# Hanging out for Hāngi

Purpose

In this unit students are faced with the challenge of ordering the right amounts of food to put down in a hāngi for the whole school.  They carry out a statistical investigation into the preferred choices of food of the school population.

Achievement Objectives
S3-1: Conduct investigations using the statistical enquiry cycle: gathering, sorting, and displaying multivariate category and whole-number data and simple time-series data to answer questions; identifying patterns and trends in context, within and
Specific Learning Outcomes
• collect data in systematic ways
• make conclusions about what data shows in order to make informed decision
Description of Mathematics

Statistical investigations include the four aspects; pose questions, collect data, display data and discuss results. These four are closely linked as what data is collected can dictate the way that it is displayed and the conclusions that can be reached from the investigation. On the other hand, if some restrictions have been placed on the means of display, only certain types of data collection may be relevant.

By Level 3 students can begin to talk about situations they have experienced, pose their own questions for an investigation, produce a plan for a statistical enquiry, and use a variety of methods to display their data.

Associated Achievement Objective

Social Studies AO2: understand how cultural practices vary but reflect similar purposes

Required Resource Materials

Large sheets of paper to display data on, pens to writing

Copy Master 1 Problem for investigation

Key Vocabulary

hāngi, wastage, survey, questionnaire, bias, assertions, statements, tally charts, bar graphs, pie graphs, similarities, differences, preferences, collation, census, data

Activity

#### Session 1

1. Explore children's prior knowledge and experience with the process and ingredients of hāngi. You may want to refer to some articles and link the statistical investigation to literacy. 1) School Journal Level 2 August 2011- "Hāngi and Hogays" by Iona McNaughton, p.18 or 2) School Journal Part 3 Number 3 2011-"Puia Hāngi - Cooking with Steam" by Henarata Ham and the children of Room 8, Hirangi School, p.29.
2. Pose the following problem to the class – The school has decided to put down a hangi for all students to experience.  Previously when the school did a hāngi a lot of food was wasted because students didn’t like certain foods.  You have been given the task of finding out what food should be put in the hangi so that there is the least amount of wastage.
What foods are cooked in a hāngi? What would best be cooked using this process?
4. Discuss how you could find out what vegetables and meat the students in your school prefer.
5. Pair students to discuss ways that they could go about collecting this data.
6. Share the various solutions and discuss the merits of each strategy.  Make a class decision by voting or a similar means to decide the method that will be undertaken.
7. Design the questionnaire.  Look at bias, and pose such statements like ‘we are thinking of having mutton in the school hāngi, do you like mutton yes or no?’ What is wrong with this statement?  How could we reword the statement to eliminate the bias?
8. Sample survey the class to model the process of recording students' choices, by using a tally chart.
9. Ensure that the questionnaire questions are written down and consistent as different students will ultimately be surveying different classes. Why is it important that the way in which we collect the data is consistent?

#### Session 2

Prior to this session you would need to have organised for students to visit different classes to gather the data from each student.

1. Remind students of the investigation and what we are trying to find out.
Why are we trying to find this out?  (reduce food wastage)
2. Group the students so that they are divided evenly around the classes in the school. They are to gather the required data and return to class.
3. On their return, ask them to graph their data using any way they choose to show their results.  Provide large sheets of paper and coloured pens for their data to be displayed.
4. What statements can you make about the preferred meat and vegetables that need to go down in the school hāngi for your class.
5. Students conclude the session by making statements about what their data shows.  What assertions can you make?

#### Session 3 and 4

1. Provide the opportunity for each group to share their findings about the preferred vegetables and meat for each class they visited.
What similarities and differences can you see between these classes?
Is it easy comparing bar graphs and pie graphs?
What should we have done?
What trends are starting to appear?
Which meat and vegetables seem to be most favoured?
2. Using the groups’ original tally charts collate the totals to get a whole school total for each vegetable and meat choice.
3. Students could move into new groups or remain in the previous groups and be given the task of displaying the data in a specified way.  The choice may be limited depending on students’ prior experience and knowledge of displaying data in certain ways.  Prior modelling and teaching may be required for some of these graphs e.g.
• bar graph
• pie graph
• pictograph using a key – for example refer Figure it Out Statistics Level 3-4 pg 15
• strip graph
1. Teacher roving and questioning:
What labels are needed on your graph?
What would be an appropriate title for your graph?
Tell me what your graph shows?

2. Students should be given the opportunity to share their graphs and discuss their findings with the rest of the class.
3. Ask reflective questions such as:
Which graph best shows this data?
Which graphs are easiest to interpret?  Why?
Which graph is least effective?
What kind of data would this graph be better for?

#### Session 5

1. From their findings students are then asked to write a statement to sit along side their graph to answer the original problem for investigation.  What food should be put down in the hangi?
2. Other possible questions that could be considered may include: How many students can be fed from one chicken?  How many chickens would need to be purchased to feed 46 students/112 students?
Each potato can be cut into three pieces, how many potatoes will we need to purchase to feed 236 students?
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