Statistics: How many are we?
View Sequence overviewWe can represent the data that we collect in different ways.
Each group
Materials for creating data representations:
- Selection of concrete materials, such as counters, cubes, or blocks
- Selection of art materials, such as coloured pencils, sticky dots, or stamps
Each student
Sheet of A4 paper
Lesson
Revise: In the last lesson we asked the question: How many are in our class? What was the answer to our question? How did we work out the answer?
Allow students to share what they remember and their reflections on the previous lesson.
Ask: How many do you think might be in our class today?
Discuss with the students that they can predict how many might be in class today, based on what was learnt in the previous lesson.
Ask: How many are in our class today? How might we find out?
Invite students to offer suggestions for working out ‘how many’. Choose a few data collection methods as a class, carry out the counts and record the number of students present on the board or the class chart.
Ask: What do you notice about the number of students in our class today?
Ask students to suggest reasons for the number being the same or different.
Pose the question: How could you show how many are in our class today, so it is easy for someone from another class to see without having to ask?
Predictions based on evidence
Students are asked to predict how many students are in the class today. To answer this question, students should use the data collected in the previous lesson to inform their answers. Always ask students to share the reasoning from the data for their prediction, as this reinforces the idea that data provides us with evidence. The number of students present may, or may not, be the same as yesterday, so it is important that predictions are expressed with uncertainty.
Students are asked to predict how many students are in the class today. To answer this question, students should use the data collected in the previous lesson to inform their answers. Always ask students to share the reasoning from the data for their prediction, as this reinforces the idea that data provides us with evidence. The number of students present may, or may not, be the same as yesterday, so it is important that predictions are expressed with uncertainty.
Provide each student with a variety of concrete materials and art materials and a sheet of A4 paper.
Ask the students to use the concrete and/or art materials to represent the number of students in the class in a way that makes sense to them.
The number in the class may be higher than some students are able to count. You can count aloud for students as it is helpful for them to hear the number sequence and practice counting. If students find it difficult to represent the larger number, you can ask them to represent a smaller number such as the number of students in their table group.
If students create a physical model, take a photo and/or ask them to draw a picture of their physical representation on their sheet of paper. Ask students to give their representation a title. This title should relate to the story of the data.
Can students invent their own recordings?
When we ask students to invent their own recordings, they have the opportunity to remember and express the story of their experiences, as well as being able to explain the meaning of their representation to others. Asking students to give their recording a title can offer an insight into the meaning it holds for them and the story it expresses.
Students are unlikely to use the conventions of statistical representations as they express their understanding about data through their invented recordings. Yet the representations that students create express meaning for the student who created them as well as for other students.
In the early years, allowing students to record their understanding in their own ways, rather than using more formal conventions, helps them to become comfortable with their data and so their representations hold meaning for them.
When we ask students to invent their own recordings, they have the opportunity to remember and express the story of their experiences, as well as being able to explain the meaning of their representation to others. Asking students to give their recording a title can offer an insight into the meaning it holds for them and the story it expresses.
Students are unlikely to use the conventions of statistical representations as they express their understanding about data through their invented recordings. Yet the representations that students create express meaning for the student who created them as well as for other students.
In the early years, allowing students to record their understanding in their own ways, rather than using more formal conventions, helps them to become comfortable with their data and so their representations hold meaning for them.
Invite some students who have used different representational forms to share their work with the class.
Discuss:
- What did you notice that is different about the representations?
- Students’ representations will look different, and students may have used different materials.
- What did you notice that is similar about the representations?
- Each representation is presenting the same data, that is, the number of students in our class. Each data point is used to represent one student in the class.
- Which representations were you able to see how many easily? Why?
- Allow students to share which ones they found easy to see ‘how many’ and why. Share some that you found easy to see ‘how many’. Highlight features such as accurate recording, organisation and clear connection between the count and the representation.
Discuss how the representations may look different, but they share the same information. Using this data, we can answer the question How many are in our class? for this particular day. We can look back on our representations in the future and know how many were in a class on this particular day.