# Maths-Stats by stariya

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```									                                                         NZTA: Safer Journeys and the BIG Event                                                                                                                                                              Mathematics and Statistics
Hooked on Thinking Curriculum Model Planning Framework

BIG [adjective] 1. Large. 2. Above average in size, quantity, magnitude or extent. 3. Significant
Event [noun] 1. An important incident. 2. Something that happens at a given place or time. 3. A gathering. 4. An organised occasion. e.g. ceremony, meeting, festival, concert, sporting competition

Learning Area:                       Level:                                Values:                     Key Competencies:              Integration: Suggestions

Mathematics and                      Level 1                               Excellence                  Thinking                       English
Statistics.                          Level 2                               Innovation                  Managing self                  The Arts
Diversity
Level 3                                                           Participating and              Health and Physical Education
Equity
Kei hopu tou ringa ki te aka         Level 4                                                           contributing                   Learning Languages
taepa, engari kia mau ki te aka                                            Community and
matua.                                                                     Participation               Relating to others             Mathematics and Statistics
Teachers to highlight                 Ecological Sustainability   Making meaning                 Science
In mathematics and statistics,       relevant level                        Integrity                   from language,                 Social Sciences
students explore relationships in                                          Respect                     symbols and text               Technology
quantities, space, and data and
learn to express these
relationships in ways that help
them to make sense of the world
around them.
Key Concept Understanding:           Driving Question:                                                 Subsidiary Questions:          These are the questions that students will be able to respond to.

When you travel smart,               Are you ready to travel to the BIG Event?                         1. Describe safe travel (when going to and from an event).
you travel safe.                                                                                       2. Explain how smart choices can result in safe travel (when going to and from an event).
3. Create a resource to help people travel smart and safe (when going to and from an event).

Achievement Objectives:              Learning Intentions:                                              Learning Experiences: These have been written in three areas.
1. Bringing in ideas 2. Connecting and linking ideas 3. Putting ideas into another context
Select the achievement objectives    Schools will have their own criteria for developing learning
that best match the abilities of     intentions. Examples are included below. Highlight the Learning   Your Challenge:
your students.                       Intention/s that best match the abilities of your students. Use   Use statistics to investigate a road you use and care about.
Statistical Investigation                                                                                      About 40 billion kilometres a year are travelled on the nation's local roads and state highways. State Highway 1 in central
Define ‘statistical investigation’.                                       Auckland is the busiest road in New Zealand, carrying more than 200,000 vehicles every day. (NZTA - Counting the traffic
Level One
Conduct investigations using the
statistical enquiry cycle:           Pose a question/s.
- posing and answering questions;                                                                      Do you know enough about how people use a road near you? People who adopt a beach or a river work with others to keep it
Gather relevant data.
- gathering, sorting and counting,                                                                     clean. Your challenge is to adopt a road and find out as much as you can about the way people use it so you can provide safety
and displaying category data;                                                                          advice to any chickens and or people wanting to cross.
Sort and count information using a range of methods.
- discussing the results.
Level Two
Conduct investigations using the                                                                       many vehicles use a road in your local community that it is hard for pedestrians to cross the road safely? Do vehicles travel too
Graph relevant data using a range of methods.
statistical enquiry cycle:                                                                             fast on a road near your school? Is your street a fast street or a slow street? Is your local street safe for all road users? If you
- posing and answering questions;      Analyse the data.                                                     were a chicken wanting to cross the road, what day of the week would you choose? Can you use this information to make other
displaying category and whole-         Interpret statements to make meaning.
number data;
Identify patterns and trends within datasets.                         You could investigate:
- communicating findings based
on the data.                                                                                                 How many different types of road users use a local road you use and care about (two directions) when you are going to
Identify patterns and trends between data sets.                       [school/place/venue/event].
Level Three
Conduct investigations using the       Justify these trends and patterns from the data collected.            How many different types of vehicles use a local road you use and care about (two directions) at different times of the day?
statistical enquiry cycle:
Compare and contrast results.                                         How many different types of road users use a local road you use and care about (two directions) at different times of the day?
- gathering, sorting, and
displaying multivariate category       Formulate questions that will gather relevant information.
and whole number data and                                                                                    How many vehicles use a local road you use and care about (two directions) at different times of the day?
simple time-series data to answer      Use the data gathered to form a generalisation that
questions;                                                                                                   How many road users use a local road you use and care about (two directions) at different times of the day?
communicates findings.
- identifying patterns and trends
in context, within and between                                                                               How many vehicles use a local road you use and care about (two directions) at the same time on different days of the week?
Using the data gathered, reflect and justify your findings.
data sets;
- communicating findings, using                                                                              How many road users use a local road you use and care about (two directions) at the same time on different days of the week?
Present in a way that will inform others.
data displays.
How many vehicles use a local road you use and care about (two directions) at the same time on different days of the week?
Evaluate the effectiveness of statistical investigations by others.

