M1a Modelling session 1.ppt Slides 1.1 –...

1 Modelling: Handouts for participants © Crown copyright 2002

M1a Modelling session 1.ppt Slides 1.1 – 1.3


M1a Modelling session 1.ppt Slide 1.13


Handout 1

M1d

Setting up a model on a spreadsheet1 Times need to be recorded from zero to some maximum (say, 12

minutes) with equal increments (say, 1 minute).

For example, if cell B11 holds the initial time (0):

• the formula for cell B12 is =B11+1

• the formula for B12 needs to be replicated down as far as, say, B23.

Alternatively, use the fill handle to generate the sequence or use the fill series.

2 The column of corresponding temperatures based on the initialtemperature and the drop each minute needs to be calculated.

For example, if cell B11 holds the initial time, cell C11 will hold the initialtemperature.

Store the initial temperature in an easily-accessible cell such as C7.

Enter the loss of temperature each minute into a cell from which it can easilybe changed, for example, H7.

The temperature at time 0 will be given by =C7, and at time 1 it will be givenby =C11–H7.

What happens if this formula is dragged down to cell C23?

3 Distinguish between relative and absolute cell references.

What errors were reported and why did they occur?

C11, which we want to change while dragging, is a relative cell referencewhile H7, which we want to stay constant, is an absolute cell reference.

4 Change cell reference to absolute.

For example, $H$7 is an absolute cell reference so edit the formula for C12 toread =C11–$H$7 and replicate this to the block C12:C23.

The <F4> key in Microsoft Excel automatically enters the reference as anabsolute one. Alternatively, cell ranges can be named and referred to.

5 Data need appropriate graphical representation, e.g. scatter graph.

For example, highlight the block B11:C23 and enter the Graph Wizard.

Decide:

• on an appropriate graph style;

• the ranges to be used on each axis;

• how to label the axes;

• whether a legend is needed;

• where to put the titles on the graph;

• where the graph should go on the sheet.


Handout 2

M2b

Techniques and the teaching unitsStarting a model – raw data, raw structure and raw assumptions

Load the file M2c Mobyphone 1.xls. This file is the starting point for developing amodel for mobile telephone tariffs in sample teaching unit 8.4, lesson 2.

Discuss:

• the importance of the structure and layout of the model;

• what the raw data tell us;

• which tariff gives the best value;

• whether the assumptions made for the model are appropriate.

More complex assumptions can be added as the model is developed. What mightthese be?

Using the fill handle to replicate formulae

Load M2d Table square.xls. This file is the starting point for demonstrating theeffects of using the fill handle on sequences of data, in sample teaching unit 7.4,lesson 1.

Investigate the effects on numbers, months and days of the week when they aredragged by means of the fill handle. Note that you will the need to select more thanone cell when trying to copy a sequence of numbers.

Discuss:

• how lists and sequences can be created this way;

• the meaning of the term ‘replicate’ and its significance to cell references in acopied formula.

Monday Jan

Tuesday Feb Table square M2d

Wednesday Mar x 2 3 4 5 6

2 4 6

3 6 9

4 8 12

5 10 15

6


Handout 2

M2b cont.

Return to the file M2cMobyphone 1.xls. This is used with handout 3 Phoneworksheet to explain the construction of formulae, and how they can be copied, in sample teaching unit 8.4, lesson 2.

Investigate how the model has been set up to calculate costs (outputs) for eachtariff given a value (input) in B5 for the number of minutes. This sort of model takesa given input, processes the data within the spreadsheet and reports acorresponding output value. Models that follow the ‘input – process – output’system are called ‘deterministic models’.

Practise using the fill handle for dragging and copying formulae.

Comment and callout boxes

Note the use of comment and callout boxes in the last example. These giveguidance on how the formula has been constructed. Make sure you know how to:

• add comments to a cell;

• activate and/or view comments permanently;

• print comments either on or below the spreadsheet for reference.

