Preparing for the hāngī
This is a level 3 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers’ notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Use rules to find unknowns in patterns.
Preparing for the hāngī
Achievement objectives
NA3-8: Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
Required materials
- Figure It Out, Level 3, Algebra, "Preparing for the hāngi", page 8
See Materials that come with this resource to download:
- Preparing for the hangi activity (.pdf)
Activity
Remind students to read and consider all the information, including that in the speech bubbles, before trying to solve the problems on this page.
Before students begin working on this activity, you may want to discuss how to vary Aunty Wikitoria’s rules so that people get both chicken and pork. The most likely scenario is that Hine and Rāwiri need to halve the amount of chicken and pork, but you could discuss any other options that students have. When students have decided what the revised rules will be, encourage them to use division as the most efficient way to answer the question.
There are good discussion points here.
- Hine and Rāwiri need 7.5 chickens. Can you buy half a chicken?
- They need 3.75 kilograms of pork. Is it possible to buy part of a kilogram of pork?
Students can use algebraic symbols and equations to answer these questions. For example, to calculate how much kūmara the children need:
- number of kūmara = one kūmara x number of people
or
- number of kūmara for n people = 1 x n.
The calculation for the number of carrots needed is slightly more complex. You might want to talk through this with students:
- There are six carrots for every five people. How do we find out how many groups of five people there are?
Students can do this by dividing by five. To find out how many carrots are needed, they multiply the number of groups of five people by six:
- number of carrots = (number of people ÷ 5) x 6.
If students have difficulty with this method, they could use a table or model the problem with counters or multilink cubes.
Activity 1
Everybody gets an equal amount of chicken and pork. Each person would eat only half as much chicken as they would normally eat if they were served only chicken. The same is true for the pork. So, the new rules are:
1 chicken for every 4 people and 1 kg of pork for every 8 people.
For 30 people, Hine and Rāwiri need 30 ÷ 4 = 7.5 chickens and 30 ÷ 8 = 3.75 kg pork. (They may have to buy 8 chickens.)
Activity 2
Shopping list:
40 kūmara
50 cobs of corn
36 carrots
15 potatoes
30 handfuls of pūhā
6 kamokamo
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