What to do
Note to teacher: This internal assessment activity is an example that MUST be adapted before use, ensuring that all requirements of the Achievement Standard are still met. This textbox should be removed prior to sharing the activity with your students.
Note to teacher: This internal assessment activity is an example that MUST be adapted before use, ensuring that all requirements of the Achievement Standard are still met. This textbox should be removed prior to sharing the activity with your students.
Ākonga at a local kura are currently learning about raranga. As part of the learning on whiri (a braiding technique used for rope), their kaiako shares a pūrākau about Maui and the sun.
Pūrākau are Aotearoa New Zealand narratives that might describe how the world looks today. This pūrākau tells how Māui and his brothers worked together to slow down Tama-nui-te-rā, the sun, in order to get more daylight. You are going to explore some possible mathematical problems related to this pūrākau.
For this activity you will need to:
- explore options for finding the total length of taura, flax ropes, that Māui and his brothers wove
- discuss the progress of each brother in relation to the other brothers
- find the maximum angle of elevation Tama-nui-te-rā could rise out of the pit without the brothers running out of taura
- find the maximum height Tama-nui-te-rā would rise to at the maximum point of elevation
- explain any assumptions you made when solving the problems and how these may create limitations on your solution, or lead to generalisations or predictions
- explore other mathematics behind the action of slowing Tama-nui-te-rā.
Ākonga at a local kura are currently learning about raranga. As part of the learning on whiri (a braiding technique used for rope), their kaiako shares a pūrākau about Maui and the sun.
Pūrākau are Aotearoa New Zealand narratives that might describe how the world looks today. This pūrākau tells how Māui and his brothers worked together to slow down Tama-nui-te-rā, the sun, in order to get more daylight. You are going to explore some possible mathematical problems related to this pūrākau.
For this activity you will need to:
- explore options for finding the total length of taura, flax ropes, that Māui and his brothers wove
- discuss the progress of each brother in relation to the other brothers
- find the maximum angle of elevation Tama-nui-te-rā could rise out of the pit without the brothers running out of taura
- find the maximum height Tama-nui-te-rā would rise to at the maximum point of elevation
- explain any assumptions you made when solving the problems and how these may create limitations on your solution, or lead to generalisations or predictions
- explore other mathematics behind the action of slowing Tama-nui-te-rā.
How to present your learning
In exploring these problems, you should:
- show calculations, as appropriate, that you have used in your exploration of the problem
- use correct mathematical statements
- explain what you are calculating at each stage of the solution
- describe how your mathematical working relates to Māui and the pūrākau.
The quality of your mathematical reasoning and connections, and how well you link these to the context of the pūrākau will determine your overall grade.
You may present your answer in any way that effectively communicates your working and conclusions. You must show all working including how you may have used technology.
In exploring these problems, you should:
- show calculations, as appropriate, that you have used in your exploration of the problem
- use correct mathematical statements
- explain what you are calculating at each stage of the solution
- describe how your mathematical working relates to Māui and the pūrākau.
The quality of your mathematical reasoning and connections, and how well you link these to the context of the pūrākau will determine your overall grade.
You may present your answer in any way that effectively communicates your working and conclusions. You must show all working including how you may have used technology.
Timeframe
Your kaiako will inform you in advance of the date that the activity will be completed and the amount of in-class time to complete the activity (approximately two hours — not including group discussion or planning).
Your kaiako will inform you in advance of the date that the activity will be completed and the amount of in-class time to complete the activity (approximately two hours — not including group discussion or planning).
Getting started
Engage with the pūrākau provided. You will have 30 minutes to work with a group to start unpacking the activity. Refer to the student resources section for information that you will need in order to begin your thinking.
Akonga at the local kura made suggestions about the mathematics that could relate to the pūrākau. You may find you need to make further suggestions to make progress with the mathematics. Discuss these with your group. Following this, you will work individually to plan how you will explore the mathematical problems.
You will be given 20 minutes to make your own plan including sketches and notes that outline the mathematical processes you intend to use.
Check with your kaiako that your plan will allow you to demonstrate your learning at the correct level.
Engage with the pūrākau provided. You will have 30 minutes to work with a group to start unpacking the activity. Refer to the student resources section for information that you will need in order to begin your thinking.
Akonga at the local kura made suggestions about the mathematics that could relate to the pūrākau. You may find you need to make further suggestions to make progress with the mathematics. Discuss these with your group. Following this, you will work individually to plan how you will explore the mathematical problems.
You will be given 20 minutes to make your own plan including sketches and notes that outline the mathematical processes you intend to use.
Check with your kaiako that your plan will allow you to demonstrate your learning at the correct level.
Student resources
Māui me te rā by Wiremu Grace:
- Māui me te rā | te reo Māori (Te Kete Ipurangi)
- How Māui slowed the sun | te reo English (Te Kete Ipurangi)
After discussing the pūrākau of Maui and the sun, ākonga at the local kura agree it is likely that the brothers would have worked at different rates to produce taura. They suggest the following rates for the brothers:
Brother 1 works at a constant rate and produce 1200m of taura over the five days.
