In this unit students are faced with the challenge of ordering the right amounts of food to put down in a hāngī for the whole school. They carry out a statistical investigation into the preferred choices of food of the school population.
- collect data in systematic ways
- make conclusions about what data shows in order to make informed decision
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
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
- allowing students to create their own plan for data collection
- allowing students to create their own questionnaire
- increasing or decreasing the variety of graph formats provided to students, and varying the level of support and modelling provided when students are graphing their data
- providing sentence starters, and modelling ‘think alouds’, to support students in writing summary statements
- introducing the terms median, mean, and mode and asking students to calculate these measures of average using their data (see the Level 3 unit Time for Breakfast for further learning around the concept of average)
- organising students with mixed levels of mathematical knowledge and confidence into groups to encourage peer support, learning, and extension (tuakana teina)
The contexts for this unit can be adapted to suit the interests and cultural backgrounds of your students. For example, instead of framing the investigation around the context of hāngi, you could use the context of investigating the amount of food that should be bought for the school disco, your class camp, a birthday party, brought to a cultural-celebration day at school, or donated to a local food bank. You could begin the unit with a discussion of hāngi, before working with the students and whānau to link this learning to other meaningful contexts from their lives.
Te reo Māori vocabulary terms such as kauwhata (graph), kauwhata ira (dot plot, dot graph), kauwhata pou (bar graph), tūtohi tatau (tally chart), tūhuratanga tauanga (statistical investigation), haukume (bias), and whakatairite (compare) could be introduced in this unit and used throughout other mathematical learning.
Graphing and data collection resources (e.g. access to Microsoft Excel, chosen graphing and data collection templates)
Session 1
- Explore children's prior knowledge and experience with the process and ingredients of hāngī and other culturally-relevant celebrations involving the preparing and sharing of food. You may want to refer to some articles and link the statistical investigation to literacy. 1) School Journal Level 2 August 2011- "Hāngī 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.
- Pose the following problem to the class:
The school has decided to put down a hāngī for all students to experience. Previously when the school did a hāngī 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 hāngī so that there is the least amount of wastage. - Ask:
What foods are cooked in a hāngī? What would best be cooked using this process? - Discuss how you could find out what vegetables and meat the students in your school prefer.
- Pair students to discuss ways that they could go about collecting this data. Ensure they think about how they will collect the data (e.g. table, tally chart), what they will ask (their survey question), who they will ask (their sample), and why they will ask their sample their chosen question (what will it tell them?)
- Share the various solutions and discuss the merits of each strategy. Encourage students to think about which methods will be most systematic - meaning organised and able to be followed according to a plan. Make a class decision by voting or a similar means to decide the method that will be undertaken.
- Design the questionnaire. Look at bias, and pose such statements as:
We are thinking of having mutton in the school hāngī, do you like mutton yes or no?’
What is wrong with this question? Explain that this question shows bias because the surveyor is already thinking about having mutton. Because they have said this, it may affect how the person answering the questionnaire might answer. This means that they have not given an equal chance to both possible answers to the question.
How could we reword the question to eliminate the bias? - Sample survey the class to model the process of recording students' choices, by using a tally chart. If appropriate, direct students to use a tally chart, and provide a table, or help them to construct one. Alternatively, you could give students the option of collecting the data with a method they discussed earlier. Digital tools such as Google Forms or Padlet could be used alongside hard-copy tables.
- Ensure that the questionnaire questions are written down and are 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.
- Remind students of the investigation and what we are trying to find out.
Why are we trying to find this out? (reduce food wastage) - 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.
- On their return, ask them to graph their data. If necessary, you could teach them to construct a specific type of graph (e.g. bar graph, dot plot, pie chart, strip graph, pictograph using a key) using a digital or hard-copy graphing template. Alternatively, you could allow students to graph their data using a method of their choosing. Ensure you support students to include the important features of their chosen graph type by asking questions such as:
What labels are needed on your graph?
What would be an appropriate title for your graph?
Can you tell me what your graph shows? - What statements can you make about the preferred meat and vegetables that need to go down in the school hāngī for your class? You might show one group’s example and model using specific points of the data to make summary statements (for example, I can see that 2 people said they preferred carrots, this was the least preferred vegetable).
- Students conclude the session by making statements about what their data shows. What assertions can you make?
Direct students to make a presentation (e.g. a video, infographic, set of Google slides) that shows the questions they asked and why, their ‘raw’ data, their graph, and 3-5 summary statements.
Session 3 and 4
- Provide the opportunity for each group to share their findings about the preferred vegetables and meat for each class they visited. Allow students to give and receive constructive feedback to and from their peers in response to the presentations. After all of the groups have shared, display all of the graphs and ask questions such as;
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? - Using the groups’ original tally charts collate the totals to get a whole school total for each vegetable and meat choice.
- Students could move into new groups or remain in the previous groups and be given the task of displaying the new data in another specified way, or in a way chosen by the students. You could use this as an opportunity to teach students about a new graph type, or to consolidate knowledge of a previously-visited graph type.
- From their findings students should write a statement to sit alongside their graph to answer the original problem for investigation. What food should be put down in the hāngī?
Session 5
- Students should be given the opportunity to share their graphs and discuss their findings with the rest of the class.
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? - Other possible questions that could be investigated 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?
Dear parents and whānau,
In maths our focus is on statistics. We have been carrying out a survey to establish the students' food preferences for a school hāngī as a way to reduce food waste.
Please ask you child to explain the results of their survey and listen to the statements they make. Ask them questions like:
What would be good to put down in the hāngī if you want to make sure everyone eats their food?
What kind of foods could you try that might not be traditional choices?
Explain your different graphs to me-what do they show?
Thank you for your support and interest.