Mathematics in Indigenous Contexts

Balladoran 2004

Artist: Lionel Phillips Artworks: Culcha Disc, Australian Indigenous Images Volume 1 Available from Keeaira Press www.kpress.com.au

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 Outcomes for Balladoran activities Working Mathematically Stage 2 WMS2.2 Asks questions that could be explored using mathematics in relation to Stage 2 content. WMS2.2 Selects and uses appropriate mental or written strategies, or technology, to solve problems. WMS2.3 Uses appropriate terminology to describe, and symbols to represent, mathematical ideas. WMS2.4 Checks the accuracy of a statement and explains the reasoning used. WMS2.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 2 content. Stage 3 WMS3.1 Asks questions that could be explored using mathematics in relation to Stage 3 content. WMS3.2 Selects and applies appropriate problem-solving strategies, including technological applications, in undertaking investigations. WMS3.3 Describes and represents a mathematical situation in a variety of ways using mathematical terminology and some conventions. WMS3.4 Gives a valid reason for supporting one possible solution over another. WMS3.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 3 content. Stage 4 WMS4.1 Asks questions that could be explored using mathematics in relation to Stage 4 content. WMS4.2 Analyses a mathematical or real-life situation. Solving problems using technology where appropriate WMS4.3 Uses mathematical terminology and notation, algebraic symbols, diagrams, text and tables to communicate mathematical ideas. WMS4.4 Identifies relationships and the strengths and weaknesses of different strategies and solutions, giving reasons. WMS4.5 Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 4 content. Number Stage 2 NS2.2 Uses mental and written strategies for addition and subtraction involving two-, three, four-digit numbers. NS2.4 Models, compares and represents commonly used fractions and decimals, adds, subtracts decimals to two decimal places, and interprets everyday percentages Stage 3 NS3.2 Selects and applies appropriate strategies for addition and subtraction with counting numbers of any size.

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 NS3.4 Compares, orders and calculates with decimals, simple fractions and simple percentages. Stage 4 NS4.1 Recognises the properties of special groups of whole numbers and applies a range of strategies to aid computation. NS4.3 Operates with fractions, decimals, percentages, ratios and rates Data Stage 2 DS2.1 Gathers, organizes data, displays data using tables and graphs, and interprets the results. Stage 3 DS3.1 Displays and interprets data in graphs with scales of many-to-one correspondence. Stage 4 DS4.1 Constructs, reads and interprets graphs, tables, charts and statistical information. Measurement Stage 2 MS2.1 Estimates, measures, compares and records lengths , distances and perimeters in metres, centimeters and millimetres MS2.3 Estimates, measures and compares and records the areas of surfaces in square centimeters and square metres. Stage 3 MS3.1 Selects and uses the appropriate unit and device to measure lengths, distances and perimeters. MS3.3 Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms. Space and Geometry Stage 2 SGS2.1 Makes, compares, describes and names three-dimensional objects including pyramids, and represents them in drawings. Stage 3 SGS3.1 Identifies three-dimensional objects, including particular prisms and pyramids, on the basis of their properties, and visualizes, sketches and constructs them in given drawings of different views. Stage 4 SGS4.1 Describes and sketches three-dimensional solids including polyhedra, and classifies them in terms of their properties

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004

Mathematics in Indigenous Contexts Gilgandra 2004

Timetable for Balladoran excursion 29 October 2004 Time Activity Responsibility 9.30 Leave school Team

9.45 10.00 Introductory talk about Balladoran Ralph Centre Groups and rotation activities explained 10..05 – 10.30 First activity station

