Archive for the ‘Chapter 6: Location, Location, Location’ Category

August 21, 2008

Story
In this science-fiction, fantasy scenario four friends are whisked through the earth to a different hemisphere. This situation, which requires students to work scientifically and develop technology. forces them to use their ingenuity to work out the local time (using the sun) and invent a timing device that will help them return.

Parts of this chapter may challenge students with spatial understanding of time zones and location, yet all students should be able to complete the enquiry and design activities.

Location 1: An Australian Park

Discussion question Why do we create rules for games? Suggested answers (1) Most rules are about control and management of groups of people. (2) Most rules are about fairness, reciprocity, dignity (e.g., conflict resolution rules), to develop responsible attitudes and procedures (e.g. safety rules).

Follow on questions or extension discussion: Where do school rules fit within this?

Background information for teachers:
Children’s play involving games is an active and interesting branch or research:

  • All over the world, there is a consistency in the types of games children play at different ages. Preschoolers enjoy chants, hide-an-seek type games, rhymes and chants. By the time children are about 7, most are beginning to play games that require rules, within a few years (age 10-11), learn to invent rules for new games themselves.
  • As with any young mammals, for example, kittens, where play is a precursor for learning to ambush prey, there is a serious developmental purpose to the play of children. Game rules develop values of justice and fairness, and children who play games learn essential skills in conflict resolution. http://www.umext.maine.edu/onlinepubs/htmpubs/8048.htm

Humans are a social species. Such species have consistent patterns of behaviour that enable them to cooperate and compete in ways that are not self destructive. Human rules for behaviour may therefore have their origins in deep time, when society consisted of families, clans or nomadic groups

Activity 1 : Create a sundial

Build-up – pre-requisite subject knowledge or background information
Do students understand shadows are indicate ‘absence’ of light/ and always fall in straight lines? Do students understand the apparent motion of the sun (the real motion is the Earth’s) across the sky each day?

Approach – suggestions for organising students, equipment etc.

Ideas for the perpendicular gnomon:

  • This could be a stick pushed in the ground, a stick placed vertically inside a tin filled with plaster of Paris, and left to set, or a retort stand.

Answers
What happens at noon? The shadow should be shortest; noon is the highest point the sun reaches.

Think of some different ways to show your results – including tables or graphs.
This could be the circular style, or on a graph, as sundial information is often shown.

Example produced by MYP 1 student

Example produced by MYP 1 student

If the Earth were not tilted, would your results be different? If the earth was not tilted, we would not have seasons – so the sundial would cast the same shadows wherever you were on earth.

A range of activities is available on
http://www.spacescience.org/education/extra/kinesthetic_astronomy/ and on http://hea-www.harvard.edu/ECT/the_book/toc.html

Extension work/ discussion you might consider with this activity:

  • How will your results change during (i) Daylight saving/ Summertime (if this occurs in your region)? Daylight saving/summertime will not change the actual shadows, but the hour name you give it will – it is important students recognise the concept of ‘time’ is human ingenuity – but the shadows come from cosmic reality.
  • At mid summer? At mid summer the sun is highest overhead – the shadows will be shorter at noon. Also the days are ‘longer’ – so the arc transcribed by the sun will be larger (take up more of the 360o of the circle.
  • At mid winter? At mid winter the sun is low on the horizon – the shadows will be longer at noon relative to the summer position – but noon will still give the shortest shadow. Also the days are ‘shorter’ – so the arc transcribed by the sun will be smaller (take up less of the 360oof the circle.

Think about the shape of the Earth and how it might look from different positions – if you were a sunbeam.
This might be worth modelling with a pin stuck in a Styrofoam ball, with light coming from different positions.

What kinds of changes might happen to your diagram if your stick was at

  • One of the Earth’s poles – for example, in the Arctic? At the poles the situation will be more extreme – 24 hours of light ‘the midnight sun’ in summer, and no light in winter.
  • Near the equator – for example, on a Pacific Ocean island? At the equator the patterns will be similar throughout the year.

