Location, Location

Introduction

Want to show off your town? Show what's great where you live by designing a tour that highlights the best and most interesting landmarks for visiting tourists.

Task

In order to create the most time efficient, interesting and safest tour you can, you are going to need to develop your knowledge of the mathematical concept of location. 

In creating your tour you will need to consider;

  • The landmarks you want to show off to tourists - Will you be able to recognise and find them using a map?
  •  The direction you need to travel in to get to each land mark and the time it takes to travel between each by bus.
  • The shortest route between each landmark to cut down on travel time.
  • A contigency plan for unexpected events such as roadworks, flooding or bus break-down. 
  • Client safety - ensure you are able to locate the hospital from every part of your journey and be able to specify your location at all times using a grid-reference system.

 

Process

LANDMARKS

The first step in designing your tour is to learn how to identify landmarks on a map. Visit google maps https://www.google.com.au/maps/@-34.925709,138.6008116,14z , type in the name of your town, find a famous landmark (it could be a hill, river or building) sketch it and the surrounding area as you see it from the view of the map in your workbook then swap with a friend to try and identify some of the landmarks they have drawn while they try and label yours.

Go to different views on the google map website. What do you notice about the map perspective and the satellite image? Discuss your observations with your partner.

It is commonly explained that maps are a 2D representation of a 3D world. Do your observations lead you to this conclusion? Using your map, can you give an example of this concept? 

Different cultures represent landmarks differently to the maps we have just viewed. Australian Indigenous people represent country through their artwork, view the documentary below to gain an alternative perspective on landmark representation. Think about why the artwork has been created. http://aso.gov.au/titles/documentaries/painting-country/clip2/

A really good example of a painting of country can be found at the following website. It is interesting to note that the artist Maureen Hudson was able to paint her country from an aerial perspective even though she had never been over it in an aeroplane. This is what is known as an abstract frame of reference, Maureen Hudson knows her country so well she is able to see her country from the perspective of being "outside of the map" 

Form a small group to discuss some of the similarities and differences of the aerial views from an Indigenous perspective, topographic view and town map view. http://www.aboriginalartstore.com.au/artists/maureen-hudson-nampijinpa/post-1/ 

Compile your ideas with the whole class and create a Venn diagram to highlight the relationship between the different aerial views. 

As a class discuss a possible ending for this sentence; The main purpose of a map is to....

 homework: observe and record where the sun sets and rises, try to identify a well known landmark near by to explain the location of where you saw it rise and set.

COMPASS DIRECTIONS

In groups discuss your homework observations.

In Australia the sun always rises in the East and sets in the West. How could we use this information to find our way and describe our location? (navigate)

Go to the school oval when you get there point one arm at the sun that arm is like 12 o'clock on the clock, point your other arm to the closest hour, in between these two points is North.

Make four signs with North, East, South and West written on them, see if you can place them in the correct locations on the oval. Afterwards conduct the experiment from the website below to gain an understanding of the connection between the sun, stars and compass points http://www.wikihow.com/Determine-Directions--to-North,-South,-East,-and-West 

On the oval create a minefield of objects then guide a partner through using directional language to get them safetly across to the other side using only your voice to guide them. As a group discuss some of the advantages of using compass points to direct rather than left and right.

Follow the links to the math games that will help develop your sense of direction http://www.mathsisfun.com/games/mazes.html. Go to the medium compass maze on this site as it is the one most relevant to the lesson outcomes. This game is more challenging than the one on the other site, use the first as a warm up or head straight to this one if you're ready for it. http://www.mathsisfun.com/games/mazes.html.

Begin thinking about directions in terms of your proposed tour. What direction will you be traveling in to visit all the sites? Consider the safety of the driver and passengers how can you limit or eliminate the amount of time spent driving into the sun?  Go to the google maps website https://www.google.com.au/maps/@-34.925709,138.6008116,14z and begin planning your tour with the above considerations in mind, work in small groups to find more than one possible route between the landmarks you wish to visit. Discuss the advantages and disadvantages of each. Use your mathematical knowlege of landmarks and directions to convince your group to choose the route you consider to be the safest.