Investigate the use of callouts (from Autoshapes) to supplement the explanation forthe user. How useful do you think these tools might be for:

• annotating files for pupils;

• pupils annotating their own work?

Phone worksheet 1 BackgroundThe spreadsheet shows the start of a mobile phone model that you are going todevelop. The estimated number of minutes used per month can be entered incell B5 as shown.

1 Ensure you have file M2e Mobyphone 1.xls loaded (as shown).

2 Change the number of minutes in B5. What happens to the values in column Eunder the ‘minutes used’ heading? Why does this happen?

3 Wh t d ll E11 t E16 t i ?

Handout 3M2e


Handout 2

M2b cont.Data validation

Keep the file M2c Mobyphone 1.xls loaded. Locate cell B5 and investigate:

• what happens when you try to insert a number outside the given range of100 to 600;

• how to enter data validation limits;

• how input messages and error alerts can be attached to a given cell.

Discuss the use of data validation to capture incorrect values or to check thatextreme values are suitable, for example:

• to trap the wrong year of birth for a Year 9 pupil on the school database;

• to check if an age is really 102;

• to confirm unusual registration plates.

Selecting non-adjacent columns, charting data and editingcharts

Load the file M2f Mobyphone 2-extended model.xls. This file, when used withhandout 4 Phone worksheet 2, demonstrates how to create charts and how tolink interactively with the mobile telephone data, in sample teaching unit 8.4, lesson 3.

Investigate how:

• to use the instructions on screen for using the Chart Wizard;

• to select non-adjacent columns for charting;

• each part of the chart is an ‘object’ and may be edited separately.

Phone worksheet 2BackgroundThe questions and tasks below focus on how the model can be extended byusing absolute cell references.

Load the file M2f Mobyphone 2 extended model.xls.

1 The model has been reorganised slightly so that you can investigate otherways of analysing the data. What formula do you need to create in F11? Trynot to use 100 in the formula but make F10 an absolute cell reference.

Handout 4M2g


Handout 2

M2b cont.

Load: M2h Mobyphone 2-extended model answers.xls. This file, alongsidehandout 4 Phone worksheet 2, can be used to compare and manipulate graphs.They are used to show how graphs of mobile telephone tariffs could be extendedto make detailed comparisons, in sample teaching unit 8.4, lesson 4.

Investigate how graphs can be enhanced by:

• changing scales;

• using gridlines;

• changing the weight of lines;

• choosing appropriate intervals;

• using colour;

• saving them separately from their source data.

Are the graphs appropriate for the data they are showing? Discuss commonmistakes pupils make, for example, using line graphs for discrete data, creatingmeaningless or distorted graphs by using 3D doughnut effects.

Use step 1 of the Chart Wizard to run through the customised graphs available, forexample, lines with different scales on the two vertical axes for comparative graphs.

Using random number generation in a model

Load the file M2i coin.xls.

100 200 300 400 500

Talk 15 Talk 30 Talk 45 Talk 60 Timefree Talk Pay As Y

Tossing a coin 10 times

0

1

2

3

4

5

6

7

8

9

10

Heads Tails


Handout 2

M2b cont.

This file is the starting point for generating random numbers, between given limits,as test data for the mobile telephone model in sample teaching unit 8.4, lesson 4.

Additional guidanceIf the RANDBETWEEN function is not already active on the computer, for example, inMS Excel, go to Tools, Add-Ins... and select Analysis Toolpak VBA to activate it.

Reload the file M2c Mobyphone.xls. Select the completed worksheet to show thedata and graph.

Investigate how the input cell in B5 can be changed to calculate a random numberbetween given limits, using the RANDBETWEEN function:

• type =RANDBETWEEN(100,600) into B5 to produce a random numberbetween the limits given;

• press the <F9> key several times to generate different random numbers.

This is a useful modelling tool for repeating calculations that incorporate randomnumbers.

Note how the graph changes interactively each time the <F9> key is pressed.

