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Level Four > Geometry and Measurement

# Direction and Position

Purpose:

This unit of work is based on the Māori medium unit Te Ahunga me te Taunga, and investigates the main compass directions, degree measures of direction and the use of a grid system to define locations on a map.

Achievement Objectives:

Specific Learning Outcomes:

Students will learn:

• the vocabulary and language of describing direction
• the main compass directions
• how to define a direction using a degree measure
• the use of a grid system to define position.
Required Resource Materials:
protractor
a compass
a variety of maps
Activity:

Session 1

Discuss with students where the sun rises in the morning and where it sets in the afternoon. Some possible discussion questions include:

• Which windows does the sun come into our classroom in the morning?
• Which windows does the sun come in to the classroom in the afternoon?
• What names are given to the directions that the sun rises and sets? (Two of the main Māori words for these directions relate to the action of the sun: rāwhiti – the rising of the sun for east, and rātō the setting of the sun for west).
• How does the sun travel through the sky between east and west over the duration of the day?
• What is the difference between how the sun travels through the sky in winter and summer. Why is it like this?
• In addition to east and west, what are the other two main directions?
• How do we draw these directions on a page?
• Why is it important to know where these main direction points are?
• What are some landmarks in our area that are to the north (east, south, west) of the school?

Play a game with students, giving them directions to walk so many steps in certain directions (limited to east, west, north and south at this stage). What letters of the alphabet can be ‘walked’ using only the four main compass points?

Introduce the directions in between the four main directions. Possible questions include:

• Draw a diagram showing the four main directions. Now show the direction that is half way between east and north. What name would this direction be called? (In Māori, one of the words ‘rāwhiti mā raki’ translates as ‘east-north’, rather than north-east. One reason for this is that the east and west directions are known to us because of nature (the rising and setting of the sun), and from this we know the directions of north and south.)
• Draw all the other directions in between the four main directions and name them.
• What letters of the alphabet can we now ‘walk’ using all eight directions?

The book He Kōrero Pūrākau mō ngā Taunahanahatanga a ngā Tūpuna Place Names of the Ancestors A Māori Oral History Atlas published by the New Zealand Geographic Board in 1990 contains examples of how Māori use the direction in text (oral and written) to create ‘pictures’ of journeys and the lay of the land.

Session 2

This session starts with a listening exercise, where the students are given a partially completed map such as the one below, and have to listen in order to complete other aspects of the map.

 Map Māori text English translation Ka piki atu au i taku taumata i a Puketeitei, ka titiro iho ki te whenua e hora nei i mua i te aroaro. Ka titiro whakateraki, ko te awa o Huka e rere atu nei mai i te uru ki te au moana. Ki tua atu o te awa, e toro whakateraki ana ngā pae maunga o Taratara. Whakaterāwhiti mā raki taku titiro, ka tau atu ki a Reponui, ki waenga i a Taratara me te takutai moana. Ka huri whakaterāwhiti taku titiro, ka kitea te Motu o Aramoana. Ki tua mai ko Pohatunui e tū mai ana, e ākia ana e te tai. Whakatetonga haere taku titiro, ko te pae maunga o Hiwiroa e toro atu ana ki te uru mā tonga. Ko te ngahere tērā ki tua atu o Hiwiroa. Ka hoki anō taku titiro ki te rāwhiti, ki tua mai o te tai, ko te Marae-o-Tīpuna e tū mai ana hei kāinga whakamarumaru i te iwi. I ascend to the peak of my ancestral mountain, Puketeitei, and look to the land spreading away before me. I look to the north and see the river called Huka, flowing from the west to the sea. Beyond the river stretching to the north I see the Taratara mountain range. My gaze turns to the north-east and my eyes fall upon the wetlands Reponui, between Puketeitei and the coast. I turn to the east and see the island called Te Motu o Aramoana, and between there and the mainland the rock Pohatunui being bashed around by the tide. I look to the south and see the Hiwiroa range stretching to the south-west. Beyond Hiwiroa is our forest. My gaze returns to the east and situated before the coast line is our marae called Marae-o-Tīpuna, a shelter for its people.

Repeat this listening exercise with other maps until students get used to identifying places that are described to them using the main directions.

Students could make up their own texts and partially completed maps to describe the ‘lay of the land’ from their own mountain top, or from the roof of a tall building.

Session 3

Overlay a grid drawn on transparency to the map that was completed in Session 2:

Talk about the directions designated by the vertical and horizontal lines of the grid. Talk about different ways of aligning the map and the grid depending on where a particular direction runs. For example how would the grid sit on the map if the direction from Hiwiroa to Reponui was west, or south-east for example.

Use the grid to describe the location of one aspect of the map in relation to another. For example:

• Hiwiroa is south of Puketeitei
• Pohatunui is west of Aramoana
• Taratara is mostly west and a little bit south of Aramoana

Students could write direction questions for other students to answer. For example:

• What lies south of the river?
• Describe the location of the marae.
• If you are standing on Pohatunui rock, what direction do you look in order to see Reponui?

Introduce the degree system that is used to describe directions:

• Draw a full circle of degree measurements on transparency and lay this over a diagram of the 8 main directions.

• Discuss the degree equivalents of each of the main directions. Possible discussion questions include:
o Where do the degree measures start counting from, and in which direction around the protractor do they go.
o How many degrees between east and west? Why is it 180°?
o How many degrees between east and south? Why is it 90°?
o What is the degree measure exactly in the middle of east and south-east?
o Make up an appropriate name for a direction of 022.5°
o What direction is closest to 240°?
• Align the protractor transparency correctly on top of the map and work out approximate directions in degrees needed to complete the table. Students could be asked to estimate the degree measure first, and also add more to the table:
 From: To: Direction: Te Marae o Tīpuna Te Motu o Aramoana Reponui the forest Pohatunui Hiwiroa
• Students could be set a similar exercise to that above but using a different map, such as a map of the school, a map of the local area or a map of Aotearoa New Zealand.

Session 4

Overlay a numbered grid on the map and discuss how ordered pairs are used to locate places on the map. For example Pohatunui is located at approximately (10,5). Get students to use ordered pairs to describe the location of other places on the map.

• Get students to use the number grid transparency on other maps to find locations of places.
• By using the numbered grid and the protractor transparency students could write position and direction stories for another student to follow. For example:
o I’m standing at (3,4) and looking in a direction of 030°. What do I see?
• Give students a map of the school and get them to draw a walkway with about 6 or so straight paths. They should describe each part of the walkway with a beginning and ending point and a direction.

Session 5

To finish off the unit get students to draw a map (from memory) extending about 2km in each direction from where they live (their house is in the middle of the map). Using the map, a protractor transparency and the numbered grid transparency, students could:

• Describe the lay of the land as viewed from the roof of their house.
• Give directions from their house to various landmarks on the map.
• Give locations of various landmarks on the map.
• Estimate distances from their house to various landmarks on the map.

Create a table showing the directions each student in the class travels to get to school. Students decide on the intervals for grouping the directions. For example:

 Direction Number of students between 000° and 045° between 045° and 090° between 090° and 135° between 135° and 180° between 180° and 225° between 225° and 270° between 270° and 315° between 315° and 360°

The numbers of students for each interval could be shown on a histogram, and the distribution discussed in terms of where the school is located in relation to the housing areas of the town/district.

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