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. these to write your WALTs. 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 road users. NZTA <http://www.nzta.govt.nz/network/operating/counting-traffic/index.html>) 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. Use a tally chart. How do road users use the roads in your local community? How do pedestrians use the roads in your local community? Do so 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 - gathering, sorting, and road users safer on roads in your local community? Does a road in your local community need calming? 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]. features of simple data displays Compare and contrast road users [on a local road/on roads around an event stadium] on a weekday with road users at a 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. Evaluate the effectiveness of Make a generalisation from your data about how [your local community can make local road users safer on local roads/we can 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. Evaluate your generalisation about road use on [a local road you use and care about/roads around an event stadium]. Level Four Evaluate statements made by Suggested research data to support your generalisation 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 instead of cars for personal 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 If the answer is ideas on collecting and analysing data, representing data through physical and graphical “roundabout”, what is the 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> Downloaded booklet, including teacher notes and activities. Clink on the links on the page for 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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