Year 5 Navigating using the sun, stars, and mathematical principles

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Teacher Note: These activities have been inspired by the University of Melbourne Indigenous Knowledge Institute resources available here.

Overview

Through these cross-curricular CLIL lessons, students will learn about techniques used by Aboriginal and Torres Strait islander people to navigate using the stars and the sun in a variety of ways, using mathematical principles. 

This learning occurs in the context of a bilingual school across three integrated Maths and Science lessons of 50 minutes each.

4Cs Curriculum Connections for CLIL

CONTENT

This resource addresses the following Content Descriptions from the Victorian Curriculum: Mathematics 

  • Estimate, construct and measure angles in degrees, using appropriate tools, including a protractor, and relate these measures to angle names (VC2M5M04) 
  • Construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement (VC2M5SP02)

Science (Earth and space sciences)

  • Earth is part of a system of planets orbiting around a star (the Sun) (VCSSU078) 

COGNITION

  • Checking/testing predictions, remembering, identifying, locating, explaining, discussing, summarising, drawing, calculating, problem solving, analysing, planning, comparing, note-taking 

CULTURE

  • Aboriginal and Torres Strait Islander people also developed techniques to navigate using the stars in a variety of ways, using mathematical principles. 
  • Using Indigenous Knowledge about cardinal points to find our way across the landscape. 
  • Inquiry/Learning culture as a mathematician. 

COMMUNICATION

Language Of Learning　

  • 名詞 Nouns 角度 , ＿度 , 体の部位（手、うで、ゆび） はば、大きさ、長さ、校庭にあるものの名前 
  • 動詞 Verbs のばします、たちます、はかります 
  • 形容詞 Adjectives 同じ 
  • 助詞 Preposition ～のあいだ 
  • 方角Cardinal points 東西南北(East, West, South and North)
  • 座標 grid system 
  • Counting いっぽん、にほん、さんぼん、よんほん、ごほん、おやゆび、ひとさしゆび、なかゆび、くすりゆび、 こゆび

Language For Learning

  • Classroom instruction language　＿＿ています、＿＿ているとおもいます.
  • Record observations 〜たら、手が＿＿＿より＿＿＿く見えました。
  • Report findings わたしは、____度の角度のものをさがしました。＿＿さんは、わたしとちがうものをみつけました。それは、＿と＿です。 
  • Gallery Walk explanations わたしは、＿＿さんの手順書がとてもいいとおもいました。なぜかというと、＿＿＿＿だからです。
  • Language for group discussions (facilitator, minute-taker, norm reporter, dictionary master) 

Language Through Learning

  • (This is the unplanned language students discover through their learning)

Teaching and Learning Activities

Lesson 1

Powerpoint: Lesson 1

Learning intention: 

Estimate, measure and compare angles using techniques used by Aboriginal and Torres Strait Islander people. 

Success Criteria: 

  • I can measure and identify the angle using their technique.
  • I can compare the angles using their technique. 
  • I can estimate the angles of the two objects and measure using degrees.  

Hook Activity: Pair talk followed by whole class share time

  • Activating students’ prior knowledge about the relationship between Aboriginal and Torres Strait islanders and their knowledge of the stars. Show the picture from the Moana using her hand to measure altitude of Orion’s belt stars. (Refer to slides)
    Teacher asks: これは、ポリネシア諸島にすむ人たちです。いつもふねにのって海にでていました。なにをしていますか。 
    Students discuss their thoughts with their elbow buddy using the phrase ＿＿ています。（＿＿ているとおもいます。） 
    Students then share their ideas with the whole class. 
    Teacher collects any words and content knowledge students might already have. Key words can be added to the word wall.  

Mini lesson

  • Display the slide which shows a picture of aboriginal people with night stars showing how they also use their hands and the stars to navigate. Demonstrate how students can use their hands and fingers to measure angular distances in degrees. Explain that when you hold your hand out at arm’s length, the width of your little finger is about 1°. For reference, the diameter of the Sun and Moon are about half a degree. Three fingers is about 5°, a fist is 10°, and so on using the following image from the slides 

Image source: https://indigenousknowledge.unimelb.edu.au/curriculum/resources/stellar-navigation-and-mathematics

Application activity 1

  • Take students outside so they can use this technique to measure the angular distance between two objects.  Students can work in pairs to take notes, draw diagrams and write sentences in their notebooks to explain what they found.  They need to take at least 3 different measurements.
    All students need to find two items which have an angular distance of 15 degrees between them.

“Check for Understanding” questions

  • Ask students: 
    あいだの角度が１５度のものは何と何ですか。 
    (What two objects have an angular distance of 15 degrees between them? What and what?)
    _____と＿＿の間の角度は何度ですか。
    What was the angular distance between ___ and ____?

Application activity 2 

  • Ask students to stand in a line.
    Students need to use their hand to find two objects that have 10 degrees between them.
    Ask students to take 15 steps forward.
    Ask students to now compare how those objects look compared to their hand. Smaller or bigger?
    Ask students to go back to their original spot and then go backwards for 15 steps.
    Again ask students to compare how the objects look compared to their hand. Smaller or bigger? 
    Students can write and draw their observations in their notebook using: 
    まえに１５歩あるいたら、手が＿＿＿より＿＿＿く見えました。
    うしろに１５歩あるいたら、手が＿＿＿より＿＿＿く見えました。

Share time 

  • Ask some students to share their findings with the whole class. 
    Students do a gallery walk to see other students’ findings and to look for someone that found different objects with the same degree as they found. They can share what they found using:
    わたしは、____度の角度のものをさがしました。
    ＿＿さんは、わたしとちがうものをみつけました。
    それは、＿と＿です。 

Dictionary time:

  • Students write new words and phrases from this lesson in their dictionary book. 