Additional guidanceThe method given for generating random numbers is for Microsoft Excel. It may bedifferent in other spreadsheet software. The use of random numbers in models willbe discussed in detail in session 3.

Using Goal Seek … to forecast values

Select the mobile plan completed worksheet and refer back to handout 3 Phoneworksheet 1. Reset the value in B5 to 300. Goal Seek … is introduced in lesson 2of sample teaching unit 8.4 and is used to work the model ‘backwards’.

So far, you have used the model to calculate outputs from a given input but youcan reverse this by stating a desired output value and forecasting the input valueneeded to reach it. This would make it possible to calculate the number of minutesyou would get with Talk15 Plan if you had only £16.50 per month to spend.

Try out the Goal Seek … function from the Tools menu to do this. Check that itcalculates an exact input value of 123.3333 minutes!


Handout 2

M2b cont.

Goal-seeking follows an 'output – process – input' system and is a powerfultechnique for exploring ‘What if…?’ scenarios.

Using absolute cell references

Additional guidanceAbsolute and relative cell references have not yet been mentioned in this session.The required result has been achieved by:

• repeating the same data into other cells, for example, by entering =B5 into E11to E16;

• typing in each formula manually, rather than copying.

Although each of these methods is legitimate, the spreadsheet can becomecumbersome and time-consuming to edit.

A formula generally includes references to other cells. When it is copied the cellreference adjusts according to row or column movement. References of this kindare called ‘relative cell references’. Sometimes it is important for the reference tostay fixed to the contents of a particular cell, for example, when referring to the unitcost of a particular item. References of this kind are called ‘absolute cellreferences’.

Load M2j Disco model.xls and click on ‘Disco stage 5’. The model of the schooldisco is developed throughout sample teaching unit 7.4, in a layout designed toavoid the need for absolute cell referencing.

Data are carefully setout so that all formulaerefer to cells in thesame column. There isno need for absolutecell referencing.


Handout 2

M2b cont.

Practise entering formulae with absolute cell references in F11 to K11. The values inF10 to K10 need to remain fixed or absolute when they are entered into formulae.The $ symbol is used to indicate an absolute reference. It is inserted before eachpart of the cell reference, for example, $F$10. You can use the <F4> key to togglea cell reference within a formula between absolute and relative. Try out the effect ofthe <F4> toggle.

• The first press fixes the cell: $F$10.

• The second press fixes the row: F$10.

• The third press fixes the column: $F10.

• The fourth press returns to the relative address: F10.

Discuss this question.

• Since all your values are in row 10 and since you stay in the same column,could you use the second version (F$10)?

Using comparative test data from other sources

The next activity is used in sample teaching unit 8.4, lesson 4, to compare acommercial model with the one that pupils have generated.

The Kelkoo site at http://www.buy.co.uk/kelkoo/r5/mobiles.asp compares costs ofitems, including mobile phones. Access the site and enter appropriate details sothat the model can establish the best-value product for you.

Discuss:

• the Kelkoo website as a commercial supplier of comparative data aboutproducts including mobile phones;

• the personal user profile for mobile phones on the Kelkoo site.


Handout 2

M2b cont.

Investigate how to review a call profile. The site gives a profile based on an industryaverage and a breakdown of costs from each provider. Select the information iconnext to the results of your search comparison.

Discuss these questions.

• How could these data be applied to the existing mobile phone model?

• What questions should you ask about the data?

• How else could pupils collect data to develop their models?

You should conclude that they would need to know about the limitations, validityand accuracy of the data. Pupils could also collect data from questionnaires andtelephone bills.


Handout 3

M2e

Phone worksheet 1 BackgroundThe spreadsheet shows the start of a mobile phone model that you are going todevelop. The estimated number of minutes used per month can be entered incell B5 as shown.

1 Ensure you have file M2e Mobyphone 1.xls loaded (as shown).

2 Change the number of minutes in B5. What happens to the values in column Eunder the ‘minutes used’ heading? Why does this happen?

