Teresa and the tuck shop

Teresa and the tuck shop

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about planning an investigation

Here is the lunch menu at Teresa’s school. She wants to find out which of the eight items on the menu students buy the most. She decided to ask some people. 

 

a)
Which of these people would it be best for Teresa to ask?
 
 
(A)   all of her friends
(B)   all of the students in her class
(C)   all of the teachers at the school
(D)   all of the students who bought lunch 
(E)   all of the students at the school
 
b) Why are these people the best to ask?
 

 
 
 
 
c) Write a question that Teresa could ask them.

 
 
 
 
 
d)  How could Teresa collect the information?
 

 
Task administration: 
This task is completed with pencil and paper only.
Level:
2
Curriculum info: 
Maths, Statistics, Statistical investigations
Key Competencies: 
Thinking, Using language, symbols, and texts
Keywords: 
planning investigations, data collection, work samples
Description of task: 
Students plan how to do a statistical investigation about a question that has been posed, and think about how they will collect their data.
Curriculum Links: 
This resource can be used to help to identify students' ability to identify a good, unbiased group to sample .
Key competencies
This resource involves students thinking critically to identify a good sample, and to communicate their reasons for this. These relates to the Key Competencies: Thinking and Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 3
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y4 (10/2010)
a) D

moderate
b) Any 1 of:
Statements that identify:

  • Reasons why only the people who bought lunch need to be asked.

    • Because they know what they buy.
    • They are the ones that bought lunches so they know best.
    • They know what is on the menu … and which one they like best.
    • Because they know what other people buy.
    • They saw what other people bought
    • When you were in the line to get lunch, what did people get?
    • Because they bought lunch (with no other qualification).
    • Because they already bought the food.
    • They bought their lunch.
  • Reasons why the other groups are not as good to ask.

    • People who don't buy lunches don't know [what people buy].
    • It would be no help as they don't get anything from the menu.

Accept "The class is typical of the whole school" if they give B to part a).

difficult
a) Any 1 of:

  • "What food items did you buy (most of) today?"
  • "What food items do you usually buy?"
  • "What food items did other people buy today?"
  • "What food items do other people usually buy?"
  • "What food items do you like most?"
  • "What food items do you think I should buy?" [with D for part a)]

Any other reasonable question.

moderate
a) Any 1 of:

  • Tally chart
  • Graph
  • List
  • Grid

Any other reasonable method of collection.

Do NOT accept "in a notebook"; "on paper"; or "write it down", as these are not specific enough.

difficult

Based on a representative sample of 191 students. NOTE: Responses such as "vote for the best lunch." indicates the student is addressing the wrong question (i.e., the question "What food would be most popular with all students?" rather than "Which food sells the most?").

Teaching and learning: 

The key ideas this question resource looks at are:

  • Identifying a suitable group to survey to answer a research focus, and justify their choice;
  • Write a specific question to ask them; and
  • Plan how to collect their data.

Students may identify other valid statistical issues. Likely ones are:

  • The bigger the sample size the better (because it gives a more accurate result);
  • Too big a sample size takes too much time (or money);
  • A group that is easy to sample will make the investigation easier (or cheaper); or
  • A group may be representative of the whole population.

If students make these responses, assure them that they are reasonable issues, but refocus them to the specific question they need to address and the key ideas.

  • This question aims to test students' ability to do part of a statistical investigation when a research focus has already been posed for them. This is the "planning" part of the statistical enquiry cycle (SEC – Pose; Plan; Data collection; Analyse and conclude; communicate findings).
  • Students need to:

    • identify who to ask, justifying their choice;
    • write an appropriate question; and
    • specify how to collect the results.
Diagnostic and formative information: 

Common alternative responses showing statistical insight
A number of other statistically sensible answers are possible that do not directly address the central question of which food currently sells the most. Students who made these responses have lower mean ability that those with correct responses, but higher mean abilities than other incorrect answers. The first and fourth of these addresses a separate, but closely related question "What food would be most popular with all students?" 