Assessment:
The IB does not recommend every task MYP students complete be assessed. Assessment should occur only after completion of a major assignment or period of learning.

The MYP assessment criterion D Scientific Inquiry and criterion E Interpreting data may be relevant unpacked for Year 1 in student-friendly language.

Discuss qualities of a well-written science report. Science reports are generally written under Sciences Criterion D. (Scientific Inquiry), calculations and graphical representations are generally assessed under Sciences Criterion E (Processing Data)

Wording unpacked for students in MYP 1 – Example

CRITERION D (Scientific inquiry) is about

  1. Stating problems
  2. Developing hypotheses
  3. Planing variables
  4. Selecting equipment
  5. Evaluating results
  6. Evaluating method

These experiments are major pieces of work, not student-lead teacher-suggested demonstrations

Modified CRITERION D (for MYP 1)

0 work shows no evidence of processing data

1-2 work is generally illegible or poorly presented

· Hypothesis – The expected shape of the shadows – not stated or poorly expressed

· Aim Not clear, lacks background

· Method:

No planning evident.

Diagrams may be in ink, unlabelled, or small and cramped. There is no evidence a ruler was used.

· Results: Data is missing, inaccurate, illegible or incomplete.

· Discussion: Not supported by the data. Limited understanding of purpose of the experiment. Relationships not seen. No evidence of extra reading or research to understand the data.

· Conclusion Does not relate to aim or not stated.

3-4 work generally needs improved presentation and attention to detail

· Hypothesis – The expected shape of the shadows -stated, but needs more explanation

· Aim needs some background theory and explanation.

· Method Some planning evident, recording process explained. Procedures and equipment stated, details needed.

Diagrams need better scale, not in pencil or without a ruler.

· Results present but poorly summarised or not well organised. Units may be missing from tables or graphs.

· Discussion: Explains what the results show. Does not clearly understand limitations of the method.

· Conclusion answers the aim but no detail in explanation.

5-6 work is well presented and organised:

· Hypothesis The expected shape of the shadows -clearly stated and with a testable explanation (If….then.. format is recommended).

· Aim includes some background theory. Explain why research is important.

· Method: Clear planning and recording process explained Procedures and equipment clearly stated in detail.

Diagrams at least ½ page, using pencil and ruler.

· Results: Tables and graphs should be accurate with clear titles and/or units.

· Discussion: Explain what the results show. Relate (if possible) the results to past research, and real life patterns and examples.

Explain any results that don’t fit patterns.

Suggest improvements to experimental technique, and further investigations to be made.

· Conclusion must answer the aim and present a logical explanation.

Criterion E is about

  1. Designing graphs and tables
  2. Reading graphs and tables
  3. Predicting trends
  4. Problem solving
  5. Simple calculations

This may or may not be part of a practical report

Modified CRITERION E (for MYP 1)

1-2 work involves ability to

· Present data in simple formats only. Draw simple graphs, under supervision.

· Solve simple numerical problems and calculations

· Draw obvious conclusions

· Interpret simple diagrams, tables and graphs.

3-4 work involves ability to

· Present tables or graphs, but the format, layout or labelling may not be the most appropriate (eg, histograms where line graphs should be used).

· Solve some, but not the most difficult, numerical problems.

· Identify trends and patterns, but not consistently.

· Interpret some trends in data and draw some conclusions

5-6 work involves ability to

· Show a logical and clear presentation, for example, tables and calculations. Draw graphs of appropriate size and scale

· Use relevant calculations to solve problems of a range of difficulties

· Interpret trends in data and draws conclusions consistent with evidence

· Infer and make logical predictions consistent with data

Location 2: Alien Landscape

Discussion question What do you think the numbers in the box on the sundial refer to? Answer: The numbers in the box are the latitude and longitude of the new location, the students have found themselves in. If students have studied the previous chapter The Arctic Connection, they will understand how to locate these on a map. Schools connected to the World Wide Web may be interested in looking for the location using Google Earth Download Google Earth Pro

Build-up – pre-requisite subject knowledge or background information
The analemma is the figure-of-eight path transcribed by the sun if you photographed it each week for a year from the same location. The exact shape is affected by latitude, season and the speed of the Earth’s motion around the sun. This movement is slightly faster at perihelion – when the sun’s slightly elliptical orbit means it is slightly closer to the earth. This happens during the Australian summer, which is why southern hemisphere summers are a few days shorter than northern hemisphere summers!