10.30 – 10.55 Second activity station

11.00 – 11.15 Morning tea

11.20 – 11.45 Third activity station

11.50 – 12.15 Fourth activity station

12.20 – 12.45 Fifth activity station

12.45 - 1.15 Lunch

1.20 – 1.45 Sixth activity station

1.50 –2.15 Seventh activity station

2.20 – 2.45 Final activity station

3.00 Return to school

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004

Cultural notes for Balladoran Activities Station 1 Car park area – shelters- height, length, shadow, 3D drawings Years ago aboriginal people did not have car parks and their only means of transport was by foot. Families moved from camp to camp by walking, they would get up early if they were going to get to the other place before the sun went down. Later on Aboriginal people rode horses but that was only related to their work placements. Today most Aboriginal people own cars. Station 2 Scale drawing from shed door – snake or kangaroo Totems are dreaming. In the dreaming human beings were a totem. Elders say yams, ants, owls, particular fish, waterlilies, emus, kangaroos and so on bring the creative spirit. Ancestors then descend into the earth as particular places emerge. Specific locations are linked with a particular species of totem. All Aboriginal peoples belonging to the earth here are dealing with Aboriginal groups and particular plants and creatures created in different regions of the Dreamtime. It is especially forbidden by law to eat the totem. The totem is sacred to the Aboriginal peoples, it is the Dreaming. It is forbidden to kill or eat the totem species that is linked with your clan. Station 3 Fractions The traditional roles of men and women were clearly defined in legends of Aboriginal ancestors in the Dreamtime. Women were required to gather vegetable food by digging for yams and tubers. They gathered seeds and fruits and made unleavened bread, ‘nardo’ from seeds. Men were required to hunt and bring home meat, usually kangaroo, wallaby, possum, snakes and giant goanna lizards for the family. They also fished with nets and spears. Everything was shared by the whole clans with strict division of the catch, carefully observed. Certain parts of the animals or vegetables were allocated to certain clan relatives. The whole group of clans would move camp if there was concern for the animals’ or bushes being in short supply. They would never take the remaining food from the area. Plants were left to grow and animals to breed. The whole area was allowed to regenerate. To encourage regeneration they would often deliberately burn out a section of the district. This got rid of unwanted weeds and stimulated plants in to extra limb growth. Fuller bushes and trees resulted, therefore more food.

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 Station 4 Distance from marked tree – Direction to Gil, Dubbo Mendooran Aboriginal people have always needed to make pilgrimages to their sacred places to conduct ceremonies. These spiritual journeys have been called ‘walkabouts’ and wanderings of aboriginal peoples. Their pilgrimages often entailed arduous walks for hundreds of miles and they always followed well delineated paths across the land. These paths are the original dreaming tracks or song lines mapped by their Ancestor spirits. Pilgrimage or walkabout mirrors the eternal movements of the sun, moon and stars. The older people use to teach us that whenever law is given we have to look after these things. There is also a deep respect between neighbouring Aboriginal groups whose countries scare common boundaries. When an Aboriginal person approaches a sacred site, she or he does approach by the most direct route but by the same route taken by the spirit ancestors associated with it. Such dreaming tracks may pass through many countries or territories of local clans and tribes. All Aboriginal people who share a dreaming track of a spirit ancestor have a secret bond of friendship and mutual clan to hospitality and protection. This enables members of clans or culet groups to travel safely along paths which lead to tribal areas. Station 5 Scale drawing – sand model boomerang Aboriginal art Some say Aboriginal people don’t have a written history only oral.. In contrast to European art our art has a story attached to it. Station 6 Measurement -Volume Rainbow Serpent (Baiame) The walk way which represents the rainbow Serpent (Baiame) to the ceremonial dance area is known to specific tribal groups as the Great-All-Father. Baiame shaped the world creating the natural features you see around you, he shaped the mountains, the lakes and rivers. Baiame created all the important features in aboriginal Culture. This walkway represents Baiame path as creation happened. Station 7 Ceremonial Area In some parts of Australia the meeting place fro sacred ceremonies is known as the bora ground or bora ring, especially in NSW, Queensland and the Gippsland area of Victoria. The word bora is a Kamilaroi term which describes the fur string belt – the belt of manhood, which was worn traditionally by men initiated into the secret cult Baiame. The bora ground was made up of two large circles twice a big as the other were dug into the earth and connected by a straight or wavy pathway. The circles always ran in an east west direction to symbolise the rising and setting of the sun. ceremonial performances are restricted to people of certain standing within the group and are only open to senior men and women. Aboriginal people say singing is considered to be effective in bringing about change in a ceremony and provides a key for how one should live one’s life with in the scared law.

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 Although this ceremonial area that you see here is different to the bora ground it is only used for corroborees where everyone can join in and the other one is to perform a smoking ceremony which means welcoming to everyone onto Wiradjuri land and a safe journey home. Station 8 Colours of rocks and plants, graph, data table Students collect samples of plants and rock and experiment with colours contained in them.

