Download data, tables, graphs, formulae

DATA, TABLES, GRAPHS, FORMULAE

The broad contextual themes provide a range of teaching and learning activities and ideas that could be used as a basis for
a learning programme in year 11 or as supporting activities and ideas.

Many examples of teaching and learning activities or ideas are given, from which teachers could select activities that best
meet the needs of the students in their class/school. In addition teachers could select teaching and learning activities that
they currently use, or source others that would meet student needs and are within the broad contextual focus.

Each broad thematic context has a list of possible achievement objectives that activities from within the theme link to and
the choice of which will depend on the teaching and learning activities selected.

Some achievement objectives could be summatively assessed directly through achievement or unit standards; others could
be assessed through in-class formative or summative assessment. Not all achievement objectives need to be assessed.
Sub themes

Data, tables, graphs, formulae

Baby names

Exploring NZ GDP

Gapminder

Vitruvian man
*means that there is a web link listed at the end
# means activity is elaborated further in the ideas for teaching and learning activities
Page 1
Ideas for teaching and learning activities
Possible achievement objectives – select from below
depending on the teaching and learning activities chosen
Data, tables, graphs, formulae
GRAPHS

Nazca lines
 Straight line graphs activity*

GDP data#
 How is GDP gathered?

Gapminder#

Napoleon’s graph – march to and from Russia

Florence Nightingale data
TABLES
 Disasters
 Number and proportions
 Tabular data
 http://exploringdata.net/patterns.htm look for an unusual incident
 Life expectancy
 Stock exchange
 Medical two-way tables
FORMULA
 Forensic formulas activity*
 Newsworthy – Geek logic
 Aircraft average passenger weight
 Calendar maths
DATA

100m times
 100m times activity*
 Olympic gold medal times
 World record times

Number of births in NZ, globally

Baby names#

Population clock

Vitruvian Man#
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.
Page 2
Ideas for teaching and learning activities
Possible achievement objectives –
select from below depending on the
teaching and learning activities
chosen
#Baby names
Beginning the session
Students go to the ‘baby 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 next peak of name Jack be?
Page 3
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.
Ideas for teaching and learning activities
Possible achievement objectives – select from
below depending on the teaching and learning
activities chosen
#Exploring NZ GDP
Students / or teacher on data projector, go to GDP link*
Beginning the session
Students in groups 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: “Group 1 thinks that NZ’s
economy is declining…”etc
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, 5 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
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
Page 4
Ideas for teaching and learning activities
Possible achievement objectives – select from
below depending on the teaching and learning
activities chosen
Gapminder*
Show 2006 Hans Rosling 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
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.
Page 5
Ideas for teaching and learning activities
Possible achievement objectives – select from
below depending on the teaching and learning
activities chosen
Vitruvian Man
Look at 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
o
lines of best fit
o
describing lines of best fit
o
what does the gradient tell you

use CensusAtSchool data*
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.
Page 6
*WEB LINKS

100m sprint times http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Learning-programme-design/Broadcontextual-themes/Data-tables-graphs-formulae/Activity-100m-sprint-times

Straight line pictures http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Learning-programme-design/Broadcontextual-themes/Data-tables-graphs-formulae/Activity-Straight-line-pictures

Forensic formulas http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Learning-programme-design/Broadcontextual-themes/Data-tables-graphs-formulae/Activity-Forensic-formulas

Baby names http://www.babynamewizard.com/voyager

NZ GDP - Google public data
o
http://www.google.com/publicdata?ds=wb-wdi&met=ny_gdp_mktp_cd&idim=country:NZL&dl=en&hl=en&q=gdp

Hans Rosling 2006 TED talk http://www.ted.com/talks/hans_rosling_shows_the_best_stats_you_ve_ever_seen.html

Gapminder http://www.gapminder.org/

Vitruvian Man – Wikipedia http://en.wikipedia.org/wiki/Vitruvian_Man

CensusAtSchool http://www.censusatschool.org.nz/
LEARNING FROM THIS THEME COULD POTENTIALLY PROVIDE EVICENCE TOWARDS THE
FOLLOWING ACHIEVEMENT STANDARDS
1.1
Apply numeric reasoning in solving problems
4 credits
Internal
1.3
Investigate relationships between tables, equations and graphs
4 credits
External
1.4
Apply linear algebra in solving problems
3 credits
Internal
1.11
Investigate bivariate numerical data using the statistical enquiry cycle
3 credits
Internal
1.12
Demonstrate understanding of chance and data
4 credits
External
Page 7