically, using ruler and vertex methods





Equations

Inequalities

Online auto-marked activities which provide a recap on GCSE work.

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Multi-topic and/or extended activities – Teacher overview

Summary of content: This section contains a mixture of activities which involve project work which often covers a range of topics. Teachers may wish to use these as a follow up or introduction to related sections.

Pre-requisites: (see descriptions below)

Approximate guided learning hours: Pricing products 3-5 GLHComparing climates 3-5 GLH Time seriesThe Big Mac Index 1 GLHThe richest country in the world? 1 GLHIncome, wealth and inequality: Autonomous task. 2 – 3 hoursGini Index 1- 2 GLH

Guided learning hours can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students. These skills should be of use in most of the other sections when working on problems.


Folder name: Pricing products


Pricing products v2 powerpoint

Product pricing - Template

In this task students investigate the balance between sales, cost and profit in a product pricing scenario. The task starts with a specific problem and them builds into a more general investigation.

A spreadsheet is used for this task so some basic knowledge of Excel would help.


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The results can also be plotted onto a graph and interpreted.

Folder name: Climate comparison

This activity is intended as a student project/investigation. The aim is to give students the opportunity to experience investigating a situation using data. A data set has been provided (see spreadsheet Nenana 2018)

Credit – Thank you to the CMSP for introducing me to this interesting data source.


Nenana Ice Classic 2018

Nenana bar charts

Spreadsheet containing the data set (the results of the Nenana Ice classic from 1917-2018)

There are several tabs/sheets containing different configurations of the data and related diagrams. These link to the suggestions in the teachers notes.


Nenana Ice box plots

Student sheet – Nenana Ice challenge

These are GeoGebra files containing diagrams displaying the data from the spreadsheet.

A2 interpret and construct tables and line graphs for time series data; calculate, interpret and use moving averages


A6 recognise correlation and know that it does not indicate causation

A7 apply and interpret explanatory (independent) and response (dependent) variables, interpolate and extrapolate apparent trends while knowing the dangers of doing so

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A8 draw estimated lines of best fit and make predictions; use and interpret the product moment correlation coefficient, recognising its limitations

Nenana Ice classic 2018 The student materials for this activity A5 interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency, including quartiles, inter-quartile range, calculate and use variance and standard deviation

Folder name: The richest country in the world


The richest country in the world .PPT

The richest country in the world worksheet

This resource introduces students to Gross Domestic Product (GDP) and calculations related to GDP, including GDP per capita and GDP per capita, Purchasing power parity (PPP)

Students explore further about GDP and interpret two sets of data related to GDP and GDP per capita.


Folder name: How much does a Big Mac cost?


Big Mac .PPT

Big Mac worksheet

Introduction to how the cost of a Big mac is used across the world as a simple measure of the cost of living.

Starts with an example of how the Big Mac index


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Big Mac fill the gaps

is calculated and moves on to investigate how long people would need to work in different countries to buy a Big Mac.

A table of calculations with some calculations and key information missing. Students use problem solving skills to insert the correct calculations and information that is missing.



Folder name: Income, wealth and inequality; Autonomous task


TBC

Folder name: The Gini coefficient


Gini .PPT This resource starts looking at inequality, then some measures of inequality and finally focussing on a specific measure, the Gini Coefficient. Following on from this students can explore the Gini Coefficient online interactive activity.



Gini Coefficient Students explore inequality and look at a measure of inequality, the Gini Coefficient, that is used internationally to compare levels of inequality. They will use percentages, interpreting graphs and plotting using 2 axes that are built up using cumulative percentages.



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Documents

meiassets.blob.core.windows.net · Web view2021. 4. 12. · Teacher notes, solutions and any other support materials are contained in the teacher folders. ... Students learn about