Level Four                                                                                                   How many road users use a local road you use and care about (two directions) at the same time on different days of the week?
Plan and conduct investigations        Statistical literacy
using the statistical enquiry cycle:   Interpret statements from statistical investigations.                 How many vehicles use two roads you use and care about (two directions) at the same time and day?
- determining appropriate              Compare statements from statistical investigations.
variables and data collection          Evaluate the effectiveness of different statistical data displays.    How fast do vehicles travel on roads you use and care about in your local community?
methods;                               Evaluate statistical generalisations.
- gathering, sorting, and                                                                                    Define the population concerned, e.g. all the road users of XXX road, all the vehicles using XXX road.
displaying multivariate category,                                                                            Describe the variables to be measured, e.g. different groups of road users (discrete data), number of road users travelling past a
measurement, and time-series                                                                                 given point in a given time (discrete data), number of vehicles travelling past a given point in a given time (discrete data), speed
data to detect patterns,                                                                                     or velocity of road users on a local road (continuous data).
variations, relationships, and                                                                               Describe the sample size.
trends;                                                                                                      Collect data. For example, use surveys, observations, questionnaires, or interviews to identify local roads that might need
- comparing distributions visually;                                                                          calming. Survey road users about the traffic congestion and road user risks they experience as they use local roads to travel to
- communicating findings, using                                                                              [school each day/a Rugby World Cup stadium]. Travel - walk, drive, bike, public transport, school bus.
appropriate displays.                                                                                        Keep a road log of the number of cars that pass through the roads identified as unsafe for road users, for example, at the
pedestrian crossing on a main road outside the school between 8.00 am and 9.00 am. View a Traffic Cam
Statistics                                                                                                   <http://metservice.com/national/traffic-cams/index?gclid=CLCk56n7pZ8CFYswpAodEXdjzg> and tally the number and type of
Statistical literacy                                                                                         road users on the road in both directions over a 30 minute time frame.
Sort data, e.g. record this survey data in a tally chart.
Level One                                                                                                    Summarise the data.
Interpret statements made by                                                                                 Present the data. For example, choose the most appropriate method of presenting data: bar charts, histograms, frequency
others from statistical                                                                                      tables, tally charts, pictograph, strip graph, pie chart, table, graph, dot plots, time series.
investigations.                                                                                              Analyse the data. Use average, mean, mode.
Compare and contrast data, e.g. the average number of road users on local road one with the average number of road users on
Level Two                                                                                                    local road two, at the same time of the same day. Compare and contrast road users who are walking [to school/
- Compare statements with the                                                                                place/venue/event stadium] with road users who are driven [to school/ place/ venue/ event stadium].
from statistical investigations or                                                                           weekend.
probability activities undertaken                                                                            Compare and contrast your data with national survey data on road use and walking in New Zealand. For example, refer Ministry
by others.                                                                                         of Transport: Walking for transport Survey 2008 <http://www.transport.govt.nz/assets/Walking-for-transport-2008.pdf>
Draw a conclusion from the data analysis about the problem you have investigated.
Level Three                                                                                        Make a generalisation from a multitude of data.
different displays in representing                                                                 make road users safer as they travel to an event stadium or venue].
the findings of a statistical                                                                      Present your data in a way that will inform others. For example include your statistical analysis in a claymation animation like
investigation activity undertaken                                                                  Chicane – Animated Street Calming http://www.streetfilms.org/chicane-animated-traffic-calming/A 24 second stop-animation
by others.                                                                                         street film on chicanes as street calming devices.
Level Four
others about the findings of                                                                       Define ‘traffic calming’. To help find out what a word means, you can use Google’s define feature. For example, type ‘define:
statistical investigations and                                                                     traffic calming’ into the search box and press Enter. For help finding web page content that is more suited to children, add ‘for
probability activities.                                                                            children’ to your search term. For example, type ‘traffic calming for children’ into the search box and press enter.
Sequence the changes in road use over time, e.g. steam train, bicycle, car.
Compare and contrast patterns of road use since the 1950s, e.g. public transport, private vehicle, bicycle, walking etc.
Explain how the introduction of affordable private transport has affected road use, the distance between homes, services and
facilities, and people’s ability to walk.
Find out the number of new cars being put on the road each day in New Zealand.
Find out the number of cars per person in New Zealand.
List the methods of road use in New Zealand.
Rank the methods of road use in New Zealand from most common to least common.
Rethinking Streets in Paris <http://www.streetfilms.org/category/traffic-calming/> This video explores traffic calming amenities
installed in Paris.