GRID REFERENCES:

The next step in designing your tour is to understand the concept of Grid References. By the end of this lesson you will understand that Grid References are used to describe location.

Using a copy of a town map find a landmark you wish to visit, without using your finger to point,describe the location of your landmark to a partner, time how long it takes them to find it. As a class, discuss more effective ways of finding and locating points on a map. Look at the sides of the town map, how could the letters and numbers help in describing location? Where have you seen a line of numbers like this before? How does a knowledge of the number line assist in reading a grid reference? When reading a grid reference the X axis along the bottom is read before the Y axis up the side because X comes before Y in the alphabet or "crawl before you walk" How does this impact the way you read and understand a grid reference? What happens if you read or describe it the other way? Experiment reading grid references on different maps such as a topographic map. What differences do you notice?

The following links will help to develop your understanding of a grid reference system and introduces you to what is known as the cartesian co-ordinate system,a knowledge of these systems is important for other mathematics areas such as algebra and graphing. The principles of grid references are the same. What are the differences?

http://www.shodor.org/interactivate/activities/GeneralCoordinates/ 

http://www.mathplayground.com/locate_aliens.html.  

http://www.shodor.org/interactivate/activities/MazeGame/ 

Keeping your tour in mind work out the grid references for all the sites you plan to visit. As a class discuss the advantages of using grid reference systems when describing location over a phone or radio especially when out of town and using a topographic map where man-made landmarks are few and far between.

  DISTANCE

The final stage of planning your tour is to learn how to measure distances on a map. This is an important factor in helping you decide the best possible route.

Take a look at your town map, see if you can find the scale. A scale shows how distance is represented on a map most town maps scales are represented as a ratio of 1:25 000 this means that 1 cm is equal to 25 000 cm in real life. Follow the link to find out how to convert cm into metres. http://eps.mq.edu.au/courses/GEOS264/maps/mapch2/cdista.htm In your groups work out the scale on your town map in metres. Discuss how you could measure distance on a map using the scale and a ruler, piece of string or even your fingers. Work in small groups to measure the different routes for your proposed tour record the distances in ascending order. Use google maps directions to compare your working out. https://www.google.com.au/maps/@-23.6846874,133.8599566,14z Google directions is a useful tool in helping you determine how far and how long it takes to travel between landmarks. As a class discuss the importance of knowing how to calculate distance without the assistance of google maps.

The final step in this learning process is to put all the parts together to make the ultimate town tour. Don't forget whenever you are navigating you need to remember the 4D's Direction, Distance, Duration and Description.

Goodluck and have fun!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Evaluation

Once all groups have finished designing their tour use the following guide to provide  feedback for each design.

Criteria Above Satisfactory Satisfactory Below Satisfactory
Route Groups design shows many possible routes highlighting the safest and most time efficient group design shows a few possible routes and highlights the safest, most time efficient one group design shows only one possible route

Grid References

All site locations are described using correct Grid References All sites are described using Grid References that are mostly correct group design does not describe sites using grid references or grid refences are mostly incorrect
Landmarks Landmarks are identified correctly using different types of maps Landmarks are identified correctly on a town map landmarks are not identified on any map.
Directional Language Group uses correct navigational terminology to describe route at all times Group uses some correct navigational terminology (e.g. North, South) to describe route some of the time Group fails to use any navigational terminology to describe route.
Distance

All distances have been correctly calculated

Most distances have been correctly calculated  distances have been calculated incorrectly
Conclusion

WELL DONE! through completing this webquest you have learnt how to; identify landmarks on a map, use and understand directional language, use and understand grid reference systems, work out distances using the scale on a map and you now have a greater understanding of the concept of location. This knowledge is valuable and will help you in many areas of mathematics as well as in life.

Credits

Australian Curriculum, Assessment and Reporting Authority. (2012) Australian Curriculum Mathematics - year 3-6 curriculum version 4.0. Retrieved April, 5, 2014 from <http://www.australiancurriculum.edu.au/mathematics/Curriculum/F-10?layout=2#page=5>.

Battista, M.T. (2007). The Development of geometric and spatial thinking. In F.K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 843-908). Reston, VA: NCTM.

