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AQA Mathematical studies- 2C Critical path and risk - 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, then stretch them to fit the number of weeks you require. The shapes contain links, which can be activated in the usual way (Ctrl and click), to navigate to areas of the scheme with more details on the activities and the specification content covered. You can return to this page by pressing simultaneously the Ctrl and Home keys.

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Percentages Estimation Income Tax and NI

Exchanging Currency

Sampling and data

Critical analysis

Represent & interpret data1

Represent & interpret data2

Saving and borrowing

Numerical calculations and

modelling

Motion graphs and the meaning of

gradients

Exponential growth and decay

Multi topic and/or extended

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Percentages – Teacher overview

Summary of content: Provides an opportunity revise GCSE work on percentages, including; percentage of amounts, percentage changes, repeated percentage changes and reverse percentages, using a range of contextual scenarios. Further aspects of GCSE mathematics such as averages and measures of spread can be revised in the activity “which plant should close?” This section provides an opportunity to recap on work on percentages covered at GCSE and prepares students for forthcoming work on financial maths

Pre-requisites: Some knowledge of percentages, averages and measures of spread would be helpful, but not essential.

Approximate guided learning hours: 3-5 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.

Auto-marked online assessment: Percentages section test

(Solutions available in the teachers section only)

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

Folder name: Percentages: Which plant should close?

Activity title Description Specification learning outcomes

Teacher led classroom activity

Title: Which plant should close?

Includes, an overview of the task, teacher notes and data sheet

This task provides an opportunity for students to use their knowledge of percentages alongside other GCSE work, including work on averages and measures of spread (including the interquartile range) in a decision-making scenario.

A data sheet and teacher notes are provided.

F2.1 interpreting percentages and percentage changes as a fraction or a decimal and interpreting these multiplicatively

F2.2 expressing one quantity as a percentage of another

F2.3 comparing two quantities using percentages

F1.4 finding approximate solutions to problems in financial contexts

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Learning points related to the use of spreadsheets and displaying/interpreting data may also be applicable, depending on what approaches the students use when arriving at and present their decision.

Student interactive study packages

What are percentages?

Working with percentages

Working with multipliers

These three online H5P interactive packages provide a recap on GCSE work on percentages, including:

Percentage of amounts Percentage changes Repeated percentage changes Reverse percentages

The packages offer a range of contextual scenarios.

F2.1 interpreting percentages and percentage changes as a fraction or a decimal and interpreting these multiplicatively

F2.2 expressing one quantity as a percentage of another


F2.4 working with percentages over 100%

F2.5 solving problems involving percentage change including percentage increase/decrease and original value problems, including simple and compound interest

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Estimation and Fermi estimates – Teacher overview

Summary of content: Being able to produce fast and sufficiently accurate estimates is a skill which is useful across a range of settings from multi-million pound projects, to planning your own celebration, trip or project. In this section students have the opportunity to develop their estimation skills using a range of contexts and activities. This topic is a key component of Core Maths and the skills developed in this section should be practiced and enhanced throughout the whole of the course.

Pre-requisites: GCSE number skills and understanding of which calculation to use where will be helpful.

Approximate guided learning hours: 7-10 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. These skills should use in most of the other sections when working on problems.

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

Folder name: Population signs


Teacher notes

Presentation

This activity asks students to think the degree of accuracy which should be used when quoting population figures. This is a nice introduction to Core Maths thinking and reasoning. This provides an initial experience of the uncertainty which surround estimates

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

E1.3 interpreting results in the context of a given problem

Folder name: Estimation


Put these in order A short puzzle where students are asked to place quantities in order, then reflect on their


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thinking. E2.1 making fast, rough estimates of quantities which are either difficult or impossible to measure directly

Estimation questions to try

÷

A series of estimation questions for students to try.


