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# Theme: Cell phones

## Cell phone pricing

Start
Class gather all the different plans from the different companies (including plans tied in with Internet and telephone and family). There will be prepay with different conditions and cost for number of phone minutes, number of texts, and data rates (Internet access). These costs will vary within and across providers (pending legislation change).

Note
This is quite a complex issue.

• What if they want to go oversees or to a different town/region?
• Who do they text or talk to the most?
• Why do they have the cell phone?

Big question/issue

• What is the best cell phone plan for you?
• How can we compare the plans?

Modelling
Starting with a complex situation that we want to understand, and so we model it. We simplify the situation and look at different variables separately. At each stage you have to suspend reality and then look at the end to see how close it is to reality, which leads to refining the model.

#### Possible questions to explore

• Compare (companies or different plans in one company) just one thing at a time (cost per text, per call, other).
• Is there a minimum amount required to operate the phone (hidden fixed cost)?
• Which company gives the best deal for you and justify.
• Fix some condition, like the number of minutes, and compare two companies texting.
• Devise methods to compare prepay and pay as you go plans. Compare with other countries plans. (Take into account exchange rate).
• Explore costs and benefits – best mates and fixed term.
• For \$20 per month which is the best plan?
• If you need to use your phone out of the country, for example, Australia, what would your best plan be?
• On credit – what is the real cost, including rates?

Activity: Cell phone pricing plan

### Possible achievement objectives

Select from below depending on the teaching and learning activities chosen.

#### Number strategies and knowledge

• NA5-1 Reason with linear proportions.
• NA5-4 Use rates and ratios.
• NA5-5 Know commonly used fraction, decimal, and percentage conversions.
• NA6-1 Apply direct and inverse relationships with linear proportions.
• NA6-3 Apply everyday compounding rates.
• NA6-4 Find optimal solutions, using numerical approaches.

#### Equations and expressions

• NA5-7 Form and solve linear and simple quadratic equations.
• NA6-5 Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.

#### Patterns and relationships

• NA5-9 Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
• NA6-7 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
• NA6-8 Relate rate of change to the gradient of a graph.

## Cell phone packaging

• Explore ratio of length to width of the phone.
• Measuring button size (are these standard?) How does hand size affect your use?
• Volume the phone takes up in purse/pocket/pencil case.
• Surface area for buying skins (measure the amount of waste if having to cut to size, or make their own 'skin' out of paper for their phone).
• Design a logo for a skin that meets certain requirements and then prepare instructions for another student to create their same design.

Activity: How does your cell phone measure up?

### Possible achievement objectives

Select from below depending on the teaching and learning activities chosen.

#### Number strategies and knowledge

• NA5-1 Reason with linear proportions.
• NA5-6 Know and apply standard form, significant figures, rounding, and decimal place value.
• NA6-1 Apply direct and inverse relationships with linear proportions.

#### Measurement

• GM5-1 Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
• GM5-2 Convert between metric units, using decimals.
• GM5-3 Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms.
• GM5-4 Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.
• GM6-1 Measure at a level of precision appropriate to the task.
• GM6-2 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.
• GM6-3 Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.

#### Shape

• GM5-6 Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations.
• GM6-5 Recognise when shapes are similar and use proportional reasoning to find an unknown length.

#### Transformation

• GM4-8 Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
• GM5-9 Define and use transformations and describe the invariant properties of figures and objects under these transformations.
• GM6-8 Compare and apply single and multiple transformations.
• GM6-9 Analyse symmetrical patterns by the transformations used to create them.

## Cell phone cameras

Using the camera function:

• Explore pixels – what gives high definition or good enough?
• Which cameras give the best picture – is the number of pixels the only thing that matters?
• Measure items in a picture using scaling – put a student ID card or other item of known size in the photo and use that to determine the size of other items in the picture (real use: crime scenes).

Activity: Measuring with digital pictures

### Possible achievement objectives

Select from below depending on the teaching and learning activities chosen.

#### Number strategies and knowledge

• NA5-1 Reason with linear proportions.
• NA5-4 Use rates and ratios.
• NA6-1 Apply direct and inverse relationships with linear proportions.

#### Measurement

• GM5-1 Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
• GM5-2 Convert between metric units, using decimals.
• GM5-3 Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms.
• GM5-4 Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.
• GM6-1 Measure at a level of precision appropriate to the task.
• GM6-2 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.

#### Transformation

• GM5-9 Define and use transformations and describe the invariant properties of figures and objects under these transformations.
• GM6-8 Compare and apply single and multiple transformations.