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 ACTIVITY 1

EQUIPMENT: Measuring tape

STEPS: 1. In the space provided below draw a three-dimensional drawing of the shelter

2. Measure the length, breadth and height of the shelter (using the pencil method). Write the measurements on your drawing

EXTENSION ACTIVITY

Heights can also be found using the length of shadows

Shelter Stick

Shadow Shadow

Measure the following:

Shadow of shelter =

Shadow of stick =

Height of stick =

Now do this calculation: height of shelter = Height of stick x shadow of shelter Shadow of stick

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 ESTIMATION SHEET

Fill out the table below, estimating the distance and direction from one activity to the next, then answer the questions.

Estimation in metres Direction [N, NE, S, SE….]

From - activity 1 to activity 2

activity 2 to activity 3

activity 3 to activity 4

Activity 4 to activity 5

Activity 5 to activity 6

Activity 6 to activity 7

Activity 7 to activity 8

Activity 8 to activity 1

total

* Explain how you estimated

* How did you decide on the direction?

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 ACTIVITY 2

EQUIPMENT: Ruler

STEPS: 1. Measure the length of one box on your grip and write it down 2. Measure the length of one box on the large grip on the shed door 3. Write down the scale of the real length to the drawing 4. Complete the scale drawing on the grid below

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 ACTIVITY 3

Vegetable Patch

Audrey and Ralph want to plant a vegetable patch that involves using indigenous plants. Your job is to design their vegetable patch using 6-8 plants (including actually measurements).

Plants

Nardoo - Type of fern, seed pods ground into flour and used to make dough Pigweed - Seeds ground into flour and baked into cake – leaves and shoots eaten raw or cooked Ruby Saltbush Berries eaten raw and are juicy and sweet-tasting, young - leaves can be boiled and eaten Bloodwood When cracked open reveals a grub which can be eaten apple - raw Tree orchid - The pod/kernel can be eaten raw, tastes similar to peanuts – juice from stems used as glue or medicine Spinifex - Collected and used as a form of bush glue or putty Lolly bush - Main root dug up, roasted, then eaten Scurvy weed Used as green vegetable to ward off scurvy

As a group: 1. Measure vegetable patch to find actually measurements 2. Use whiteboard to record your design 3. Each plant is to be given a different sized fraction e.g. nardoo = 2/6 of vegetable patch 4. Draw the design your group decided on

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004

This page to be used for working out/completed design of vegetable patch

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 ACTIVITY 4 QUESTIONS Use the diagram to answer the following questions

1. Follow the footprints and give directions without using North, South, East or West as to how you would travel from the campsite to the waterhole and back to the campsite.

2. In what direction are the berry bushes from the campsite and how far away are they?

3. How far are the cave paintings from the marked tree?

4. Name 3 types of food on the map that could have been eaten by this tribe.

5. Which direction is the emu form Little Rock?

6. What kind of animal tracks are near the camp and in what direction are they?

7. Can you think of ways early Aboriginal people used to tell direction and distance.

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 ACTIVITY 5

EQUIPMENT: Measuring tape Artefact Markers Hoe

STEPS: 1. Place the object on the ground and mark a point on the ground to measure from 2. Measure from this point to the ends of the object and other points

See diagram

3. Write the measurements in the table

Point Measurement Measurement x 100

4. Multiply your measurements by 100 and fill in the table 5. Measure from your original point through to the marked point, e.g. A, to these new distances. Mark these new points on the ground.

See diagram

6. Join all the new points that you marked on the ground with the hoe to form the outline of the enlarged object

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 ACTIVITY 6

ESTIMATING DISTANCE AND COST

STEP 1 Walk the length of the snake and count the number of paces

Number of paces

STEP 2 Now you need to measure the length of your stride

Stride length

STEP 3 Now you can determine the length of the snake by performing a calculation:

Distance = stride length x number of steps taken

=

=

STEP 4 CALCULATION THE COST OF THE SNAKE If it costs $4 a metre in labour and materials to lay each metre of the snake how much would it cost to copy the snake?

What is the totem for the Wiradjuri? ______

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004

ACTIVITY 7 ELEVATIONS of structures in the ceremonial area

What is and elevation?

______

______

Top elevation Side elevation

Front elevation Prisms

Volume of prism + area of face x ‘height’

The ceremony area structures look like a prism. If the ends were closed they would be ……………….. prisms.

Calculate the area of one of the ceremony area structures.

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004 ACTIVITY 8

DATA TABLE Name: ______

LEAVES FLOWERS ROCKS SOIL GRASS

Gilgandra Mathematics in Indigenous Contexts at Balladoran 2004