The shape drawn on a flat(tish) surface can also be used to produce an interactive sundial that requires a standing person to act as a gnomon.

Analemma sundail 1

Analemma sundial 1

Analemma sundail 2

Analemma sundial 2

If discussing or studying the analemma sundial in more detail:

Useful definitions that may help you interpret the diagram, and relate the analemma sundial to the sundial activity completed by students :

  • A solstice is a time during the year when the sun appears to stand still. The summer solstice is the longest day, and the winter solstice the shortest day of the year. The diagram below shows sunrise and sunset during the summer and winter solstices.
  • An equinox is a day when the period of light and darkness is equal (this follows from having day length varies over the course of a year) The equinoxes occur in Autumn and Spring. Most calendars give 21st/22nd March and 21 st /22nd September as the dates, most years. Note: The story happens close to an equinox:
  • Where does the central line point to? It should point to True North – this is not the same as magnetic north given by compasses, but the point around which the Earth rotates. As magnetic north will change over time, refer to a recent map for confirmation of how to find it.
  • What is the connection between it and the positioning of the non-sun arm on the watch-compass? It is the same
  • What do the numbers probably indicate? The numbers indicate 24 hour time.

Diagram of analemma sundial

Diagram of analemma sundial

Note: Why is ‘Sunrise’ shown on the west?

Sundials work by reading shadows, which will fall in the opposite direction from where the sun is – eg, if the sun is rising in the east, the shadow indicating ‘sunrise’ will be read on the Western side.

Useful References
Software that draws analemmas at any specific latitude and longitude can be purchased for $US15 from http://www.jgiesen.de/GeoAstro/GeoAstro.htm. The result, reproduced on A3 paper, can be mounted on a board and used with a pin as the gnomon.

Alternatively the mathematically inclined can calculate the shape from various equations given in http://plus.maths.org/issue11/features/sundials/feat.pdf

It is a very affirming experience for students to tell the time with an analemma sundial designed for one’s exact location given by Latitude and Longitude– it tells us the earth is a sphere and gives confidence in human ingenuity. It is fun to have such an accurate time keeper.

Follow on questions or extension activities
Students may enjoy exploring how the shape of the analemma changes at different locations on Earth, for example, typing a range of Latitudes and Longitudes associated with different chapters in the book on the site: http://www.jgiesen.de/hsd/hsd300.html

  • Canadian Arctic
  • Fiji
  • Canadian Rockies/Grand Canyon
  • Istanbul

There is no assessment rubric associated with this activity – understanding the analemma is a challenge in itself.

So Long, Location 2

Activity 2, Taking the Time

Build-up – pre-requisite subject knowledge or background information
The ‘Design cycle’ is the core process underpinning MYP Technology. The assessment criteria underpin this process. The task for students, to design, plan, create and create (the task has been defined in the story) a timing device.

  • Criterion A Investigate (this has been set in scenario)
  • Criterion B Design
  • Criterion C Plan
  • Criterion D Create
  • Criterion E Evaluate
  • Criterion F Attitudes in technology (it might be more appropriate to assess this in a longer-term project)

Have available items such as

  • Materials: Empty soft drink bottles, tins, cardboard tubes (such as you may find in haberdashery stores), string, paper clips, masking tape, pieces of cardboard.
  • Creating Tools: nails and hammer
  • Evaluation Tool: a watch with second hand, or stopwatches.
  • candles

A suggested approach:
Discuss the design cycle and expectations.

