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Unit Planner for Learning in Mathematics Learner context
Topic Focus: Graphical Representation and Data Analysis Level of schooling: Year Level 5 School and class context: It is a Catholic School. There are 24 students in class and 4 students are with special needs. The student with autism and severe intellectual disability have NEP (Negotiated Education Plans) in place and have support staff who come in to help them.
What is the learning focus?
Concept(s): Thinking and Working Scientifically Mathematically
Different types of data: The data can be discrete, continuous, numeric, non-numeric or random.
Sorting and organising data
Sets of data: Ranges of data, average, mean, median, mode, maximum and minimum values.
Describing and summarising data
Comparing sets of data
Different types of graphical representation: Similar sets of data can be represented using different graphs such as bar charts, pie charts, line graphs etc.
Representing data in tables, graphs and charts
How will the students engage with this learning? (Provide here an outline of a learning experience with using the given structure)
Prior knowledge learning experience is significant in a classroom. According to Van De Walle (2010, p. 33):
‘teaching should begin with the ideas that children already have, the ideas they will use to create new ones’. How Multicultural is our classroom? Introduce the concept of data collection.
Students will be given a prepared questionnaire to find out how multicultural our classroom is.
They will survey the students within their own class and collect data.
In groups of three, they will summarise results using either graphs or data tables.
Present their findings to the class. The template of this survey is sourced from Making Multicultural Australia (2015). Please refer to Appendix A for the survey.
After the collection and representation of data, analyse the representations, examine and discuss the results. Discuss ways in which data was represented and why a particular representation is useful. According to Van De Walle (2010, p. 21):
‘Classroom discussion based on students’ own ideas and solutions to problems is absolutely “foundational to children’s learning”’.
Activity 2: Handspan Data Cards
Students will measure and enter their handspan in the table on the board. They will also write their handspan on a data card.
In pairs, they will then complete the frequency table for handspan.
The teacher will explain the concept of quartiles, mean, mode and median. In groups, the students will utilise floor space in the room to sort the data cards in ascending order and quartiles, mean, mode and median will be calculated. The teacher move around the room and assist each group in their calculation.
They will then create histograms to represent this set of data. Discuss why histograms were used to represent data and the advantages of calculating mean, mode and median. Discuss how these measures can assist us in data analysis. Activity 3: Investigate your school Students will work in groups to design their own survey and find out about either TV viewing habits or food preferences in the school. They will carry out the survey, categorise the data in tables, represent them graphically and then analyse them. Discuss what conclusions they could draw and why. Do TV viewing habits vary for different ages, gender or family size? Do food likes and dislikes vary with age? Discuss why they used a particular graphical representation and how have they derived their inferences. The learning activity is sourced from the book Mathematics at work; modelling your world (Lowe 1988). Activity 4: What’s the weather like?
Explore weather data from one of the weather websites, such as, www.weatherzone.com.au www.bom.gov.au/sa/forecasts/adelaide.shtml and www.willyweather.com.au.
Make comparisons over time and find answers to interesting questions.
Here are some aspects to consider: o Compare data from the three different weather stations. o Compare different months of the year, or different seasons. o Look for trends over time - how has temperature or rainfall changed over the years?
This learning experience will provide opportunity to students to study large sets of secondary data which has already been collected and examine different types of trends in data. This activity is sourced from NRICH (2015). Activity 5: Anno’s Magic Seeds
Distribute worksheets to the students.
Read the story Anno’s Magic Seeds by Anno Mitsumasa. Read it until Jack says “This can go on and on in the same way forever”.
Ask students to complete the data table. Once it has been completed, ask the following questions: o What do you notice about the number of seeds produced every year? o Jack thought “This can go on and on in the same way forever”, is he right?
Sport Shop (A problem solving activity) Norman wants to open a sports store in an area of the coast where:
Population is expanding
There are reasonable number of people with above national average income
Tourists population is growing Students will work in groups of 3 or less to design an investigation, collect data, represent and analyse the results. The groups will carry out their investigations within the school community. Each group will present their results and critically reflect on how these data inferences can help Norman in making decision. When the groups have presented this analysis and inferences, discuss what lead to this conclusion. Also discuss other ways in which the data could be analysed. The learning activity is sourced from the book Mathematics at work; modelling your world (Lowe 1988).
Describing and summarising data. Comparing sets of data. Representing data in tables, graphs and charts.
Teacher observation and student conferencing. Teacher observation, student conferencing and class discussion. Student work samples and teacher observation.
NRICH 2015, ‘Handling, Processing and Representing Data’, University of Cambridge, viewed 16 August 2015, <http://nrich.maths.org/public/leg.php?ct=1&cl=2&dl%5B0%5D=1&dl%5B1%5D=1&dl%5B2%5D=1&group_id=44&cldcmpid=&code=193>.
Van de Walle, J, Karp, K & Bay-Williams, J 2010, Elementary and middle school mathematics: teaching developmentally, 7th ed, Pearson, New York.
Making Multicultural Australia 2015, ‘Lesson Ideas for Teachers’, Making Multicultural Australia, viewed 27 Oct 2015, <www.multiculturalaustralia.edu.au>.
Student Resources (resources that engage students with the learning)
Anno, M 1994, Anno’s Magic Seeds, New York, Penguin Putham Books.
References: Anno, M 1994, Anno’s Magic Seeds, New York, Penguin Putham Books. Lowe, I 1988, Mathematics at work; modelling your world, Australian Academy of Science, Canberra, pp. 59-67. NRICH 2015, ‘Handling, Processing and Representing Data’, University of Cambridge, viewed 19 October 2015, <http://nrich.maths.org/public/leg.php?ct=1&cl=2&dl%5B0%5D=1&dl%5B1%5D=1&dl%5B2%5D=1&group_id=44&cldcmpid=&code=193>. NRICH 2015, ‘What’s the weather like?’, University of Cambridge, viewed 19 October 2015, <http://nrich.maths.org/10470>. Van de Walle, J, Karp, K & Bay-Williams, J 2010, Elementary and middle school mathematics: teaching developmentally, 7th ed, Pearson, New York.