Brother 2 uses 100m of taura woven from a previous task and extend it by weaving 40m of new taura per hour.
Brother 3 starts a day later than the other brothers, claiming they can work faster by producing 1600m by the end of weaving.
Brother 4 works with increasing productivity over the 5 days completing 56m by the end of day one, an additional 168m on day 2, a further 280m on day 3, and continued with this pattern for two more days.
Brother 5 slows down over the course of the five days, with output modelled by the equation L = - 1.125t2 + 75.75t with L being the total taura produced, and t being the time in hours since weaving first begun.
This is further information for exploring the situation:
- Māui and his 4 tuākana (brothers) will combine their taura (flax rope) and redistribute it evenly when they attempt to harness the sun.
- Before Māui slowed Tama-nui-te-rā there were 6 hours in a day.
- Each of the tuākana work separately to produce taura.
- The tuākana built their huts 30 m from the edge of the pit.
- Tama-nui-te-rā rose straight up out of the pit.
Māui me te rā by Wiremu Grace:
- Māui me te rā | te reo Māori (Te Kete Ipurangi)
- How Māui slowed the sun | te reo English (Te Kete Ipurangi)
After discussing the pūrākau of Maui and the sun, ākonga at the local kura agree it is likely that the brothers would have worked at different rates to produce taura. They suggest the following rates for the brothers:
Brother 1 works at a constant rate and produce 1200m of taura over the five days.
Brother 2 uses 100m of taura woven from a previous task and extend it by weaving 40m of new taura per hour.
Brother 3 starts a day later than the other brothers, claiming they can work faster by producing 1600m by the end of weaving.
Brother 4 works with increasing productivity over the 5 days completing 56m by the end of day one, an additional 168m on day 2, a further 280m on day 3, and continued with this pattern for two more days.
Brother 5 slows down over the course of the five days, with output modelled by the equation L = - 1.125t2 + 75.75t with L being the total taura produced, and t being the time in hours since weaving first begun.
This is further information for exploring the situation:
- Māui and his 4 tuākana (brothers) will combine their taura (flax rope) and redistribute it evenly when they attempt to harness the sun.
- Before Māui slowed Tama-nui-te-rā there were 6 hours in a day.
- Each of the tuākana work separately to produce taura.
- The tuākana built their huts 30 m from the edge of the pit.
- Tama-nui-te-rā rose straight up out of the pit.
What to do
Note to teacher: This internal assessment activity is an example that MUST be adapted before use, ensuring that all requirements of the Achievement Standard are still met. This textbox should be removed prior to sharing the activity with your students.
Note to teacher: This internal assessment activity is an example that MUST be adapted before use, ensuring that all requirements of the Achievement Standard are still met. This textbox should be removed prior to sharing the activity with your students.
Ākonga at a local kura are currently learning about raranga. As part of the learning on whiri (a braiding technique used for rope), their kaiako shares a pūrākau about Maui and the sun.
Pūrākau are Aotearoa New Zealand narratives that might describe how the world looks today. This pūrākau tells how Māui and his brothers worked together to slow down Tama-nui-te-rā, the sun, in order to get more daylight. You are going to explore some possible mathematical problems related to this pūrākau.
For this activity you will need to:
- explore options for finding the total length of taura, flax ropes, that Māui and his brothers wove
- discuss the progress of each brother in relation to the other brothers
- find the maximum angle of elevation Tama-nui-te-rā could rise out of the pit without the brothers running out of taura
- find the maximum height Tama-nui-te-rā would rise to at the maximum point of elevation
- explain any assumptions you made when solving the problems and how these may create limitations on your solution, or lead to generalisations or predictions
- explore other mathematics behind the action of slowing Tama-nui-te-rā.
Ākonga at a local kura are currently learning about raranga. As part of the learning on whiri (a braiding technique used for rope), their kaiako shares a pūrākau about Maui and the sun.
Pūrākau are Aotearoa New Zealand narratives that might describe how the world looks today. This pūrākau tells how Māui and his brothers worked together to slow down Tama-nui-te-rā, the sun, in order to get more daylight. You are going to explore some possible mathematical problems related to this pūrākau.
For this activity you will need to:
- explore options for finding the total length of taura, flax ropes, that Māui and his brothers wove
- discuss the progress of each brother in relation to the other brothers
- find the maximum angle of elevation Tama-nui-te-rā could rise out of the pit without the brothers running out of taura
- find the maximum height Tama-nui-te-rā would rise to at the maximum point of elevation
- explain any assumptions you made when solving the problems and how these may create limitations on your solution, or lead to generalisations or predictions
- explore other mathematics behind the action of slowing Tama-nui-te-rā.
How to present your learning
In exploring these problems, you should:
- show calculations, as appropriate, that you have used in your exploration of the problem
- use correct mathematical statements
- explain what you are calculating at each stage of the solution
- describe how your mathematical working relates to Māui and the pūrākau.
