HolidaysJessica Cook, Mahshid Shad

& Suzy Cipollone

Maths in Holidays

Time zone differences

Budget calculations

Expected time of arrival

Distance travelled

Currency conversions

How much do you tip?

Frequent flyer points

Timetables

Shapes in flags

Directions and maps

Country sizes

Modes of transport - speed

Measurement e.g. most direct flight path

Baggage weight allowance

Links to other KLAs

Great potential to link the ‘holidays’ theme to many other KLAs depending on the focus of the particular lesson(s).

As approximately ¾ to ⅘ of our daily estimations and mental computations are focused around issues of time and money (Grant, 2012), these are the two main subject areas of our three lessons.

Strong links to HSIE (Cultures strand) English (esp. Reading strand) and Science and Technology (Earth and its Surroundings)

Our hypothetical class (Stage 3, Year 5/6)

From the K-6 Mathematics Syllabus (Board of Studies, 2002), an outline of student capabilities relevant to tasks included in the following lessons:

Students ask questions and undertake investigations, selecting appropriate technological applications and problem-solving strategies. They use mathematical terminology and some conventions and they give valid reasons when comparing and selecting from possible solutions, making connections with existing knowledge and understanding.

Students read, write and order numbers of any size, selecting and applying appropriate mental, written or calculator strategies for the four operations. They compare, order and perform calculations with simple fractions, decimals and simple percentages and apply the four operations to money in real-life situations.

Students select and use the appropriate unit to estimate, measure and calculate. They use 24-hour time in real-life situations and construct timelines.

How would you implement the topic with Stage 3 students?

Constructivism allows for the learner to construct their own understanding and knowledge of the world through experiencing and reflecting on those experiences. According to Marsh (2010), constructivism is problem based learning. The emphasis is on the student and making sense of the information after instruction. Characteristics of constructivism according to psychologists such as Piaget, Vygotsky and Dewey:

Construct own meaning

Active learning rather than passive learning

Learners engage in concrete tasks rather than abstract tasks. This means that students use physical materials and manipulative interactive tasks

Learners are encouraged to have open communication with peers and teacher to enhance learning

Scaffolding may be used to encourage students

Teaching and learning strategies to be adopted

In addition to the adoption of a constructivist approach, the following strategies will also be adopted for our hypothetical class, including:

Brainstorming

The inclusion of open-ended questions to assist with informal assessment

The requirement of increased oral and mental work from students

Debriefing sessions to clarify thinking

Encouragement of students’ own and informal written methods as the link between mental maths and the formal algorithm

Use real life resources and strategies which emphasise the importance of appropriate mathematical language

Planned assessment of student learning

‘The informal assessment practices that were once valued only as a means of conducting day-to-day teaching are now being seen as essential in a balanced assessment program.’ (Booker et al, 2010)Outcomes Assessment Strategies

Working Mathematically Applying strategies WMS3.2Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigations

Reasoning WMS3.4Gives a valid reason for supporting one possible solution over another

Observation of group work – how did students arrive at a particular answer? How did initial answers obtained through mental computation compare with those obtained by other means?

Probing questions such as ‘How did you arrive at that answer?’ and ‘Justify your groups’ particular method.’

Outcomes Assessment Strategies

Number OutcomesAddition and Subtraction NS3.2Selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

Multiplication and Division NS3.3 Selects and applies appropriate strategies for multiplication and division

Measurement OutcomesTime MS3.5Uses twenty-four hour time and am and pm notation in real-life situations and constructs timelines

Comparison of each table groups’ answers. If different, ask questions about strategies utlised to arrive at a certain answer. What strategies did other groups use?

Student worksheets – successful completion of task set in lessons 2 & 3 and observation of group work.

In my maths lesson…

https://mathsholidays.wikispaces.com/file/view/MyMathsLesson.pdf

You need to get your whole table group to Hawaii!

Lesson One - BudgetingIntroduction:

Students partake in mental maths warm ups. Simple addition, multiplication and division. Students brainstorm with teacher on IWB on things for which need to be budgeted for on holiday. Students asked to think about their own holiday experiences to give them ideas, e.g. flights, accommodation and food. Teacher introduces budgeting. Teacher and students discuss budgeting. T asks “what does it mean to budget?” and “how can you budget for a holiday?”

Body:T sends students back to table groups (at each table there are brochures and activity sheets). T advises Ss that they have $4 000 budget. Ss are given a hypothetical family. Ss state how many are going on the holiday on the activity sheet. Ss work in groups to decide the family’s holiday destination, and whether they are going to use a package deal or buy everything independently. From what the Ss decide they will then plan the holiday for their hypothetical family. Ss will use multiplication, addition and division to arrive at their answers.

Conclusion:T then asks each table group about what they decided for the hypothetical family, are they going for a package deal or not? What prompted their decision?

Lesson Two - TimetablingIntroduction

T reviews the previous lesson. T introduces new concepts and vocabulary such as digital and analogue clock, and am and pm notation. T demonstrates twenty-four hour time on a clock, e.g. 23:30 is the same as 11:30 pm.Various timetables including those involving twenty-four hour time such as bus, train, ferry and airline timetables are provided for students on IWB; e.g. the transport info website http://www.131500.com.au to indicate where 24-hour time is used and how Ss can travel between two locations considering arrival and departure time. 

Body:Using the same hypothetical family as before, groups must now try to come up with a suitable holiday itinerary for a trip to Queensland. A blank timetable is provided for each table group, together with a sheet that describes the activities that each family member would like to fit into their holiday. Resources, including a ‘Zone 4 Kids’ timetable, a coach timetable to Australia Zoo and an Activity Schedule for the resort the family are staying at will need to be consulted.Using the activity strips in the envelopes provided you must try and work out whether / how all of these activities might fit into their itinerary. Click example.

Conclusion:Ss complete worksheets. T asks Ss to briefly discuss their timetables and give a summary about what they have learned.Teacher sets a homework task; based on managing time, students should plan a simple travel itinerary.

Lesson Three – International Time ZonesIntroduction:

Introduce topic and how it relates to previous lesson dealing with local time.Develop an awareness of time zones – introduce the idea using a torch (pref. with coloured lighting) and globe (TES, 2011).

Body:Go to webpage http://www.timeanddate.com/time/map/#!cities=240 and ask Ss about time zones in Australia first.Ask Ss to note the Coordinated Universal Time line (UTC or GMT) and explain what this means. What do they notice about all time zones on the right hand side and those on the left?T hands out worksheets and assists groups to complete. Clock activity - each group given a blank clock and a country. Groups asked to place the hands correctly on their clock if it is midday in Sydney. Ss stand up holding their clock and city and ask the class if they agree. Swap cards and repeat for another city and another time until confident.

Close: Ask Ss which countries were easiest to work out the time quickly for? How / why? (e.g. by taking off just one hour for Buenos Aires and changing pm to am instead of working out the time -13)Challenge any misconceptions by asking questions such as ‘Can two different countries be in the same time zone?’Early finishers can consider whether or not it would make a difference to answers provided when daylight saving commences in Summer?

Resources

All resources available at:

https://mathsholidays.wikispaces.com/Resources

Follow-up discussion questions

Have you seen ‘holidays’ used as a theme for Mathematics and / or other KLAs out on Prac?

We have focused on three strands (Working Mathematically, Number and Measurement), what sort of activities relating to the theme ‘holidays’ could be implemented for other strands? (Patterns and Algebra, Data, Space and Geometry)

Could these lessons be adapted for Stage 1 and 2 students? If so, how?