INforM – Interactive Notebooks for MathematicsBook 11 – Wrist and neck sizes

Generating sequencesThe lesson is aimed at Year 8 pupils and the activities are related to the Key Stage 3 work in: Ma4 Handling data:

Using and applying handling data1 Pupils should be taught to:Problem solvinga. carry out each of the four aspects of the handling data cycle to solve problems: i. specify the problem and plan: formulate questions in terms of the data needed, and consider what inferences can be drawn from the data; decide what data to collect (including sample size and data format) and what statistical analysis is needed; ii. collect data from a variety of suitable sources, including experiments and surveys, and primary and secondary sources; iii. process and represent the data: turn the raw data into usable information that gives insight into the problem; iv. interpret and discuss the data: answer the initial question by drawing conclusions from the data;b. identify what further information is required to pursue a particular line of enquiry;c. select and organise the appropriate mathematics and resources to use for a task;d. review progress as they work; check and evaluate solutions.

The SMART Notebook file `wrist and neck sizes’ is designed to support lesson materials which are available for download from the Practical Support Pack Secondary Mathematics area of the DfES’ TeacherNet website at:http://www.teachernet.gov.uk/supportpack/module.aspx?t=2&s=10&y=37&p=&m=18914 The lesson plan for the activity is included in the attachments to the Notebook file as the MS Word document: `wrist_and_neck_sizes.doc’. The materials include support for the use of graphical calculators – and you may indeed have either a teacher’s graphical calculator for whole-class projection, or a copy of an on-screen emulator of a graphical calculator such as TI SmartView: http://education.ti.com/educationportal/sites/UK/productDetail/uk_smartview.html .

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This notebook provides alternative support for this lesson using a SMARTBoard together with the Microsoft Excel spreadsheet and/or TI InterActive! software: http://education.ti.com/educationportal/sites/UK/productDetail/uk_ti_interactive.html .

Scattergrams and lines of best-fit are also illustrated using the free web-based resource designed by the Mathematical Association and programmed in Flash by the Skoool team at Intel. This Mathematical Toolkit won the BETT 2006 award for Key Stage 3/4 mathematics. You and your pupils can download it from the Skoool area of the London Grid for Learning at: http://lgfl.skoool.co.uk/content.aspx?id=657

The Mathematical Toolkit is now included in the Mathematics resource area in the latest Gallery for SMART Notebook at: http://education.smarttech.com/ste/en-US/Ed+Resource/Software+Resources/Notebook+collections/Mathematics/General+resources/Mathematical+Toolkit+-+interactivity.htm

Organisation of the materialsThe SMART Notebook file is saved as `wrist and neck sizes.notebook’.It consists of 10 pages of which the first is the title page, shown above.There are 8 pages to support the activity and its extension. Page 9 is a blank page.Page 10 contains teacher notes which are amplified here.

The first activity

Pages 2 and 3 of the Notebook are set up to support the `Starter’ activity from the Practical Support Pack resources.

StarterYou might like to start by asking pupils the following questions.How do we find the mean?How do we find the range?What do these tell us about the data set?

Show the pupils two sets of five numbers with the same mean but different ranges. Ask the pupils to work in pairs to construct two sets of five numbers with the same mean but different ranges. Then ask pupils, What does this tell us about the two data sets? The answer is they can have a wide range and yet still have the same mean.

Page 2 is set up to help you run this activity from the board.

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Show the pupils two sets of five numbers with a different mean and the same range. Ask pupils, What does this tell us about the two data sets? The answer is they can have numbers of a different order of magnitude and yet will still have the same range.

Page 3 is similarly set up to help support this part of the Starter.

The main activity: (again taken from the Practical Support Pack)Start by posing the problem, How do clothes manufacturers decide the size of collars and cuffs for clothes? Invite suggestions from pupils.Ask pupils what they know about the size of collars and cuffs. Encourage pupils to move towards quantitative conjectures and ask them to record them on Conjecture analysis and results.Example conjectures are as follows.Boys’ neck circumference varies more than girls'.Neck circumference is three times wrist circumference.The ratio between neck and wrist circumferences is different for boys compared to

girls.