Give students in groups, time to discuss strategies. An open ended approach is probably best, but you could identify the materials in your ‘box of goodies’ and suggest possible approaches

  • Sand timer – like an egg timer (2 plastic bottles, dry sand, a device to control rate of movement, possibly made out of cardboard.)
  • Water clocks – 1. A tin with small holes so that it will empty after exactly 1 minute. The rate is controlled by the size of the hole. 2. A device that slowly fills with water (could also be a tin, tucked inside a slightly bigger tin) and sinks when full. It fills in exactly 1 minute. The rate is controlled by the size of the hole, and the mass of the tin.
  • Marble ramps This kind of device requires a ramp (made from cardboard tubing, perhaps) so a marble placed at the top takes exactly 1 minute to roll down. The rate is controlled by the slope of the ramp.
  • String systems This kind of device consists of a string which carries a load over a certain distance. The rate is controlled by the angle of the string, and the friction between the string and the link (possibly a paper clip) holding the load.
  • Candles [but you may not approve of fire in your classroom – and many factors affect the rates candles burn.]

Expect students to Design (could be a sketch) and list materials before helping themselves to the ‘box of goodies’.

Have extra items such as masking tape, and cardboard, in case they need to modify their original plan.

Assessment
The IB does not recommend every task MYP students complete be assessed. However, here is a possible task-specific rubric for MYP 1:

Criterion B

Design

Not done

You design one timer only

You consider a few different designs.

No reasons given for chosen task.

You consider several different designs.

You then select one, and give reasons given for selection, and why the others were rejected.

Achievement level

0

1-2

3-4

5-6

Criterion C

Plan

Not done

Your plan does not list every step, and/ or

Some details of required materials are missing.

Your plan shows all the logical steps.

All the materials needed are listed.

The plan is not evaluated.

Your plan shows all the logical steps.

All the materials needed are listed.

A reason is given for the plan.

Achievement level

0

1-2

3-4

5-6

Criterion D

Create

Not done

You complete at least part of the plan, but the timer is not accurate.

You complete at least part of the plan.

Any changes to the plan are explained, with reasons given

The timer works

Your timer is made according to the steps in the plan. The timer matches the design.

Any changes to the plan are explained, with reasons given

The timer works very accurately

Achievement level

0

1-2

3-4

5-6

Criterion E

Evaluate

Not done

You judge the timer in a basic way in terms of how accurate it is, and

how well you followed your plan

You judge the timer terms of how accurate it is, and how well you followed your plan

You suggest improvements, and how these could be tested.

You judge the timer terms of how accurate it is, and how well you followed your plan at each stage of the design cycle.

You suggest improvements, and how these could be tested.

You evaluate the impact of the timer on life, society and/or the environment.

Activity 4: Use the clues in the story to work out where the friends may have travelled to. This question can be answered on many different levels, depending on student interest.

(1) Simple answer: From the southern to the northern hemisphere. Clues: seasons (autumn in the Park, spring in the alien landscape) as indicated by the state of the trees.

(2) More sophisticated answer
Latitude and longitude numbers appear of the northern hemisphere destination appears on the analemma sundial.

The location of the park (in the story): somewhere in South East Australia-Victoria.

(3) Outstanding, sophisticated answer (perhaps for the Albert Einsteins in you class!)

Really smart people might realise that if you cut the earth (sphere) in half you get a circle.Note: a circle is 360o and a day is 24 hours – therefore each hour is 360÷24 = 15o

Bawen never changed his watch and it is 9.00 pm, yet Zoë thought it was 10.30 pm – a difference of 1.5 hours. This suggests that the children did not go to exactly the opposite side of the earth (12 hours or half of 24) away, but were 10.5 hours towards the west.

(4) The beyond-sophisticated answer (are there really 11-12 year olds that smart?)

Working eastwards from the location on the analemma (add 15o x 10.5 = 157.5o).

However, the Northern hemisphere latitude is West of Greenwich, so 9 o.44’ needs to be subtracted to give the Australian location to the East of Greenwich – so about 147o16’.

This longitude certainly crosses through Victoria in Eastern Australia – check using Google Earth!


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