Central Art Aboriginal Art Store. (2014). Central Aboriginal Artstore. Retrieved March, 28, 2014 from

http://www.aboriginalartstore.com.au/artists/maureen-hudson-nampijinpa/post-1/

Clements, D.H. (1998). Geometric and Spatial Thinking in Young Children. National Science Foundation Arlington VA. Retrieved March, 28, 2014 from

<http://cognitrn.psych.indiana.edu/rgoldsto/courses/concepts/bowerman.pdf>.

 Google. (2014). Googlemaps. Retrieved April, 20, 2014 from

https://www.google.com.au/maps/@-34.925709,138.6008116,14z

Interactive. (2014). General Coordinates game, Shodor. Retrieved March, 20 2014 from

http://www.shodor.org/interactivate/activities/GeneralCoordinates/

Interactive. (2014) Mazegame, Shodor. Retrieved March, 20, 2014 from

http://www.shodor.org/interactivate/activities/MazeGame/

Lian, A. (2014) Lecture 3 (ppt). Retrieved March, 20, 2014 from

https://online.cdu.edu.au/webapps/portal/frameset.jsp?tab_tab_group_id=_4_1&url=%2Fwebapps%2Fblackboard%2Fexecute%2Flauncher%3Ftype%3DCourse%26id%3D_29496_1%26url%3D.

Marsh, C. (2010). ‘How Students Develop and Learn’, in Becoming a Teacher Knowledge Skills and Issues. (5th edn). Frenchs Forest, NSW: Pearson. pp 37-56.

Maths is fun. (2010). directions nsew, Maths is fun. Retrieved March, 20, 2014 from

<http://www.mathsisfun.com/games/direction-nsew-.html>

Mathplayground (2014). Locate the alien. Retrieved March, 20, 2014 from

<http://www.mathplayground.com/locate_aliens.html>

Australian Screen. (2014). Painting Country. Retrieved March, 20, 2014, from

http://aso.gov.au/titles/documentaries/painting-country/clip2/

Verdie, BN, Golinkoff, RM, Pasek-Hirsh K, Newcombe NS. (2014). ‘Finding the missing piece: Blocks, puzzles, and shapes fuel school readiness’ Trends in Neuroscience and Education, vol. 3, no. 1. Retrieved March, 28, 2014, from

<http://www.sciencedirect.com/science/journal/aip/22119493#FCANote>

 

Wikki How. (2014). How to determine directions north, east, south ,west. Retrieved March, 20, 2014, from

http://www.wikihow.com/Determine-Directions--to-North,-South,-East,-and-West

 

Teacher Page

The following webquest has been created to help year 5 students understand the concept of location.In developing spatial sense, children will gain a deeper understanding of their world (ACARA 2012).

YEAR 5 CURRICULUM OUTCOMES:(ACMMG113) Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACARA 2012).

How the activities will achieve the desired outcome

The authentic nature of this webquest requires students to apply their problem solving abilities to fulfill the task requirements.

  • Students will use mathematical understanding by making connections between numbers represented on a co-ordinate system. Students will also develop mathematical understanding through using mathematical powers to compare and order decimals when considering the shortest distance between routes. 
  • Students will develop mathematical fluency by estimating distances between landmarks to check the reasonableness of answers and by students choosing correct units of measurement when using the scale on a map to calculate that distance.
  • Students develop problem solving skills by using measurement, time and spatial awareness to find the quickest route to different land marks.
  • Students utilise mathematical reasoning to pose questions about the data they gather to investigate the best route for their tour.  

Clements 1998, states that in order for children to become competent map users they need to develop their ability to treat spatial relations separately from their immediate environment. Children make meaning from maps by first forming relationships among objects in space (landmarks and routes), expanding the size of that space and finally linking primary (a direct relation to space on the map- putting yourself inside the map) and secondary (an abstract frame of reference- no longer inside) meanings of that information.