What if Questions:                   Print Resources:                                              Thinking strategies to         ICTs to support learning experiences.
support learning
experiences
Teachers to record print resources used and those that are    These are suggested            These are suggested ICTs only that will support the bringing in of ideas, the connecting
What if cars were banned in          available in the school that will support this teaching and   thinking frameworks            of ideas and the putting of ideas into another context.
cities?                              learning resource.                                            only. Teachers to record
here the ones they will        TKI:Exemplar<http://www.tki.org.nz/r/assessment/exemplars/maths/index_e.php#measurement>
What if you had to pay extra to                                                                    be using. Refer to             The New Zealand Curriculum Exemplars – Statistics.
take your car into the city                                                                        resource. Teachers to
centre?                                                                                            record the strategies          NCTM Illuminations: Lesson Ideas <http://illuminations.nctm.org/LessonDetail.aspx?id=U87 >
they will be using.            Lesson ideas for creating a survey, collecting data and creating graphs about favourite pizza
What if public transport was                                                                                                      toppings.
free?                                                                                              Use SCAMPER to imagine
Introduce statistical thinking to students using the exemplars from The New Zealand Curriculum
other ways of designing
TKI Exemplars: Mathematics and Statistics.
What if there were no                                                                              roads so that all users are
sidewalks and pedestrians and                                                                      safe.                          <http://www.tki.org.nz/r/assessment/exemplars/maths/index_e.php>
cars used the same road                                                                                                           Refer to the units of work on the New Zealand Maths website, New Zealand Maths: Units of Work:
spaces?                                                                                            Do a PMI on reducing the       Statistical Investigations <http://www.nzmaths.co.nz/welcome-statistics> for introductory ideas
speed travelled on a road      on teaching statistical thinking to students. Also look at Census at School NZ
What if everyone used bikes                                                                        you use and care about to      <http://www.censusatschool.org.nz/> A nationwide online survey for Year 5 - 13 students which
30 km.h-1                      provides real, relevant data and classroom activities to enhance statistical enquiry across the
transport?                                                                                                                        curriculum.
Brainstorm all the different
road users who use a road      Use the lesson ideas on the National Council of Teachers of Mathematics site to teach students
you use and care about.        how to conduct a statistical inquiry.
NCTM: Pizza Pizza! <http://illuminations.nctm.org/LessonDetail.aspx?id=U87> Lesson
ideas on collecting and analysing data, representing data through physical and graphical
question?                              means, drawing conclusions from the data, communicating their findings to fellow
classmates, making a double-bar graph to display information, and exploring the
Use a Venn diagram to                  mathematical idea of combinations of two items.
compare a traffic light with           NCTM: Eat your veggies <http://illuminations.nctm.org/LessonDetail.aspx?id=U114>
a school bell.                         Lesson ideas for collecting and displaying data - tallies and pictographs, representing data
using bar graphs, line plots, circle graphs, box-and-whisker plots, and glyphs.

Figure it out <http://www.tki.org.nz/r/maths/curriculum/figure/level_2_3_e.php>

different levels.

NZ Maths

<http://www.nzmaths.co.nz/statistical-investigations-units-work>

Statistics area of NZ Maths. Units of work. Each unit has a link to an exemplar.

Exemplars - TKI

<http://www.tki.org.nz/r/assessment/exemplars/maths/stats_display/sd_overview_e.php>

Data display progression Level 1 through to Level 5.

The New Zealand Curriculum Exemplars - Statistics

<http://www.tki.org.nz/r/assessment/exemplars/maths/index_e.php#measurement>

Examples of children’s work at different levels for data display and probability.

Games

<http://www.bbc.co.uk/education/mathsfile/gameswheel.html>

BBC website. ‘Fish Tank’ – probability; ‘Train Race’ – mean, median and range; ‘Data Picking’ –
frequency table and graphs.

Statistics New Zealand

<http://www.stats.govt.nz/tools_and_services/services/schools_corner.aspx>

The NZ census – School’s Corner.

NCTM Illuminations – ‘Eat your veggies’
<http://illuminations.nctm.org/LessonDetail.aspx?id=U114>

Lesson ideas for collecting and display data - tallies and pictographs, representing data using bar
graphs, line plots, circle graphs, box-and-whisker plots, and glyphs.

NCTM Illuminations – ‘Pizza, pizza’

<http://illuminations.nctm.org/LessonDetail.aspx?id=U87>

Lesson ideas for creating a survey, collecting data and creating graphs about favourite pizza
toppings.

NCTM Illuminations – ‘Weather watchers’

<http://illuminations.nctm.org/LessonDetail.aspx?id=L287>

Lesson ideas for stem-and-leaf plot.

Assessment for Learning: Teacher/Peer/Self
Teachers to highlight learning experiences that will be used for assessment for learning throughout the unit. These can be recorded in portfolios/school management systems.

Example rubric:
Teachers to code in the first column the symbols that they use in the school for assessment. These could be against levels, MOE guidelines or internal criteria. The rubric can be
written against the AOs or rewritten as success criteria for children depending on the preference of the school.

I can reflect on findings and make a generalised statement/justification about their meaning to the investigation.
I can compare data within and between graphs and explain trends and patterns.
Can use a range of simple graphs to show information.
I can use a tally chart to record information.
I need help to use tally charts and simple graphs.

Refer: Ministry of Education. (2007). The New Zealand Curriculum for English-medium teaching and learning in years 1–13 Wellington: Learning Media.

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