## Cell phone towers

• Find out where are local cell phone towers are located.
• What are the ranges of cell phone towers? How is range affected by tall buildings or mountains? Describe these loci.
• Create a scaled map showing the towers and write instructions to locate one tower from another using bearings and distance.
• Find the area of coverage.
• Investigate an area that doesn’t have cell coverage, where would you place a tower to correct the problem, what if there are obstacles?
• Structure of purpose built towers – draw a scale diagram, make a net.

### Possible achievement objectives

Select from below depending on the teaching and learning activities chosen.

#### Measurement

• GM5-1 Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
• GM5-4 Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders.
• GM6-1 Measure at a level of precision appropriate to the task.

#### Shape

• GM5-6 Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations.
• GM6-5 Recognise when shapes are similar and use proportional reasoning to find an unknown length.
• GM6-6 Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions.

#### Position and orientation

• GM5-7 Construct and describe simple loci.
• GM5-8 Interpret points and lines on co-ordinate planes, including scales and bearings on maps.
• GM6-7 Use a co-ordinate plane or map to show points in common and areas contained by two or more loci.

#### Transformation

• GM5-10 Apply trigonometric ratios and Pythagoras’ theorem in two dimensions.

## Cell phone usage statistics

Investigations

• Collect student data:
• number of text sent/received
• time sent/received
• day of the week for highest/lowest activity
• categorise who send/receive from (friends, family, teachers/police/other)
• Internet usage.
• Compare with international surveys. (Analyse other results and graphs.)
• Compare boys vs. girls, juniors vs seniors.
• Compare sent and received.
• Investigate trends and patterns in their data, for example, days of the week, time of the day.
• NZMaths: Texting Olympics - sprint, hurdles, marathon

Literacy

• Finding and evaluating existing reports on cell phone issues:
• texting and driving
• increase in their use among different age groups
• feedback on specific phone quality
• comparing usage among teens in various countries.

### Possible achievement objectives

Select from below depending on the teaching and learning activities chosen.

#### Statistical investigation

• S5-1 Plan and conduct surveys and experiments using the statistical enquiry cycle:
• A - determining appropriate variables and measures
• B - considering sources of variation
• C - gathering and cleaning data
• D - using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets
• E - comparing sample distributions visually, using measures of centre, spread, and proportion
• F - presenting a report of findings.
• S6-1 Plan and conduct investigations using the statistical enquiry cycle:
• A - justifying the variables and measures used
• B - managing sources of variation, including through the use of random sampling
• C - identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
• D - making informal inferences about populations from sample data
• E - justifying findings, using displays and measures.

#### Statistical literacy

• S5-2 Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.
• S6-2 Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.

## Cell phone batteries

• How long do they last?
• When used for texting only
• When used for talking only
• What uses the most power?
• ½ life of battery power
• Different makes of batteries how do they compare?

### Possible achievement objectives

Select from below depending on the teaching and learning activities chosen.

#### Number strategies and knowledge

• NA5-1 Reason with linear proportions.
• NA5-4 Use rates and ratios.
• NA5-5 Know commonly used fraction, decimal, and percentage conversions.
• NA5-6 Know and apply standard form, significant figures, rounding, and decimal place value.
• NA6-1 Apply direct and inverse relationships with linear proportions.
• NA6-3 Apply everyday compounding rates.
• NA6-4 Find optimal solutions, using numerical approaches.

#### Measurement

• GM5-1 Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.
• GM5-2 Convert between metric units, using decimals.
• GM6-1 Measure at a level of precision appropriate to the task.
• GM6-2 Apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.

## Achievement standards

Learning from this theme could potentially provide evidence towards the following achievement standards.

• AS91028 Mathematics and statistics 1.3 Investigate relationships between tables, equations and graphs – 4 credits; External
• AS91029 Mathematics and statistics 1.4 Apply linear algebra in solving problems – 3 credits; Internal
• AS91030 Mathematics and statistics 1.5 Apply measurement in solving problems – 3 credits; Internal
• AS91032 Apply right-angled triangles in solving measurement problems (1.7) – 3 credits; Internal
• AS91033 Mathematics and statistics 1.8 Apply knowledge of geometric representations in solving problems – 3 credits; Internal
• AS91034 Mathematics and statistics 1.9 Apply transformation geometry in solving problems – 2 credits; Internal
• AS91035 Mathematics and statistics 1.10 Investigate a given multivariate data set using the statistical enquiry cycle – 4 credits; Internal
• AS91036 Mathematics and statistics 1.11 Investigate bivariate numerical data using the statistical enquiry cycle – 3 credits; Internal
• AS91037 Mathematics and statistics 1.12 Demonstrate understanding of chance and data – 4 credits; External

Last updated October 3, 2012