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Theme: Data, tables, graphs, formulae

Data, tables, graphs | Baby names | NZ GDP | Gapminder | Vitruvian man | Links | Achievement standards

Data, tables, graphs, formulae

Graphs

  • Nazca lines
  • NZ GDP data:
    • How is GDP gathered?
  • Gapminder
  • Napoleon’s graph – march to and from Russia
  • Florence Nightingale data

Activity: Straight line pictures

Tables

  • Disasters:
    • Number and proportions
    • Tabular data
  • Looking for patterns – look for an unusual incident
  • Life expectancy
  • Stock exchange
  • Medical two-way tables

Formula

  • Newsworthy – Geek logic
  • Aircraft average passenger weight
  • Calendar maths

Activity: Forensic formulas

Data

  • 100m times:
    • Olympic gold medal times
    • World record times

Activity: 100m sprint times

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.
  • 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.

Statistical investigation

  • S5-1 Plan and conduct surveys and experiments using the statistical enquiry cycle:
    • D – using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets
    • F – presenting a report of findings.
  • S6-1 Plan and conduct investigations using the statistical enquiry cycle:
    • C – identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
    • 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.

Baby names

Beginning the session
Students go to the Name Voyager website and answer the questions in pairs.

  • Look up your name / or at the graph shown:
    • I notice – What does this graph show?)
    • I wonder – What questions do you have about the graph/data?
  • Explore the two different representations of the name you have chosen, what information do they give?
  • What conclusions can you reach?

Alternative: teacher displays different starting letters for groups of students and has students discuss the questions in pairs, then select three names and look at them in more detail.

Working in groups
Students go to the 'name mapper' tab:

  • Teacher circulates amongst groups and gets ideas to lead a whole class discussion about key ideas.
  • Or student groups, one at a time, control the graphs on screen and get other students to do 'I notice, I wonder'.

Class discussion
Key ideas could include:

  • How many variables are shown?
  • What do the axes represent?
  • Where does the data come from?
  • Would NZ be same / different?
  • What groupings within NZ?
  • In baby voyager graph the overall frequency of names decreases – why?
  • What does a peak represent? Is the scale changing?

Next investigation
Either give Excel spreadsheet of NZ data (comes from Births, Deaths and Marriages) or pre-prepared version for other students to discuss representations.

  • Is your name popular or original?
  • What does the table show that the graph doesn’t and vice versa?

Extending the learning

  • Is there evidence of a cyclical repeating of names? (for / against) (trig modelling)
  • When will the next peak of name 'Jack' be?

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.

Exploring NZ GDP

On the data projector, students /or teacher go to NZ GDP link.

Beginning the session
In groups students comment using 'I notice/I wonder' for the different graph combinations.

  • Look at NZ
  • Look at NZ / US
  • Look at NZ / Singapore
  • Look at NZ / Fiji
  • I notice – What does this graph show?
  • I wonder – What questions do you have about the graph / data?

Teacher encourages students to discuss the evidence they have for their 'I notice' statements, and ask how they could find out for their 'I wonder' statements. Teacher also looks for claims that can/can’t be supported and uses these for whole class discussion below, for example 'Group 1 thinks that NZ’s economy is declining…'

Teacher could have groups argue for and against a statement like the one above.

Class discussion

  • Is this big/small – frame of reference?
  • Effect of scale
  • 'Eye of the beholder
  • Standard form/representations of large numbers
  • What is GDP?
    • How is it measured?
    • Is it an effective measure of wealth?

Could be done:

  • with data projector, five mins on each graph
  • students in computer room
  • if no computer access, could be done with print outs of these graphs, though the impact of students seeing the animation is powerful.

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

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.

Gapminder

Show 2006 Hans Rosling Ted talk video.

  • Pause at key points for discussion, for example, the student pre-test.
  • Graphs are not just pie.
  • Constantly changing.
  • Stop and do the Swedish students test about what to do in the world.

Make links with other visual displays past and present, for example:

  • Florence Nightingale
  • Napoleon’s March

Possible explorations:

  • Log and linear scales
  • Compare countries
  • Compare continents
  • Line of best fit

Students create a Hans Rosling style presentation using two variables of students' choice and the PPDAC cycle.

Possible achievement objectives

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

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.

Statistical investigation

  • S5-1 Plan and conduct surveys and experiments using the statistical enquiry cycle:
    • 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:
    • 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.

Vitruvian man

Look at the picture of Vitruvian Man.

  • What do you notice?
  • Make conjecture, for example, arm span = height, head is one quarter of height etc:
    o What would you expect the graph to look like if your conjecture was true?
  • Collect data for body measurements.
  • Explore via scatter graphs:
    • lines of best fit
    • describing lines of best fit
    • what does the gradient tell you

Possible achievement objectives

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

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.

Statistical investigation

  • S5-1 Plan and conduct surveys and experiments using the statistical enquiry cycle:
    • 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:
    • 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.

Links

Achievement standards

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

  • AS91026 Mathematics and statistics 1.1 Apply numeric reasoning in solving problems – 4 credits; Internal
  • 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
  • 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

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Last updated October 4, 2012



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