E1.2 selecting and using appropriate mathematical techniques for problems and situations


E1.4 evaluating methods and solutions including how they may have been affected by assumptions made

Loch Ness map For use with the accompanying question on the teacher powerpoint

Match the facts A matching activity which offers practice in estimating quantities. (See the teachers notes for more details)


E2.1 making fast, rough estimates of quantities which are either difficult or impossible to measure directly

Exam style questions A series of examination style questions for students to try.

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'

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answer





Assessment

(Requires sheet Preliminary materials 2g see resources folder)

Preliminary materials

(for use with assessment 2f see resources folder)

A short series of assessment questions, requires preliminary materials sheet







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Accuracy

Estimation

Covers rounding to the nearest unit, decimal places and significant figures. Encourages students to think about sensible accuracy. Link well with the resource on population signs.

Starts by recapping on estimation at GCSE and introduces students to estimating quantities Core Maths style. Would be helpful as a lead into the estimation activities in the folder.



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Income Tax and National Insurance – Teacher overview

Summary of content: This section covers Income Tax and National Insurance. Some of the activities were written in 2018, 2019, others in 2020 and use the thresholds for those particular years.

Pre-requisites: Students will need to be able to calculate percentages of amount. The section on percentages could be used as preparation for this section.

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. These skills should use in most of the other sections when working on problems.

Auto-marked online assessment: Taxation section test


Folder name: Income Tax and National Insurance

Document title Description Specification learning outcomes

Student’s sheet – Percentage of pound card sort Introductory activity – could be used as an initial assessment or to provide a recap on finding percentage of amounts (answers are on teacher sheet with same name)

Student’s sheet – income tax A series of questions requiring the calculation of Income tax and National Insurance

F6.1 income tax, National Insurance, Value Added Tax (VAT)

F5.1 graphical representation, plotting points to create graphs and interpreting results from graphs in financial contexts.

Student’s sheet – incometax.xlsx Spread sheet to accompany task on – student’s sheet – income tax

F6.1 (part) income tax, National Insurance.

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Folder name: Minimum wage


Minimum wage ppt Powerpoint to support the teaching of this activity

Minimum wage worksheet for display Large print version of sheet below. F6.1 (part) income tax, National Insurance.

Minimum wage worksheet The idea behind this piece of work is to give students an insight into the minimum wage that workers should be legally paid. Many 16-18 learners have or will get a part time job and later will get full time employment, they are interested in knowing about their employment rights and what they should be paid.



Income Tax – Incomes below £100,000

Income Tax and National Insurance

This activity provides an introduction to Income Tax and National Insurance. It contains a link to a GeoGebra applet which demonstrates how tax is calculated for a range of salaries.


Exchanging currency – Teacher overview

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Summary of content: This section contributes to a wider set of financial maths skills, an important feature of the Core Maths qualification. Specifically, this section looks at buying and selling currency, as well as wider issues involving currency exchange rates.

Pre-requisites: A knowledge of percentages would be helpful


Auto-marked online assessment: section test


Folder name: Exchanging Currency


Student’s sheet – Currency exchange investigation

Investigating the price of the same article on different Amazon sites – (Amazon.uk, Amazon.us, Amazon.de ….)

F7.3 Currency exchange rates

Student’s spreadsheet – Comparing prices in different countries

Spreadsheet to help with above task. (this can be adapted)

F7.3 Currency exchange rates

Student’s sheet – Four currencies sorting puzzle Mixing percentage and currency exchange F7.3 Currency exchange rates

Student’s sheet – No commission Currency exchange without commission F7.3 Currency exchange rates

Student’s sheet – Currency exchange with commission

Currency exchange with commission F7.3 Currency exchange rates including commission


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Exchanging Currency This interactive package provides a useful interactive self-study package complementing the teacher led lessons. Useful as a homework, pre or post lesson work.

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Sampling and data – Teacher overview

Summary of content: The sections looks at the different types of data, levels of measurement

Pre-requisites: The activity Jury Composition, from the critical analysis section provides a context involving sampling would work well as either a lead in task, to help with spreadsheet skills, or a follow on task to practice the knowledge, skills and understanding gained from working through this section.