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Ask pupils to consider how they can test their conjectures.What measurements are we going to make?What units are we going to use?How can we ensure consistency?How are we going to measure these?How accurately can we measure neck and wrist?Ask pupils to record their response on Conjecture analysis and results. Pupils record their neck, wrist and gender using paper strips for neck size (to nearest 0.5cm).

The Conjecture sheet is attached to the Notebook file, and reproduced on Page 4. You could flick back to the photo on Page 1 and discuss how shirts are arranged in shops.

In order to collect data from the class you might like to use the table on Page 5. Alternatively you might like to open the MS Excel file: `data sheet.xls’ using the first link provided, or the TI InterActive! File: `data sheet.tii’ from the second link. Both files are attached to the Notebook.

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The Excel link should open looking like the image below:

The TI InterActive! link should open looking like the image below:

Double click on the Data table area to open the List Editor where you use the keyboard to type in results. The columns headed GRatio and BRatio should be automatically computed when data is entered for a girls’ wrist and neck, or a boy’s wrist and neck.

The major activity now is to use the Notebook and the associated tools such as MS Excel, TI InterActive!, the Mathematical Toolkit and TI SmartView, to engage pupils in experimenting with scatterplots for the data, and to superimpose lines of best fit.

Start by explaining to the pupils that they are going to explore the relationship between the wrist and neck circumferences graphically, i.e. by drawing a scatter graph. Ask them what scale they feel should be used.

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Demonstrate how to draw a scatter graph … using whole class display onto a whiteboard. Ask a pupil to draw a line of best fit onto the whiteboard.Ask pupils the questions below.When is it appropriate to draw a line of best fit? If you have two sets of related

data plotted against each other.As wrist circumference increases, what happens to neck circumference? It also

increases.

Page 6 shows a grid already prepared, together with an extract from the adult data provided with the Practical Support Pack resources. The 5 blue and six red blobs are ready for pupils to slide onto the appropriate positions on the grid. In order to swing the orange line over the grid, click anywhere on the line and then drag the right-hand endpoint.

Page 7 has two pre-prepared scattergrams (produced using TI InterActive!). You can discuss the females and males separately, or you can drag the Male graph over the Female graph to show both data-sets on the same axes.

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Page 8 provides the tools to graph functions of the form y = m x as possible lines of best fit. The MA/Intel Mathematical Toolkit is ready loaded from the Gallery. You can use either or both of the Coordinates/Graphing and the Charting tools. An aide-memoire about the data sets and the scales for the axes is shown as a clip from the Scratchpad.

Use the Coordinates button, and enter the data for the scales of the graph. Then click on five points whose coordinates are close to those in the FW and FN table. You can then edit the coordinates in the Toolkit’s table to match them exactly – then press Update points. Using the Graphing tab you can enter the equation of a graph to superimpose.

Page 8 also has a link to the MS Excel file `Male Female.xls’. There are four sheets in this Workbook and you can use the Tabs at the bottom of each sheet to navigate around. The figure below shows the `Both’ sheet with data for Female and Male teachers together. The value of m in can be changed to vary the slope of the plotted line.

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Page 8 also carries a link to the TI InterActive! file `Male Female.tii’. You need to scroll down the file to see the three different graphs for Females, Males and both. The final page has a `slider’ to be used to change the slope m of the graph.

An alternative approach to using these software tools is to work with a graphical calculator, as suggested in the Practical Support Pack materials. In this case the TI SmartView emulator software is ideal for use on a SMARTBoard. If you are familiar with using a TI-83 or TI-84 graphical calculator you will just need to set up the female and male teacher data in lists such as FW, FN, MW, MN and configure the Stat Plot to produce a scatterplot of e.g. FW against FN. Using the Y= editor you can superimpose the graph of a function y = mx. You may prefer to load the emulator state file `Male Female.84state’ from the list of attachments.

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Page 9 is a blank page. Page 10 contains the Teacher Notes which are a condensed version of these notes.

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