Lesson 2

Powerpoint: Lesson 2

Learning Intention: 

Understand how to find the Cardinal Directions using the sun and a stick. 

Success Criteria: 

  • I can listen to the instructions and understand what to do.
  • I can write key words to do this experiment step by step. 
  • I can identify the cardinal directions on the ground and explain how to find them. 

Hook activity

  • Display slides which show images of an Aboriginal stone arrangements.
    Explain that Wurdi Youang is an egg-shaped Aboriginal stone arrangement in Victoria, Australia with possible solar indication.
    Ask students what comes to their mind when they hear the phrase “possible solar indication.”
    Brainstorm ideas as a whole class. 

    Facts:
    There are only 30 stone arrangements recorded in Victoria. (1999) 
    No known ethnographic records or oral histories exist about these arrangements. 
    Wurdi (plenty of people) Youang(mountain) consists of about 100 basalt stones, about 50m in diameter along the major axis which is aligned east-west. There are small rocks about 0.2m in diameter through to stones standing up to 0.75m high.
    This site is believed to have been inhabited from about 25000 BCE to about 1835. After this the area was occupied by European settlers.  

Application activity

  • Explain that we will do a listening task and that students will hear the instructions for how they will find the cardinal points using the sun and a stick.
    Ask students to talk with their elbow buddy about some some key words (nouns and verbs) they might hear.
    Invite students to share their predictions with the class.
    Write down some key words identified and clarify meaning as needed.

    Steps for the listening task:
    Students will need to write down keywords and key sentences while listening. They can then compare notes with their buddy and help each other if they have missed anything. They will then listen one more time before seeing the text on the board. Students need to check their notes and fill in anything missing.

Listening text:

  • 太陽で方角をしらべよう
    まず、ながいぼうをじめんにたてます。
    つぎに、かげのはしにしるしをつけます。
    そして、３０分から１時間たったら、あたらしいかげのはしにしるしをつけます。
    そのあと、そのふたつのてんをつなげるせんをひきます。このせんは東と西をさします。
    さいごに、東と西をさすせんのまん中に、９０度になるようにせんをひきます。このせんは
    北と南をさします。
    これで、東西南北のいちがわかります。
  • After completing the listening task, go outside and do the experiment in small groups. 
    While they are waiting for the half hour, students need to draw pictures next to their written text to illustrate the steps in the experiment. They also need to record their findings using text and pictures.

“Check for Understanding” question 

  • Ask students:
    文にあった絵がかいてありますか。
    Do your pictures correctly match each step?  

Share time 

  • Gallery Walk
    Find the writing you liked the best and explain why using:
    わたしは、＿＿さんの手順書がとてもいいとおもいました。なぜかというと、＿＿＿＿だからです。 Teacher asks student to elaborate their reason to differentiate their level of speaking ability. 

Dictionary time

  • Students write new words and sentences in their dictionary book. 

Lesson 3

Learning Intention:

Locate landmarks on a map using cardinal directions. 

Success Criteria: 

  • I can locate north, east, south and west on the map. 
  • I can describe the location of a landmark using a grid. 
  • I can discuss how landmarks are oriented relative to other landmarks. 

Hook activity 

  • Explain that in Warlpiri traditions (Central Desert, NT) people and objects are referred to in terms of cardinal points. eg. ジョーさんは、わたしの西にすわっています。 (Joe is sitting west of me.)
    Ask students to point to the cardinal directions in the classroom and label them on the walls. Demonstrate how to describe the location of items in the classroom using cardinal directions. Students can practice this by locating classmates and classroom items.  

Application activity

  • Provide students with a map of the school printed on a grid.
    Revise the cardinal directions learnt in the previous lesson.
    Students draw the cardinal points on their map.
    Model describing the location using: 
    例文：アートルームは、ホールのきたにあります。
    Explain the rule when using grid points to identify a location on a map.
    Ask students to write the numbers on rows and letters on the columns on their map (よこじくとたてじく、x and y).  
    Model describing the location using grid points: 
    例文：８とBがまじわるてんにあります。 
    Demonstrate how to combine these two sentences using:
    例文：アートルームは、ホールの北にあって、８と４がまじわるてんにあります。 
    Students can practice these sentences in pairs, locating other places on their map. 

Check for Understanding question

  • Ask students: 
    ＿＿は、どこににありますか。せつめいしてください。
    Students need to answer using cardinal directions and grid points 

Share time

  • Students share what they created to the class and give feedback to each other. 

Dictionary time

  • Students write new words and sentences in their dictionary book. 

Extension activity

  • Using a map of Australia, students can use grid points to identify where famous landmarks are located.  

Resources

Powerpoint: Lesson 1

Powerpoint: Lesson 2

University of Melbourne Indigenous Knowledge Institute resources

星の動き
https://www.hello-school.net/harorika022.html 

Wurdi Youang: an Australian Aboriginal stone arrangement with possible solar indications 

This work is licensed under a 
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This resource embodies traditional knowledge and traditional cultural expressions shared by Australian Indigenous communities. The information is shared for the purposes of knowledge preservation and general education, and ask that you engage with opportunities to learn from this knowledge and culture respectfully. In drawing on the material, users should consider the relevance and suitability to their particular circumstances and purposes. For more information, and to learn more about Australian Indigenous Knowledge, please visit Aboriginal and Torres Strait Islander School Curricula