©Planning for learning in mathematics and science, 2015 drafted by B.O.P.

Name: Uzma Shakil

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/Engagement Learning Experiences (s):

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.

Exploratory /Explore & Explain Learning Experiences:

Activity 1: Gender Diversity (Tinker plots)

Draw a table on the board and ask each student to enter their sex in the table.

Students will work in pairs to complete the frequency table.

They will then draw a column graph to show this and then represent the same set of data using pie chart.

They will then move onto plotting this data table on tinker plots. Teacher will demonstrate how to do this step by step.

©Planning for learning in mathematics and science, 2015 drafted by B.O.P.

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?

©Planning for learning in mathematics and science, 2015 drafted by B.O.P.

How will you know what the students have learnt? (Assessment)

What will you assess? How will you assess? When will you assess? & Who leads the assessment?

How will you record your assessments?

What forms of feedback will you provide?

Concept(s):

The data can be discrete,

continuous, numeric or

non-numeric.

Ranges of data, average,

mean, median, mode,

maximum and minimum

values.

Similar sets of data can be

represented using different

graphs such as bar charts,

pie charts, line graphs etc.

Teacher observation

and discussion.

Student work

samples and class

discussions.

Presentation of

results, student work

samples, teacher

observation and

class discussion.

Exploratory

activities 2, 3, 4 &

5.

Exploratory

activities 2, 3 & 4.

Exploratory

activities 1, 3 & 4

and investigation

activity.

Digital image of

work samples.

Take digital

image and write

comments on

observation

sheets.

Writing

observations

and taking

digital image of

work sample.

Written feedback

on work samples.

Immediate verbal

feedback and

written feedback

on work samples.

Instant verbal

feedback and

written feedback

in the form of

annotated image

of work sample.

Thinking and Working Mathematically: Sorting and organising data.

Teacher observation and discussion.

Prior knowledge activity and exploratory activities 1 & 2.

Digital image of student work.

Class discussion where all aspects of the lessons will be reviewed and

Ask students to predict the number of seeds produced in next four years and then represent this data using line graph and verify their values.

Discuss the predictions before plotting the results on line graph.

Investigations /Problem solving/Elaboration Learning Experiences:

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).

©Planning for learning in mathematics and science, 2015 drafted by B.O.P.

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.

Exploratory activities 3, 4 & 5. Exploratory activities 3 & 4 and investigation activity. Exploratory activities 3 4 & 5 and investigation activity.

Write observations. Write observation of student conferencing. Work samples.

feedback will be given to each group. Written feedback on work samples.

Links with the ACARA Framework

Strand: Statistics and Probability Sub- Strand: Data representation and interpretation

Descriptor: : Proficiencies (for

Mathematics)

General capability Achievement Standards:

Pose questions and collect

categorical or numerical

data by observation or

survey (ACMSP118)

Reasoning Literacy

Numeracy

Creative and Critical

Thinking

Students pose questions

to gather data, and

construct data displays

appropriate for the data.

Strand: Statistics and Probability Sub- Strand: Data representation and interpretation

Descriptor: Proficiencies (for

Mathematics)

General capability Achievement Standards:

Construct displays, including

column graphs, dot plots and

tables, appropriate for data

type, with and without the

use of digital technologies

(ACMSP119)

Reasoning Literacy

Numeracy

ICT

Students pose questions

to gather data, and

construct data displays

appropriate for the data.

Strand: Statistics and Probability Sub- Strand: Data representation and interpretation

Descriptor: Proficiencies (for

Mathematics)

General capability: Achievement Standards:

Describe and interpret

different data sets in context

(ACMSP120)

Reasoning Literacy

Numeracy

Critical and Creative

Thinking

Students interpret

different data sets.

Teacher Resources (What has informed your planning, background information, learning experiences, discussion of student understanding?)

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.

©Planning for learning in mathematics and science, 2015 drafted by B.O.P.

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.

Tinker Plots Software

Multicultural Survey Sheets (Appendix A)

Classroom and stationery

Handspan Data Cards

Post-it notepad

©Planning for learning in mathematics and science, 2015 drafted by B.O.P.

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.

©Planning for learning in mathematics and science, 2015 drafted by B.O.P.

Appendix A

Our Multicultural Classroom

You will need to walk and talk during this activity.

Find someone who … Name

Has traveled to New Zealand

Comes from an Island in the Pacific

Can count to 5 in Japanese

Knows four different types of pasta

Has parents that migrated from Asia

Can say ‘Hello’ in 5 different languages

Can name the Indigenous community which is the Traditional Custodian of the local area

Knows the main religion of Indonesia

Plays a sport that originally comes from England

Has one parent from Europe

Can name 5 different herbs and spices

Likes nachos, burritos and other Mexican food

Knows which country celebrates St Patrick’s Day

Has eaten at a Chinese Restaurant

Can name one country next to India

Knows 3 different French foods

Speaks another language at home

Can name the traditional German outfit

Is related to someone living in the United States of America

Has dual citizenship