Auto-marked online assessment: Levels of measurement section test

Sampling section test


Folder name: Types of variable, data and levels of measurement


Teacher presentation (all activities) A short presentation to collate students’ responses to discussion questions.

Student sheet – Type of variable Introduces the students to categorical, quantitative, continuous and discrete variables

D1.1 appreciating the difference between qualitative and quantitative data, including the difference between discrete and continuous quantitative data

D1.2 appreciating the difference between primary and secondary data, including the use of secondary data that have been processed e.g. grouped

D1.3 collecting quantitative and qualitative primary and secondary data

Student sheet - Types of data Introduces primary and secondary data. Prompts thinking about the pros and cons of different data collection techniques.

Data collection techniques re-appear in the personal research project in the sampling section.

Student sheet – Levels of measurement Examines, nominal, ordinal, interval and ratio. Some of this content extends beyond the

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specification content but is useful for students aiming for university courses where these concepts are needed.

Revision Quiz A short activity which provides a summary to the content covered on types of variable, data and levels of measurement.

D1.1 D1.2 and D1.3

Folder name: Comparing sampling techniques


1.2 SamplingSD pptx A powerpoint presentation to introduce the session and support the teaching of this section

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.

S4.1 (students studying 2A option) understanding what is meant by the term ‘population’ in statistical terms

D2.1 inferring properties of populations or distributions from a sample, whilst knowing the limitations of sampling

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

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


D2.2 appreciating the strengths and limitations of random, cluster, stratified and quota sampling methods and applying this understanding when

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technique.

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

designing sampling strategies, appreciating that improving accuracy by removing bias and increasing sample size may cost/save both time and money

D3.1 (part)

calculating/identifying mean, median, mode, quartiles, range, interquartile range, standard deviation, from raw data

D3.2

interpreting these numerical measures and reaching conclusions based on these measures

Students studying 2A option

S4.1 understanding 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

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.


D2.2 appreciating the strengths and limitations of random, cluster, stratified and quota sampling methods and applying this understanding when designing sampling strategies, appreciating that improving accuracy by removing bias and increasing sample size may cost/save both time and money

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Folder name: Setting a pass mark


Setting a pass mark pptx Powerpoint provided to help with the teaching of the session

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.

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

Learning Outcomes

Students should understand the terms population, census, and sample and how they are related.

Students should gain an understanding that a sample is a selected number of items from a larger population of data.

Students should gain an understanding of how conclusions made from a small sample could be unreliable because of the variability in the


S4.2 (Students studying 2A option) developing ideas of sampling to include the concept of a simple random sample from a population

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possible sample distributions.

Students should be able to make decisions based on the likelihood of particular outcomes from a suitably reliable sample.

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


Quantitative and qualitative data Interactive online self-study package containing video, slides and auto-marked questions.

D1.1 appreciating the difference between qualitative and quantitative data, including the difference between discrete and continuous quantitative data

Census and sampling Interactive online self-study package containing video, slides and auto-marked questions.

S4.1 understanding what is meant by the term ‘population’ in statistical terms

Population and sampling Interactive online self-study package containing video, slides and auto-marked questions.


D2.2 (part) appreciating that improving accuracy by removing bias and increasing sample size may cost/save both time and money

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Critical analysis – Teacher overview

Summary of content: One of the over-arching aims of Core Maths is to help students to become data literate and gain a sufficient understanding of numerical information to enable them to make well informed decisions. Students should understand the limitations of information and be able to determine which sources may be unreliable. It is suggested that the activities in the sections are interspersed at key points in the course rather than being done in one block. These skills should use in most of the other sections when working on problems.

Pre-requisites: (non)

Approximate guided learning hours: (see the comments below by the folder name for estimated guided learning hours) these can be used a rough guide, however the amount of time required for this section will vary depending on the needs of individual students. Teacher notes, solutions and any other support materials are contained in the teacher folders

Folder name: Jury Composition (spreadsheet modelling) – (3 - 5 GLH) Would work well as either a lead in, or follow up, to the section on sampling and data.