The quality of your mathematical reasoning and connections, and how well you link these to the context of the pūrākau will determine your overall grade.
You may present your answer in any way that effectively communicates your working and conclusions. You must show all working including how you may have used technology.
In exploring these problems, you should:
- show calculations, as appropriate, that you have used in your exploration of the problem
- use correct mathematical statements
- explain what you are calculating at each stage of the solution
- describe how your mathematical working relates to Māui and the pūrākau.
The quality of your mathematical reasoning and connections, and how well you link these to the context of the pūrākau will determine your overall grade.
You may present your answer in any way that effectively communicates your working and conclusions. You must show all working including how you may have used technology.
Timeframe
Your kaiako will inform you in advance of the date that the activity will be completed and the amount of in-class time to complete the activity (approximately two hours — not including group discussion or planning).
Your kaiako will inform you in advance of the date that the activity will be completed and the amount of in-class time to complete the activity (approximately two hours — not including group discussion or planning).
Getting started
Engage with the pūrākau provided. You will have 30 minutes to work with a group to start unpacking the activity. Refer to the student resources section for information that you will need in order to begin your thinking.
Akonga at the local kura made suggestions about the mathematics that could relate to the pūrākau. You may find you need to make further suggestions to make progress with the mathematics. Discuss these with your group. Following this, you will work individually to plan how you will explore the mathematical problems.
You will be given 20 minutes to make your own plan including sketches and notes that outline the mathematical processes you intend to use.
Check with your kaiako that your plan will allow you to demonstrate your learning at the correct level.
Engage with the pūrākau provided. You will have 30 minutes to work with a group to start unpacking the activity. Refer to the student resources section for information that you will need in order to begin your thinking.
Akonga at the local kura made suggestions about the mathematics that could relate to the pūrākau. You may find you need to make further suggestions to make progress with the mathematics. Discuss these with your group. Following this, you will work individually to plan how you will explore the mathematical problems.
You will be given 20 minutes to make your own plan including sketches and notes that outline the mathematical processes you intend to use.
Check with your kaiako that your plan will allow you to demonstrate your learning at the correct level.
Student resources
Māui me te rā by Wiremu Grace:
- Māui me te rā | te reo Māori (Te Kete Ipurangi)
- How Māui slowed the sun | te reo English (Te Kete Ipurangi)
After discussing the pūrākau of Maui and the sun, ākonga at the local kura agree it is likely that the brothers would have worked at different rates to produce taura. They suggest the following rates for the brothers:
Brother 1 works at a constant rate and produce 1200m of taura over the five days.
Brother 2 uses 100m of taura woven from a previous task and extend it by weaving 40m of new taura per hour.
Brother 3 starts a day later than the other brothers, claiming they can work faster by producing 1600m by the end of weaving.
Brother 4 works with increasing productivity over the 5 days completing 56m by the end of day one, an additional 168m on day 2, a further 280m on day 3, and continued with this pattern for two more days.
Brother 5 slows down over the course of the five days, with output modelled by the equation L = - 1.125t2 + 75.75t with L being the total taura produced, and t being the time in hours since weaving first begun.
This is further information for exploring the situation:
- Māui and his 4 tuākana (brothers) will combine their taura (flax rope) and redistribute it evenly when they attempt to harness the sun.
- Before Māui slowed Tama-nui-te-rā there were 6 hours in a day.
- Each of the tuākana work separately to produce taura.
- The tuākana built their huts 30 m from the edge of the pit.
- Tama-nui-te-rā rose straight up out of the pit.
Māui me te rā by Wiremu Grace:
- Māui me te rā | te reo Māori (Te Kete Ipurangi)
- How Māui slowed the sun | te reo English (Te Kete Ipurangi)
After discussing the pūrākau of Maui and the sun, ākonga at the local kura agree it is likely that the brothers would have worked at different rates to produce taura. They suggest the following rates for the brothers:
Brother 1 works at a constant rate and produce 1200m of taura over the five days.
Brother 2 uses 100m of taura woven from a previous task and extend it by weaving 40m of new taura per hour.
Brother 3 starts a day later than the other brothers, claiming they can work faster by producing 1600m by the end of weaving.
Brother 4 works with increasing productivity over the 5 days completing 56m by the end of day one, an additional 168m on day 2, a further 280m on day 3, and continued with this pattern for two more days.
Brother 5 slows down over the course of the five days, with output modelled by the equation L = - 1.125t2 + 75.75t with L being the total taura produced, and t being the time in hours since weaving first begun.
This is further information for exploring the situation:
- Māui and his 4 tuākana (brothers) will combine their taura (flax rope) and redistribute it evenly when they attempt to harness the sun.
- Before Māui slowed Tama-nui-te-rā there were 6 hours in a day.
- Each of the tuākana work separately to produce taura.
- The tuākana built their huts 30 m from the edge of the pit.
- Tama-nui-te-rā rose straight up out of the pit.