Data squares: Level 2


This unit introduces the students to a way of looking at information from a group of individuals, i.e. a data set. “Data Squares” are used to display information about individuals and by sorting and organising a set of data squares, students can find out things or answer questions about the group. 

Achievement Objectives
S2-1: Conduct investigations using the statistical enquiry cycle: posing and answering questions; gathering, sorting, and displaying category and whole-number data; communicating findings based on the data.
Specific Learning Outcomes
  • Write questions for investigation.
  • Collect information.
  • Sort information into categories.
  • Display information to answer questions or find out things.
  • Answer questions by sorting, organizing and arranging information.
  • Make sensible statements about the information and be able to back up their statements with appropriate displays.
Description of Mathematics

A “Data Square” is simply a square piece of paper containing information about an individual person or thing. At this level the data square is divided into three areas with the same category information in the same location on each square. In this unit the terms data and information are used to mean the same thing and are interchanged throughout.Because several pieces of information about individuals are on each data square, different categories can be looked at simply by rearranging the squares. 

This unit focuses on sorting and organising data sets, i.e. collections of information from a group of individuals. As the data set is looked at, questions or interesting things arise, which is different from starting with a question then collecting data to see if it is correct. 

Understanding the difference between individual data and group data is central to the unit. The goal is to move students from “that is Jo’s data and that is me” to making statements about the group in general. Increasing student’s ability to accurately describe aspects of a data set, including developing statistical vocabulary, is part of the unit. As students become comfortable with making statements and describing data, more precise vocabulary is to be encouraged. The meaning and usage of words like; same, similar, exactly and almost need to be explored during the unit along with the importance of using numerical descriptions, e.g. 2 more than, when describing or comparing data. 

Session One – What is a data square? Completing a data square about themselves.  Session Two - Organising and displaying a set of data squares to find out things and answer questions about a group of twelve students. Session Three - Organising and displaying the class data squares to find out things about the class and check if statements suggested are correct. Session Four - Designing and collecting their own data squares.  Session Five - Organising and displaying their own data squares to find out things and answer questions and check if statements suggested are correct.

Required Resource Materials

Session One

Show the following data square to the class and explain what a data square is, i.e. a square piece of paper contains three pieces of information about one person.

data square

Ask the class to tell you something about this student. Does anyone in the class fit this data square? Do you know someone that fits this data square that not in this class? How many different people could this data square be correct for?

Turn the data square over to reveal the name of someone familiar that fits this data square. The point to get across is that a data square could fit many people but each data square is about one particular person.

Discuss the importance of knowing exactly what each piece of data is about. What could “right handed” mean? If the data square just said “brown”, instead of “brown eyes” what could it mean?

Explain to the students that the way to view each piece of data is to see it as the answer to a question. Get them to suggest the questions that give these three pieces of information. Discuss how some students could answer the same question differently, e.g. “Are you right handed or left handed?” could give two different answers for the person who throws a ball with one hand and writes with the other. A more specific question is needed, e.g. “What hand do you write with to produce your best looking work.”

What would a data square about you look like?

Hand out a data square to each student to fill out. Have each student write their name on the back of the data square hand and have a student collect these.

After this session the teacher needs to arrange the data squares onto pieces of paper and photocopy them. One set is for each pair of students. Photocopying onto coloured paper is suggested to make it easy to recognise the class data set. This data set will be used during Session Three.

Session Two

Start the session by reminding the students about the data square they filled in during Session One. Select a data square one of the class filled out and read out the three pieces of data and ask the questions, “Whose data square could this one be?”, “Could it be anyone else in the class?”, “Could it be someone else in the school?”, “Could it be a teacher or other adult?” Repeat this several times.

Organise the students into pairs and hand out to each pair a set of Data Set One, Copymaster 1. Tell them this is a group of students from another school and get them to cut out all the data squares. Once the data squares are cut out have the students sort and organise the data squares to find out things about this data set. Remind them we are interested in the group and not individual students.

At a suitable time, as the pairs of students are organising the data squares,  have the class stop and look at the different ways the data squares have been arranged. Briefly discuss the different ways, along with writing up or drawing the different ways on to the board for all students to see. The question “What is good about this way?” or “When would it be good to organise the squares like this?” could be asked.


Ask the following questions and get each pair of students to organise the data squares into one of the above arrangements to show the answer.

  1. Are there more boys than girls? Organise into columns
  2. Which hand do most students in the class write with? Organise into rows
  3. Is green the eye colour most students have? Organise into piles
  4. Which hand do most girls write with? Arrange into groups, i.e. groups of groups

Have the students suggest similar questions they could investigate then encourage them to look at the data squares, organising and reorganising to find out as much as they can about this group of students.

Initially encourage the students to look at one category at a time to answer “How many?” type questions. Once this is able to be done confidently, encourage students to look for categories within other categories, e.g. Do more girls write with their left hands or with their right hands?

Write on a large piece of paper what the class discovers or get each pair to write up what they find out about this group. Keep this information, as it can be used later to compare with other data sets.

Session Three

Explain to the class that today they will be sorting and arranging data squares, like Session Two, except they will be using the data squares they wrote about themselves. Before the copied data squares are handed out,  discuss what the students expect to find out. “What do you think we will find out about our class?” “Will it be mainly different or similar to the group looked at in Session Two?”

Hand out the copied data squares from Session One to each pair of students. The pairs are to cut out the data squares, sort them and organise them to look for other interesting things about the class.

The teacher is to move around getting each pair to explain and show what they have found out. The teacher is to encourage the pairs to add detail to their answers, moving students from, “Yes, there are more girls than boys” to “Yes, there are 15 girls, 5 more girls than boys.”

Conclude the day by considering the statements the students made at the start of the day and seeing how many where true and discussing other interesting things found out about the class.

Session Four

Today the students, in pairs, will design and collect their own data square set. Each pair of students needs to design two questions to ask 24 other students in the class. The first question will be “Are you a boy or a girl?” with two new questions added.

Discuss and brainstorm suitable questions. Questions need to be answered with either yes or no, or an option selected. Keep the optional answers to a maximum of three options.

Sample questions:

  • Do you have a pet at home?
  • Do you have an older brother?
  • Can you swim one length of the school pool without touching the bottom?
  • If you could choose, would you sing, dance or read a book?
  • Do you like fruit or meat or vegetables best?

Once suitable questions have been developed they are to be written onto a large data square.

data square

Before starting to collect data each pair of students needs to write three statements about what they expect to find out about the class. More able students are to be encouraged to write statements about categories within categories, e.g. “Most girls will select red as their favourite colour” or “About the same number of boys as girls will be youngest in their family” or “The most common data square will be boy, blue and middle”.

Each pair of students is to cut out 24 blank data squares and number them 1 to 24. Once completed the pair of students are to ask 12 students each their three questions and fill out a data square for each student. The student’s name needs to be written on the back to make sure 24 different students are selected.

The importance of keeping the data in the same position needs to be stressed, i.e. the answer to the question “Are you a boy or girl?” is always placed top right and the place in the family always at the bottom. This makes sorting and organising the data squares later much easier.

The use of abbreviation and initials could be introduced at this point if the teacher feels that class is ready for this.

Session Five

In pairs the students are to sort and organise their 24 data squares to look for other interesting things about the class and to see if the statements they made about the class were correct.

After a set time each pair reports what they found out about the class. This could be in the form of a written report, a conference with the teacher or a presentation to the class.


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