Video Clip - Building a simulation

Spreadsheet modelling -students template

Instructions for building - Students instruction sheet (there is a PDF version in the student folder)

There is a presentation to introduce the task.

A Video clip or paper instructions on PDF and excel template spreadsheet

C1.1 criticising the arguments of others

C3.1 comparing results from a model with real data

C3.2 critical analysis of data quoted in media, political campaigns, marketing etc

(Teachers folder only) Basic 50 percent sheet The completed first spreadsheet

(Teachers folder only) Basic 40 percent sheet The completed second spreadsheet

(Teachers folder only) Spreadsheet 200 juries Combined spreadsheet with charts

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Folder name: Climate comparison

(5- 8GLH) Would work well as either a lead in, or follow up to the section, the section representing and interpreting data 1.

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.


1. Teacher sheet – Nenana Ice Challenge Provides suggestions on how to get the most from the resource.

C2.1 Summarising and report writing

D3.1 Calculating/identifying mean, median, mode, quartiles, percentiles, range, interquartile range, standard deviation, either from raw data or from cumulative frequency diagrams, stem-and-leaf diagrams or box plots

D3.2 Interpreting these numerical measures and reaching conclusions based on these measures

D4.1 Constructing and interpreting diagrams for grouped discrete data and continuous data, knowing their appropriate use and reaching conclusions based on these diagrams, including histograms with equal and unequal class intervals and cumulative frequency graphs, box and whisker plots, stem-and-leaf diagrams (including back-to-back)

2. Nenana Ice Classic 2018 Spreadsheet containing the data set (the results of the Nenana Ice classic from 1917-2008)

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

3. Nenana bar charts 4. Nenana Ice box plots

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

5. Student sheet – Nenana Ice challenge6. Nenana Ice classic 2018

The student materials for this activity

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https://www.geogebra.org/m/yx9ktxzd

https://www.geogebra.org/m/bmstsunm

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Representing and interpreting data 1 – Teacher overview

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:

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


Folder name: Interpreting data in bar chart and population pyramids


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


D4.1 (Part) constructing and interpreting diagrams for grouped discrete data and continuous data, knowing their appropriate use and reaching conclusions based on these diagrams, including histograms with equal and unequal class intervals and cumulative frequency graphs, box and whisker plots, stem-and-leaf diagrams (including back-to-back)

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population pyramids to encourage students to think more deeply about data.

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

(includes a matching task)

The students examine data from a variety of contexts.

The sheet provides guidance on how to calculate medians, Q1, Q3 and interquartile ranges. Students use these measures to compare samples.

D3.1 (part) calculating/identifying mean, median, mode, quartiles, percentiles, range, interquartile range, standard deviation, either from raw data or from cumulative frequency diagrams, stem-and-leaf diagrams or box plots

D3.2 interpreting these numerical measures and reaching conclusions based on these measures


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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.

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.

D3.1 calculating/identifying mean, median, mode, quartiles, percentiles, range, interquartile range, standard deviationeither from raw data or from cumulative frequency diagrams, stem-and-leaf diagrams or box plots

D3.2interpreting these numerical measures and reaching conclusions based on these measures

D4.1 constructing and interpreting diagrams for grouped discrete data and continuous data, knowing their appropriate use and reaching conclusions based on these diagrams

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.

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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

D3.1 calculating/identifying mean, median, mode, quartiles, percentiles, range, interquartile range, standard deviation either from raw data or from cumulative frequency diagrams, stem-and-leaf diagrams or box plots D3.2 interpreting these numerical measures and reaching conclusions based on these measures

Student worksheet Introduces the idea of percentiles using 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


D3.1 calculating/identifying mean, median, mode, quartiles, percentiles, range, interquartile range, standard deviation either from raw data or from cumulative frequency diagrams, stem-and-leaf diagrams or box plots


Student worksheet – Cumulative Frequency

Plus

Demo video – Autograph cumulative frequency

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Demo video – GeoGebra cumulative frequency





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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Representing and interpreting 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.