3 What do cells E11 to E16 contain?

4 You need to create a formula in G11 that calculates the cost of extra minutesused for the Talk 15 tariff. Work out what the formula needs to calculate. Write itin words and then as a spreadsheet formula.


Handout 3

M2e cont.

5 Now enter this formula in G11. Remember the = sign at the start. Does youranswer look reasonable? Check it.

6 Copy your formula into G12 to G16. You could use the fill handle. Check thatthe formula has been copied and that the cell references have changed foreach of the rows.

7 Add a formula in cell H10 to calculate the Total cost per month for the Talk 15tariff. Check if it appears to be correct. Copy the formula down into cells H11 toH16.

8 If you use 400 minutes per month, which tariff do you think gives the best value? How much would you pay?

9 Use your model to complete the following table to test out your prediction.

10 You have a budget of £20 per month. How many minutes would this buy on thefollowing plans? You could use Goal Seek … to help you find out.

11 What advice would you give someone who didn’t know which tariff to take up?

Estimated number Best-value of minutes tariff

100

200

300

400 Talk 60

500

Tariff Number of minutes for £20

Talk 15

Talk 30

Pay As You Go

Talk 60


Handout 4

M2g cont.

Phone worksheet 2BackgroundThe questions and tasks below focus on how the model can be extended byusing absolute cell references.

Load the file M2f Mobyphone 2 extended model.xls.

1 The model has been reorganised slightly so that you can investigate other waysof analysing the data. What formula do you need to create in F11? Try not touse 100 in the formula but make F10 an absolute cell reference.

You can click on the red dots in cells F11 and G11 to check you are on theright track.

2 Enter similar formulae for G11, H11, I11, J11 and K11. Copy each formuladown through the columns. Check that the absolute cell references have beencopied correctly.

3 Create a line graph that shows all of the tariffs at once for easy comparison.Here are some tips to help you.

• Select B10 to B16 then F10 to K16 so that minute headings are included.

• Select a suitable Chart Type for line graph – suggest first one.(Chart Wizard Step 1)

• Select rows rather than columns in Chart Source Data for correct data. (ChartWizard Step 2)

• Remove the gridlines for easier viewing – Chart Options – Gridlines tab.(ChartWizard Step 3)

• Add a suitable title and label the axes – Chart Options – Titles tab.(Chart Wizard Step 3)


Handout 4

M2g cont.

4 Print out the chart and use it to answer these questions.

a Which tariff offers the best value for money if you use 200 minutes’ worth of calls per month?

b Which tariff offers the best value for money if you use 450 minutes’ worth of calls per month?

c What is the best value if you can spend £30.00 per month?

d What is the best value if you can spend £25.00 per month?

5 There are certain points on the graph where it is difficult to see clearly. Forexample, look closely at the area around 200–300 minutes. Change the valuesin row 10 to 200, 220, 240, 260, 280, and 300 to graph this area more clearly.Now redraw the graph. You will need to rescale the y-axis. To do this:

• double-click anywhere on the y-axis of the graph;

• select the scale tab and change the minimum value from 0 to 20.

What does the graph tell you now?

What is the best value if you can afford £24.00 per month?

6 Use your model to explore other areas in detail, for example, if you usebetween 300 and 400 minutes each month.


M3a Modelling session 3.ppt Slide 3.10


Handout 5

M3c

Activity sheet 1: Heads or tailsIf you were to toss a coin ten times, how many times would you expect to get a head? How many times would you expect a tail? Test yourhypothesis.

Using a spreadsheet, you can model this experiment over and over again.

1 Open a blank spreadsheet.

2 Let 1 signify a ‘head’ and 0 signify a ‘tail’.

3 In cell A1, type =RANDBETWEEN(0,1). This function generates a randomnumber, 0 or 1.

4 Use the fill handle to copy this formula from A1 through to A10.

5 Use the <F9> key to recalculate over and over again.

6 Elsewhere in the spreadsheet (e.g. L1), calculate the number of heads by typing =COUNTIF(A1:A10,1). This function counts the number of cells in therange A1:A10 that contain a 1.