  1. The bigger the sample size the better [a) – E (or B)].
    Because all of the students at school has got the most people.
    Because you will get more (students).
  2. Sampling all is too many [a) – B or D].
    The school is too many.
    By the time she asked everyone she wouldn't be able to buy lunch.
  3. Ease of sampling [a) – A or B].
    Because it will be easier to find them. (whole class)
    Because it will be easier and quicker. (friends)
    She … would not have to be walking around the school. (class)
    So you can ask them all at the same time. (class)
  4. Asking all students is best [a) – E or sometimes B].
    It means everyone gets an opinion.
    Because you can have a vote compertishtion.

Statistical conversations
Have a guided conversation with these students, affirming that their ideas are good statistics, but don't answer the specific question. They also need to see that it is wasteful asking all students when some of them never go to the tuck shop [i.e., eliminate option (E)]. Get them to then repeat parts b) and c). It is like asking all students "What is it like to play rugby?" when it would be better to just ask those who actually play.
Some students may have replied "(C) Teachers" because the tuck shop at your school is run by teachers, so they would know what was the most popular item. Get the students to imagine that at Teresa's school some people who come in at lunchtime just to run the tuck shop.

Click on Mathematical classroom discourse for suggestions about how to have a class or group discussion.

Common incorrect responses
b) Reasons for choosing inappropriate group
Reliability of respondent [a) A (or C)]
Cuz they will tell the truth.
Because they won't lie.

Safety or comfort of interviewer [a) A (or C)]
Because they are people she knows.
Because they are nice, not bullies.
Because some people might think she is up to no good.
Because it is more safe instead of strangers.
Because there might be bullies in her class.

Teachers will know best [a) C]
Because they are smarter than us.
Because they know more things.
Because they are grown ups.
Because they will know because they are the teachers of course!
Be aware that this could be a reasonable response if teacher at your school run the tuck shop.

Healthiness of foods [often asked of teachers – C]
Because they will make sure it is healthy for you.
Because you will get healthy with a roll.
c) Inappropriate questions – not addressing the question
Healthiness of foods [often asked of teachers]
What is the best food for your body?

Question too specific
Should I eat a pizza or an apple?
How is the pizza?

Irrelevant question
What are the 8 things on the menu?
Hi, how much is the lunch?

Poorly phrased question
Assumes the group will know
[i.e., a) Friends or Teachers) followed by "What should I buy?" or "What food is most popular?"]
d) Lack of specificity about recording information
Use recording device (book, piece of paper etc.)
Use a book
Buy a notebook and write it there.
She could write it down on a piece of paper.
Write it on her hand.

Write it down (non specified)
She could write it down.

Find out by asking
By asking them
By standing at the front of the line and asking,

Manner of interviewing (politeness)
By saying "Please" and "Thank you".
Asks them nicely, not in an unnice way.
Repeats earlier part of information
Next steps: 

Reasons for choosing inappropriate group
For students who only see their friends as reliable, or worry about safety issues, reassure them that these are reasonable concerns. Ask them to repeat the question assuming everyone at school is reliable, and safe to ask.
For those who still want to ask friends or teachers, ask them "How can they be sure that their friends or teachers know", and then "Are there other group of people who would be more likely to know?" They could be asked a similar question: "Who would you ask what it is like to play rugby?" If they accept that it is better to ask those who are actively involved, they could repeat the question [with (A) and (C) removed from question a)].
 
Inappropriate questions – not addressing the question
These students need to have the intent of the investigation reinforced. They need to appreciate that they are trying to find out which of the eight food items sells the most. Ask them to read the stem and ask them what Teresa wants to find out. Emphasise their question needs to help find out what item the tuck shop is currently selling the most of. See if they can come up with a better question after a group discussion.
 
Lack of specificity about recording information
These students need to have an appropriate question to answer in part c). 

  • Settle on a question that the group agrees is fair.
  • Ask ALL students (including those who mentioned graphs, tables, or lists) to design something which could be used to collect the data. Get them to share with each other how their method works.
  • Share the different methods with the whole group. If they are having difficulty with this, get them to brainstorm different ways to collect and record data.

Many Figure It Out resources in the Statistics or Statistics in the Media series have contexts which will stimulate statistical investigations, which will involve planning investigations.