D3.2 (part) interpreting numerical measures and reaching conclusions based on these measures

C1.1 criticising the arguments of others

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.

Calculator skills

D3.1 (part) calculating/identifying mean, median, mode, quartiles, percentiles, range, interquartile range, standard deviation, either from raw data or from cumulative frequency diagrams, stem-Standard deviation pptx Powerpoint presentation provides an

introductory problem and assists with the

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teaching of this content. and-leaf diagrams or box plots)

D3.2 interpreting these numerical measures and reaching conclusions based on these measuresTeacher’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: Histograms


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



D4.1 (Part) constructing and interpreting diagrams for grouped discrete data and continuous data, knowing their appropriate use and reaching conclusions based on these diagrams, including histograms with equal and unequal class intervals and cumulative frequency graphs, box and whisker plots, stem-

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

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and-leaf diagrams (including back-to-back)

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


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)

C2.1 summarising and report writing

D4.1 Constructing and interpreting diagrams for grouped discrete data and continuous data, knowing their appropriate use and reaching conclusions based on these diagrams

including histograms with equal and unequal class intervals and cumulative frequency graphs, box and whisker plots, stem-and-leaf diagrams (including back-to-back)

6 Student sheet – Which diagram data set sheetStudents are given four data sets and asked to chose 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

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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.

C2.1

summarising and report writing




ALT – Student’s sheet – DigitalBreathTest2013.xlx

Large data set on excel spreadsheet

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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Saving and borrowing – Teacher overview

Summary of content: This section contains further aspects of financial maths and complements the earlier section on Income Tax and National Insurance

Pre-requisites: A knowledge of percentages and multipliers

Approximate guided learning hours: 20 -25 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: Budgeting


1a Lifestyle calculations exemplar.docx

1b Exemplar answers making decisions scenarios

1c Further Costing exercises exemplar answers

Exemplar answers to the activities. F7.4 Budgeting

2 Budgeting teach presentation Powerpoint presentation to introduce and support the teaching of the activities.

3a Card set 1 Employment

3b Card set 2 Accommodation

3c Card set 3 Cars

3d Card set 4 Money

4 Lifestyle questions

Lifestyle activity and scenario cards.

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5 Worksheet 1 Job offer

6 Worksheet 2 Windfall

Two worksheet with decision making scenarios.

7 Further Costing exercises 2 Further questions for consolidation

Folder name: Football tickets - Inflation


Spreadsheet Football tickets Spreadsheet for student tasks 7.1 The effect of inflation.

Retail Price Index (RPI), Consumer Price Index (CPI)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

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Folder name: Student loans


Student sheet – Initial questions Starter activity – questions F4.1 Student loans and mortgages, Annual Percentage Rate (APR)

Students question sheet Follow on questions

Spreadsheet for last question To support the final task on the spreadsheet

Folder name: AER


Student sheet 1 matching puzzles Students need to match the correct calculation to the correct situation.

F3.1 simple and compound interest

Annual Equivalent Rate (AER)

F3.2 savings and investments

Student sheet 2 AER Links to the work in the first video clip see teachers notes and ppt

Students sheet 3 Nominal interest and AER Links to second clip covering nominal rates and AER

Student sheet 4 Practice questions Contains a mixture of questions involving AER

Folder name: Exam style questions

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


Interest rates

Loans and interest rates

Repayments

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.

This interactive package provides a useful interactive self-study package covering repayment of loans. The APR formula is introduced.

F3.1 simple and compound interest

Annual Equivalent Rate (AER)

F3.2 savings and investments

F4.1 Student loans and mortgages, Annual Percentage Rate (APR)

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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

Pre-requisites: (see descriptions below)

Approximate guided learning hours:

Different Diets 3-5 GLHPricing products 3-5 GLHThe 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 use in most of the other sections when working on problems.