7 Dividing this value by 10 will give the proportion of heads. Create a formula todo this, putting the result in M1.

Was the hypothesis for number of heads (proportion =0.5) correct? Recalculate over and over again, using the <F9> key.

How often does this equal 0.5? What are the extreme values?

What does the model tell us? What doesn’t it tell us?

How could the model be improved?

8 Extend the model to 100 trials. Copying the formula down to J10 will give 100trials. Adapt your formulae for counting the number and proportion of heads.Extend to 1000.

Does the model ‘improve’ and converge to 0.5 as the number of trials isincreased?


Handout 6

M3d

Activity sheet 2: Throwing a dieIf you throw a normal six-sided die 100 times, how many times would youexpect to score a 6? How many times would you expect to score a 1 or a2? Test your hypothesis.

Using a spreadsheet, you can model this experiment over and over again.

1 Open a blank spreadsheet.

2 Let 1–6 signify the scores you get when you roll a die.

3 In cell A1, type =RANDBETWEEN(1,6). This function generates a randomnumber from 1 to 6..

4 Use the fill handle to copy this formula from A1 through to J10, to model 100throws.


6 Elsewhere in the spreadsheet, calculate the number of times each score occursby using the COUNTIF function, e.g. number of 1s is =COUNTIF(A1:J10,1). Seenote below.

7 Check that all 100 throws have been counted by simply summing the totals.

Was the hypothesis for the number of 6s correct? Recalculate over and overagain using the <F9> key.

How much variation is there?

What are the extreme values?

What does the model tell you? What doesn’t it tell you?


8 Extend the model so that there are more trials.

Does the model ‘improve’ as the number of trials is increased?

Is there less variation and/or fewer extreme values?

9 Construct a chart showing the number of times each number occurs. Use <F9>to simulate 100 throws over and over again. The chart should update itself eachtime.

Does the chart assist in analysing the variation and testing your hypothesis?

Note: You could do this by entering each COUNTIF formula separately.Alternatively, you could use absolute cell referencing and copy the formula.


Handout 7

M3e

Activity sheet 3: Throwing two diceFraming your hypothesis for throwing one die was straightforward. Now tryusing two dice. How many times would you expect a total score of, say, 6in 100 throws?

1 Use a new worksheet on your spreadsheet.

2 Use columns A and B for ‘die 1’ and ‘die 2’ respectively. Use column C for‘total score’.

3 Simulate the throwing of both dice 100 times, using the RANDBETWEENfunction, and calculate the total score for each trial.


5 Elsewhere in the spreadsheet, calculate the number of times each total scoreoccurs by using the COUNTIF function. See note below.

6 Construct a chart to display the results and update them constantly.

Was the hypothesis for a total score of 6 correct?

What does the chart tell you?

Do certain scores occur more often than others?

How much variation is there?

What are the extreme values?

What does the model tell you? What doesn’t it tell you?


7 Extend the model so that there are more trials.

Does the model ‘improve’ as trials are increased?

Is there less variation and/or fewer extreme values?

Which total score comes up more than others?

Can you explain why this is so?

Note: The average score for each die is 3.5.

Note: You could do this by entering each COUNTIF formula separately.Alternatively, use absolute cell referencing and copy the formula.


Handout 8

M3f

Activity sheet 4: Milk bottle wastageThis activity is an example of how a process can be modelled. The problemis about milk bottles and their journeys to and from the dairy.

If there are 1000 bottles and there is an 80% chance of any one bottlemaking it back to the dairy, how long does a bottle last?

Approach this problem by trying to work out the average number of trips a bottlemakes. Load the spreadsheet file M3j Milk bottles.xls.

