Data cards: Level 2

Purpose

This unit introduces the students to a way of looking at information from a group of individuals, i.e. a data set. “Data cards” are used to display information about individuals and by sorting and organising a set of data cards, 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
  • Pose investigative questions.
  • Write data collection or survey questions to support collecting information for investigation.
  • Collect information.
  • Sort information into categories.
  • Display information to answer investigative questions or find out things.
  • Answer investigative questions by sorting, organising 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 card” is simply a square piece of paper containing information about an individual person or thing. At this level the data card is divided into three areas with the same category information in the same location on each card. 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 card, different categories can be looked at simply by rearranging the cards. 

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 an investigative question then collecting data to answer the investigative question. 

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 students' 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. 

Investigative questions

At Level 2 students should be generating broad ideas to investigate and the teacher works with the students to refine their ideas into an investigative question that can be answered with data.  Investigative summary questions are about the class or other whole group.  The variables are categorical or whole numbers. Investigative questions are the questions we ask of the data.

The investigative question development is led by the teacher, and through questioning of the students identifies the variable of interest and the group the investigative question is about.  The teacher still forms the investigative question but with student input.

Data collection or survey questions

Data collection or survey questions are the questions we ask to collect the data to answer the investigative question.  For example, if our investigative question was “What ice cream flavours do the students in our class like?” a corresponding data collection or survey question might be “What is your favourite ice cream flavour?”

As with the investigative question, data collection or survey question development is led by the teacher, and through questioning of the students, suitable data collection or survey questions are developed.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

  • encouraging category within category investigative questions
  • allowing for three additional data collection questions by dividing the data cards into four rather than three
  • collecting data from another class and compare.

The context for this unit can be adapted to suit the interests and experiences of your students.

Required Resource Materials
Activity

Session One

  1. Show the following data card to the class and explain what a data card is, i.e. a piece of paper contains three pieces of information about one person.
    data square
  2. Ask the class to tell you something about this student. 
    Does anyone in the class fit this data card?
    Do you know someone that fits this data card that is not in this class?
    How many different people could this data card be correct for?
  3. Turn the data card over to reveal the name of someone familiar that fits this data card. The point to get across is that a data card could fit many people but each data card is about one person only.
  4. Discuss the importance of knowing exactly what each piece of data is about. 
    What could “right handed” mean?
    If the data card just said “brown”, instead of “brown eyes” what could it mean?
  5. Explain to the students that the way to view each piece of data is to see it as the answer to a data collection or survey question. Get them to suggest the data collection questions that give these three pieces of information. Discuss how some students could answer the same data collection 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 data collection question is needed, e.g. “What hand do you write with to produce your best looking work.”
    What would a data card about you look like?
  6. Hand out a data card to each student to fill out (Copymaster 2). Have each student write their name on the back of the data card hand and have a student collect these.
  7. After this session the teacher needs to arrange the data cards onto pieces of paper and photocopy them. One set is made 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

  1. Start the session by reminding the students about the data card they filled in during Session One. Select a data card one of the class filled out and read out the three pieces of data and ask the questions, “Whose data card 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.
  2. 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 cards. Once the data cards are cut out have the students sort and organise the data cards to find out things about this data set. Remind them we are interested in the group and not individual students.
  3. At a suitable time, as the pairs of students are organising the data cards,  have the class stop and look at the different ways the data cards 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 cards like this?” could be asked.
    arrangements
  4. Ask the following investigative questions and get each pair of students to organise the data cards into one of the above arrangements to show the answer.
    • Which hand do students in the class write with? Organise into rows
    • What eye colour do students in the class have? Organise into columns
    • Do the eye colours for boys and girls differ? Arrange into groups, i.e. groups of groups
  5. Have the students suggest similar investigative questions they could explore then encourage them to look at the data cards, 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 then, encourage students to look for categories within other categories, e.g. What hands do girls write with?
  6. 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

  1. Explain to the class that today they will be sorting and arranging data cards, like Session Two, except they will be using the data cards they wrote about themselves. Before the copied data cards 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?
  2. Hand out the copied data cards from Session One to each pair of students. The pairs are to cut out the data cards, sort them and organise them to look for other interesting things about the class.
  3. 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.”
  4. 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 using data cards. Each pair of students needs to design two data collection questions to ask other students in the class. The first data collection question will be “Are you a boy or a girl?” with two new data collection questions added.

  1. Discuss and brainstorm suitable data collection questions. Data collection questions for this activity need to be answered with either yes or no, or an option selected. Keep the optional answers to a maximum of three options.
    Sample data collection 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?
  2. Once suitable data collection questions have been developed they are to be written onto a large data card.
    data square
  3. Before starting to collect data each pair of students needs to write three investigative questions they could ask of the data they will collect and to make statements about what they expect to find out about the class for these investigative questions. More able students are to be encouraged to pose investigative questions about categories within categories, leading to statements about what they will find 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 card will be boy, blue and middle”.
  4. Each pair of students is to cut out enough blank data cards for the class and number them 1 to n (number in class). Once completed the pair of students are to ask half the students each their three data collection questions and fill out a data card for each student. The student’s name needs to be written on the back to make sure all students are asked. They need to remember to complete their data cards for themselves as well.
  5. The importance of keeping the data in the same position needs to be stressed, i.e. the answer to the data collection 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 cards later much easier.
  6. 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 cards 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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Level Two