Folder name: Different diets


Different diets Students are asked to plan a day’s worth of eating for a variety of diets and compare the cost of their options. Students then compare and contrast their menus.

F7.4 budgeting

Vegans Students investigate the growing number of people opting for a vegan diet. The students build, investigate and interpret graphical models of the data.

C3.1 comparing results from a model with real data


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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.

F5.1 plotting points to create graphs and interpreting results from graphs in financial contexts

Folder name: The richest country in the world


The richest country in the world .PPT 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)

F7.2 setting up, solving and interpreting the solutions to financial problems, including those that involve compound interest using iterative methods

The richest country in the world worksheet Students explore further about GDP and interpret two sets of data related to GDP and GDP per capita.


F2.2 expressing one quantity as a percentage of

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another


F2.4 working with percentages over 100%

Folder name: How much does a Big Mac cost?


Big Mac .PPT

Big Mac worksheet

Big Mac fill the gaps

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 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.


F7.3 currency exchange rates including commission

F2.5 solving problems involving percentage change, including percentage increase/decrease and original value problems, including simple and compound interest

Folder name: Income, wealth and inequality; Autonomous task


TBC

Folder name: The Gini coefficient

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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.

F5.1 graphical representation, plotting points to create graphs and interpreting results from graphs in financial contexts


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.

F1.1 substituting numerical values into formulae, spreadsheets and financial expressions, including bank accounts

F5.1 graphical representation, plotting points to create graphs and interpreting results from graphs in financial contexts


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Numerical calculations and modelling – Teacher overview

Summary of content This section contains a number of activities involving mathematical modelling and graphs. Students are required to use mathematical formulae, plot graphs and interpret results

Pre-requisites: GCSE algebra (substitution into formulae). GCSE graph skills.

Approximate guided learning hours: 3 - 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. Teachers may wish to use the activities periodically throughout the course rather than in one sitting.

Auto-marked online assessment:



Credit – Thank you to the CMSP for developing these teaching resources

Folder name: Reading age (1-2 GLH)


Algebra and Graphs Reading age handout A task sheet containing two formulae and sample texts for students.

F1.1 substituting numerical values into formulae, spreadsheets and financial expressions including bank accounts

F1.2 using conventional notation for priority of operations, including brackets, powers, roots and reciprocal

E1.1 representing a situation mathematically, making assumptions and simplifications


E1.3 interpreting results in the context of a given

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problem


Folder name: Wind Chill (1 GLH)


Algebra and graphs task 10 Wind chill factor handout

In this activity students explore the problem of analysing the effect of wind speed. Students substitute values into a formula.

Students task sheet.

F1.1 substituting numerical values into formulae, spreadsheets and financial expressions

including bank accounts






Folder name: Olympic ranks (1-2GLH)

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Medal table data (data set) Student’s spreadsheet of the data set F1.1 substituting numerical values into formulae, spreadsheets and financial expressions

including bank accounts






Olympic medal table (activity sheet) Students task sheet

Involves using a spreadsheet


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Motion graphs and the meaning of gradients – Teacher overview

Summary of content

These activities are based in part on work from the “Improving Learning in Mathematics” the standards box, particularly the section “interpreting distance time graphs with a computer A5”, which is available from the stem e-library https://www.stem.org.uk/elibrary/resource/26958

It would be helpful to look at some of the applets at https://www.geogebra.org/m/AjWXqFVM before the lesson.

Note - the applets Velocity 6 and beyond feature in the questions on the student sheet so are probably best avoided until the students have had an opportunity to work on them.