This webquest follows a hypothetical learning trajectory based on Van Hiele’s amended model of geometric thought (Battista 2007);
Level 0 pre recognition 
Level 1 visual
Level 2 descriptive/ analytical
Level 3 abstract/ relational
Level 4 Formal deduction
Level 5 Rigour/ mathematical 
Students will be facilitated through levels 1,2 and 3 with the assistance of Van Hiele’s proposed sequential phases of learning, they are; inquiry, directed orientation, explication, free orientation and integration (Van Hiele-Geldof, 1984). Vygotsky’s theory of Zone of Proximal Distance (ZPD) will also be utilized (Marsh 2010).  By helping students progress through these levels it is hoped that they will gain a deep understanding of the concept of location.

Firstly, students will be introduced to the concept of location through activities that build understanding about landmarks. The aim of the lesson is to spark students curiosity about landmark representation on a map. The inclusion of the documentry and Aboriginal art links expose students to different representations of landmarks, communicating to them that there are different ways of knowing and although perspectives may be different, all are as valuable and as useful as each other for the purpose of determing and describing location. This approach will increase Indigenous inclusiveness in the classroom. Creating a Venn diagram serves two purposes; the first is to reorganise information (reorganising information has been proven to be helpful for ESL and dyslexic students Lian, 2014))and to demonstrate that despite their differences all maps are vauled for the purpose of spatial orientation and representation.

Implications for learning: Students will be put into groups by the teacher to ensure knowledge and skills are spread evenly amongst the class, ensuring all students have access to peer knowledge different from their own thinking. 

Groups will need to assign roles to each group member to ensure each student has an active role in the group, ensuring all students are given the opportunity to utilise their mathematical powers.  

Activity Variation: Students who struggle to identify and sketch landmarks could be assisted to get started with an enabling prompt of a pre-prepared hand drawn mud map that students then label and/or add extra landmarks to. Student learning could be extended by being prompted to identify and represent landmarks from different perspectives such as a topographical view or to represent a landmark from an Indigenous perspective.

In the next lesson students participate in activities which help build conceptual understanding of direction. Verdie et.al (2014), explains that we can improve effectiveness of spatial instruction by exposing children to spatial language. The purpsose of setting homework in the first lesson is to encourage students to inquire about the world around them. Using the information gained from students own research, students will be directed through activities that help students understand the usefulness of that knowledge. The interactive activities and debrief are included to provide students with an opportunity to freely explore and help them reflect on the concept of direction enabling them to integrate new knowledge into their existing understanding.

Activity Variation: students with physical disabilities could be included in the physical activity by directing students through the obstacle using their voice. 

Students who are struggling to give or follow directions in the partner activity could be enabled by being provided with a shorter route to give directions for or to follow.

Students could be extended by giving/following directions for alternative routes for their location.

Implications for learning: It is important for the teacher to partner students to ensure partnerships are mixed ability and mixed gender this will ensure knowledge is spread amongst the class not just confined to a few students and also ensures female students have the same access to spatial activities as male students.

The co-ordinate activities help build students understanding of the representation of numbers as co-ordinates.The open-endness of the introductory activity helps students develop an appreciation of the usefulness of the co-ordinate system. The discussion at the end of the lesson is included to help students augment student understanding and faciltate the progression of their understanding from level 2 descriptive/ analytical to level 3 abstract/relational.

Activity Variation: students who are struggling to find a way to describe location on the map could be enabled by imaging themselves on the map and describing what they would see around them, what landmarks , streets etc. If students still struggle they could be enabled by physically placing themself somewhere in the room and describe their location by what they are near. When using co-ordinates students could be enabled by first using letter/number combinations then advancing to smaller digit combinations and finally 6 digit grid references.

This activity could be extended by pre preparing another map and proposing a scenario such as this map got wet on a hike through the bush, some of the grid references and landmarks are missing can you fill in the missing grid references and use the guiding notes to plot these landmarks.  

The final activity focuses on integration. At this stage students draw on knowlege gained from previous activities in order to complete the webquest.

 

Activity Variation: Students who are unable to get started even with the help of the group may be enabled to begin by focusing on one or fewer of the criteria to begin with  such as identifying a landmark on a map.

This task could be extended with prompts such as making a wet weather, dry weather tour, plotting accomodation grid references to show where to pick up and drop off tourists.