Model construction

1 The bottle has an 80% chance of survival on each trip, so it survives, onaverage, 8 trips in every 10. This can be represented on the model, using theRANDBETWEEN(1,10) function where 1 to 8 represent an unbroken bottle and9 and 10 represent a broken bottle.

2 Using an IF statement, you can return a 1 for unbroken and a 0 for broken,depending on the random number generated. For example:=IF(RANDBETWEEN(1,10)>8,0,1).

3 By summing the returns along row 13 you can calculate an average in A15.

4 You can construct a graph of the results and use the <F9> to restart thesimulation over and over again.

Using the model

1 What hypotheses can you make before you start the simulation? What do you expect the average number of trips to be? What is the maximum time you could reasonably expect a bottle to last? In theory, how long could this be?

2 What does it tell you about the average number of trips, the number of times 10trips, 12 trips, 15 trips are achieved?

3 How successful is the model for modelling the process?

4 How much variation is there? What are the extreme values?

5 What does the graph show? Explain its shape/form.

6 What does the model tell you? What doesn’t it tell you? How could it beimproved?


Key Stage 3

National Strategy

ICT

Session Grade: please ring Comment1 = Very good, 4 = Poor

Session 1 What is modelling? 1 2 3 4

Session 2 Teaching modelling at Key 1 2 3 4Stage 3

Session 3 Extending modelling in the 1 2 3 4classroom

Overall grade for the unit 1 2 3 4

Evaluation form: Modelling

For completion by teachers

What were the most successful aspects of today’s sessions?

What changes would you suggest if today’s sessions were repeated?

Please grade each session on the basis of how well-structured and organised itwas to meet the learning objectives identified.

School ________________________________________________________

Post held ________________________________________________________

Please return this form to your tutor before leaving.


Appendix

Next stepsThese materials were written primarily to enable ICT consultants to run training forKey Stage 3 teachers as part of the support offered to additional support schools.You have been given a copy of the training materials as you may decide todisseminate some or all of the training to colleagues in your department. Thefollowing summary will help you decide how to use these materials in school.

After the training, there are several possible ways you might want to use what youhave learned to help and support colleagues who teach ICT at Key Stage 3. Theroute you choose to take will depend on the areas for development that have beenidentified through your subject audit, as well as your own skills and confidence. Akey judgement will be whether there are particular aspects of the subject aboutwhich colleagues feel less than secure.

Whether or not you are in an additional support school you should consider:

• how you will take back into school the key messages of this training unit (TheKey Messages leaflet will help you.);

• whether the objectives of this training unit address areas identified fordevelopment in your audit;

• whether teachers will need a training session on sample teaching units 7.4 and8.4 before they begin to use them;

• how to support teachers as they use sample teaching units 7.4 and 8.4;

• teaching sample teaching units 7.4 and 8.4 yourself and then using yourexperience to take colleagues through the materials.

If you work in an additional support school your consultant will be able to work withyou to help you decide on the most appropriate next steps. Your consultant mayalso help you to run some or all of the training, or to adapt it to suit the needs ofyour school. If you are not in an additional support school you will want to talk toyour strategy manager before deciding on the best way forward.

The training unit is intended to help you, with your consultant, plan and managetraining for teaching modelling. You should use the materials flexibly, tailoringtraining to your school’s priorities and stage of development. The three sessionsfocus on the theme ‘Developing ideas and making things happen’ in the NationalCurriculum programme of study for ICT at Key Stage 3 and on the correspondingyearly teaching objectives for ‘Models and modelling’ set out in the Framework forteaching ICT capability: Years 7, 8 and 9.

Planning a training programme

If you plan to run a training session for your colleagues, you need to think aboutwhat has already been done in your school and to consider how familiar theteachers are with the ICT Framework and the yearly teaching objectives. You willalso need to be familiar with sample teaching units 7.4 and 8.4 and know how touse them in your short-term lesson planning.

The overview of the training unit on page 4 will help you select the most appropriatesessions for your staff.

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