Pre-requisites: GCSE Graph work

Approximate guided learning hours: 3-5 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: Motion graphs


4 Students sheet – Motion graphs Questions involving motion graphs

Work on motion graphs could be taken further to express the motion using an equation and interpret intersections of motion graphs as solutions of equations to cover G2.2 interpreting the solutions of equations as the intersection points of graphs and vice versa

G4.1 knowing that the average speed of an object during a particular period of time is given by (distance travelled/time taken)

G5.1 knowing that the gradient of a distance–time graph represents speed and that the gradient of a velocity–time graph represents acceleration

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https://www.geogebra.org/m/AjWXqFVM

https://www.stem.org.uk/elibrary/resource/26958

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Folder name: The meaning of gradient


4. Student sheet graph matching puzzle A card matching puzzle G3.1 interpreting the gradient of a straight-line graph as a rate of change

5 Student sheet - Meaning of gradient A thinking/discussion activity


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Exponential Growth and Decay – Teacher overview

Summary of content The students learn about exponential growth and decay in a variety of context. The activity “do Vampires exist?” from the CMSP can be used to consolidate learning. In exponential graphs, the graph matching puzzle provides an opportunity to think about a range of different functions. Using tangents examines approximating the gradient of a curve. Whist the task investigating a^x gets the students to explore exponential functions. Modelling medication looks at more complex functions which are use to model the behaviour of medication injected and taken orally.

When modelling with exponential functions, you should take the opportunity to discuss the dangers of extrapolation – this may be best done when modelling with contexts from the news.

There is currently no resource covering G6.2 using a calculator log function to solve equations of the form and but you could extend some of the tasks to include this.

Pre-requisites: Work on motion graphs and gradients

Approximate guided learning hours: 16-18 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.



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

Folder name: Exponential graphs


Bacteria graph

Depreciation graph

Half life

Savings

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

G8.2 using exponential functions to model growth and decay in various contexts

Simulating dice to use

Simulating dice example

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

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Student worksheets Materials for students.

Folder name: Do Vampires exist? (from CMSP resources)


Do Vampires exist? Lesson Teacher’s notes to support the teaching of the session


Do Vampires exist? Powerpoint A powerpoint to support the teaching of this session, includes student tasks.

Folder name: Recognising graphs


1.a Graph matching puzzle

(also PDF version)

Students sheet. You could revise plotting curves as a pre-cursor to this activity and follow up by sketching curves.

G1.1 sketching and plotting curves defined by simple equations

knowing the shapes of the graphs of linear, quadratic, cubic and exponential functions will be expected

G2.1 plotting and interpreting graphs (including exponential graphs) in real contexts, to find approximate solutions to problems

2 Finding the gradient 1

2 Finding the gradient 2GeoGebra files to assist with teaching & learning G3.1 interpreting the gradient of a straight line

graph as a rate of change

G3.2 interpreting the gradient at a point on a curve as an instantaneous rate of change understanding that some maximum and minimum points on curves occur where the gradient is zero

G3.3 estimating rates of change for functions from their graphs

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 G2.1 plotting and interpreting graphs (including exponential graphs) in real contexts, to find approximate solutions to problems

G3.1 interpreting the gradient of a straight line graph as a rate of change

G3.2 interpreting the gradient at a point on a curve as an instantaneous rate of change understanding that some maximum and minimum points on curves occur where the gradient is zero

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 distance travelled over time taken

G5.1 knowing that the gradient of a distance–time graph represents speed and that the gradient of a velocity–time graph represents acceleration

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.

G7.1 understanding that e has been chosen as the standard base for exponential functions knowing that the gradient at any point on the graph of y=ex is equal to the y value of that point4a Students sheet – investigating y=a^x

(also PDF version)

Student task sheet

Folder name: Modelling medication


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5a Student sheet exponential functionsV1

GeoGebra file 5a Exploring expV3

The aim of this project is to develop the students’ understanding of the function

y=A eλt+K

The students are asked to produce a poster to explain the results of their investigation.

G8.1 formulating and using equations of the form y=Cax and y=Cekx


6a Student sheet Modelling with exponentialsV1

GeoGebra file 6A model 1V3

This looks at an exponential function used to model the behaviour of medication given via injection



7a Student sheet – Oral medication

GeoGebra file model 2Start

This adapts the model for medication given via injection to model medication taken orally. This is a more complicated model.




H5P Exponential growth and decay G6.1 using a calculator to find values of such a function ( )

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