This unit consists of mathematical learning, at Level 2 of the New Zealand Curriculum, focused around celebrations of Matariki, the Māori New Year. The sessions provide meaningful contexts that highlight Māori culture and provide powerful learning opportunities that connect different strands of mathematics.
Session One
Session Two
Session Three
Session Four
Session Five
Session one involves subtracting single digit and two digit numbers starting at 200. As students take handfuls or counters from their "waka" they should anticipate how many counters remain. Students should use place value to calculate, as opposed to counting back. The use of a linear model for representing the calculations is recommended. A bead string is ideal and can be mounted along the edge of a whiteboard. Jumps can then be recorded on the whiteboard.
The session notes recommend linking two strings end on end to form a line of 200 beads. An important strategy in this activity is ‘back through ten’. For example, a student has 93 counters left and removes a handful of 17 counters. How many do they have left?
On the bead string, this calculation can be modelled like this:
In this diagram, 93 – 7 is calculated in two steps. First, the seven in 17 is imaged as 10 and 7. Three is subtracted from 93 to get to 90 and then four is taken away to get 86. Thus, the seven from 17 has been subtracted, leaving only the 10 to be taken away next. This is a ‘back through ten’ strategy, meaning it uses a decade number (i.e. 90) as a benchmark. Alternatively, a student might take away the ten in 17 first, and then the 7.
Session three involves dealing with "like" measures, e.g. dividing or multiplying weights. Measuring objects with devices like kitchen scales is important to the development of students’ understanding of the measurement system. For example, students will need to find out how many kilograms of kūmara need to be ordered for the hāngī. If possible, bring a few kūmara along so students can experiment and find out how many kūmara make up one kilogram in weight. They will then need to use division or multiplication to calculate how many kūmara they need in total for the hāngi. If 24 kūmara are needed and four kūmara weigh one kilogram then 26 (24 ÷ 4) kilograms of kūmara will need to be purchased.
Session four develops important geometry ideas out of whai (string figures). A common issue with the learning of geometry is that students form prototypical views of shapes. For example, they might consider an equilateral triangle to be the only shape that is a triangle. All of the shapes below are triangles:
The issue of prototypical ideas will also apply to other polygons such as hexagons and octagons.
These three shapes are all hexagons. Note that the bottom hexagon is concave as it has two internal angles greater than 180°. It is important to discuss the defining characteristics of a class of shapes like hexagons. The only required property is that the shape is closed by six sides.
Session five also involves an important mathematical idea, distinctness. Rotating or reflecting a shape does not change its properties, except orientation (direction it is facing). The idea is fundamental to determining if given shapes are similar or different. For example, all of the shapes below are similar even though they look different. They can all be mapped onto each other using translation (shifting), reflection (flipping), and rotation (turning).
Similarity is applied in Session Five by looking for different winning positions. If the positions are reflections or rotations of one another then they are not considered to be distinct.
The learning opportunities in this unit can be differentiated by providing or removing support to students, or by varying the task requirements. Ways to support students include:
Tasks can be varied in many ways including:
Although the context of Matariki should be engaging, and relevant, for the majority of your learners, it may be appropriate to frame the learning in these sessions around another significant time of year (e.g. Chinese New Year, Samoan language week). This context offers opportunities to make links between home and school. Consider asking family and community members to help with the different lessons. For example, members of your local marae may be able to share local stories and traditions of matariki with your class.
Te reo Māori language is embedded throughout this unit. Relevant mathematical vocabulary that could be introduced in this unit and used throughout other learning include āhua (shape), shape names (e.g. whetū - star), tātai (calculate, calculation), tāpiri (add, addition), ine (measure), taumaha (weight), huri (rotate, rotation), whakaata (reflect, reflection), and neke (translate, translation, move)
The activities are mostly open ended so they cater for a range of achievement levels. It is expected that students have some experience with naming and classifying basic geometric shapes, with measuring weight in kilograms, and with translating, reflecting and rotating shapes. They should also have place value knowledge to at least 200.
Matariki is a time of cultural pursuits and feasting to celebrate the New Year ahead. The hāngī or earth oven has particular significance at the time of the new moon after the rise of Matariki in the eastern pre-dawn sky. Matariki is the star at the bow of Te Waka o Rangi and her travels around the sky for eleven months of the year are exhausting. It is said the steam of the first hāngī in the New Year rises into the sky and replenishes the strength of Matariki. From the offerings she gathers strength to lead the giant canoe for another year. Without Matariki at the bow the canoe cannot travel and Taramainuku cannot cast his net to gather the souls of the departed. At the New Year the names of the dead are called out so the souls of the departed may be cast into the heavens as stars.
There are many resources already available about hāngī.
“Preparing for the hāngī” is a Level 3 activity from the Figure It Out series.
“Hanging out for hāngī” is a unit at Level 3 that develops a statistical investigation around deciding which foods to cook.
The notes below are an adaptation more suitable for Level 2 students.
Matariki was a time when food was already stored, and it was cold outside. So whānau (families) spent time together engaging in cultural pursuits such as storytelling, arts and games. Whai (string games) were popular with tamariki (children) and adults alike, especially when they involved co-operation. Whai has a long history and is common to many indigenous cultures around the world, including the indigenous tribes of North America. Traditionally whai was played with twine made from flax. The best man-made fibre to use for whai is nylon since it slides and flexes, and is soft on your hands. It is commonly used to form lines for brickwork so is available at most hardware stores in a variety of colours. Nylon string is usually available in craft shops.
In this session students learn to play the traditional Māori game Mū Tōrere which is like a form of draughts. The original game is sometimes referred to as the wheke (octopus) game or the whetū (star) game due to the shape of the board. It is appropriate that students learn to play the game at the time of Matariki, since the Māori New Year is a time of engaging in cultural pastimes. The board (see Copymaster 5) has been altered to include the nine or seven stars of Matariki, depending on the version of the game that is played. A digital version of this game is available online - search for “Mū Tōrere - HEIHEI Games”.
Dear parents and whānau,
This week we are exploring some mathematical ideas with activities to celebrate Matariki, the Māori New Year. We will be learning the legend of Tamarereti and using that story to learn about numbers of bright stones. We will look at the phases of marama (the moon) to find the best days to go fishing in the New Year period, plan and cost a hāngī, and discover geometry in whai (string patterns). Lastly we will learn to play Mū Tōrere, a traditional Māori game that takes a lot of strategy to win.
These activities involve number, algebra, geometry, measurement and statistics so we will be very busy and doing a lot of mathematical thinking.
Printed from https://nzmaths.co.nz/resource/matariki-level-2 at 5:32am on the 20th April 2024