Statistics: How many are we?
View Sequence overviewWe collect data to answer questions.
Each student
Sheet of A4 paper
Lesson
Convene a whole class discussion. Ask: What questions can we ask about our class?
Allow students to share suggestions. Some suggestions you might discuss include:
- how students got to school today.
- what students like to do at lunchtime.
- what activities students do after school.
Pose the question: One question I want to ask is: How many are in our class today? How could we find out how many we are?
Using daily routines
Daily tasks can be used to embed informal statistical inference within the routine of the early years classroom. Prediction and estimation are fundamental to statistics and can be experienced through everyday routines.
Students can be encouraged to predict what they think might happen next, or what they think a character is likely to do based on the story so far. When students have the opportunity to go beyond what is in the story to anticipate what they think might happen, they are using inference. Predicting from stories provides a context for students to engage in inferential reasoning which may then be transferable to reasoning in statistics.
Daily tasks can be used to embed informal statistical inference within the routine of the early years classroom. Prediction and estimation are fundamental to statistics and can be experienced through everyday routines.
Students can be encouraged to predict what they think might happen next, or what they think a character is likely to do based on the story so far. When students have the opportunity to go beyond what is in the story to anticipate what they think might happen, they are using inference. Predicting from stories provides a context for students to engage in inferential reasoning which may then be transferable to reasoning in statistics.
Invite students to talk with a partner about how the class could find out how many there are in the class today. Provide students with some paper and ask them to draw a picture of how we could work out how many there are in the class today.
- Do students recognise the need to count to determine ‘how many’?
- Students may not immediately realise that counting is the best way to determine how many. For example, they may suggest strategies such as having students line up or calling out names on the roll as ways to work out how many. You might have a go at some of these strategies and note anything useful that comes from the strategies. For example, lining students up is a helpful organisational tool, but it doesn’t tell us how many.
- Can students suggest systematic ways of counting?
- Do students consider ways of organising the count (i.e. the students) so that the data can be reliably collected? For example, students may suggest counting everyone in the class, but if everyone is the class is wandering around then it is hard to know if each person has been counted. Challenge students to consider how they will organise the data (students) so they can count all.
Invite students to share their plan with the class. Discuss the different plans suggested by students.
Discuss: How are the plans similar and how are they different?
- The plans may suggest counting as a way to find out ‘how many’. The differences between the plans may be the counting methods used.
Explain: It seems that counting could be a good way to work out ‘how many’.
Select one or two methods shared and use them to determine how many there are today. Choose methods that do not keep track of who has been counted, as we want to establish with the students that we need to be organised to ensure we have counted everyone.
Discuss:
- Did we count everyone just once? How do we know?
- Establish with the students the need to keep track of the count.
- We need to make sure that we keep track and count all the data. How could we make sure we have counted everyone who is here?
- Ask students if they can think of other suggestions for keeping track of the count. These can be added to the chart. Some helpful strategies might include:
- students stand up or sit down as they are counted.
- students each have a block/counter, and these are collected and counted to find the total.
- students each record a mark on the board and then the class counts the marks.
- Ask students if they can think of other suggestions for keeping track of the count. These can be added to the chart. Some helpful strategies might include:
Ask: I wonder if we would get the same number of students if we followed a different plan for collecting our data?
Invite student responses and encourage students to provide reasons for their answers.
Select one of the other data collection methods, conduct the count and record the results. Repeat the count again with a different method.
Explain: We have collected our data using some different methods. Each time we got the same result.
Trusting the count
In Foundation, most students are still learning to “trust the count”. Siemon and colleagues (2021) explain that trusting the count involves:
- counting to find “how many”.
- access to a range of mental objects for numbers to 10.
- recognising that counting the same collection again will produce the same result.
Giving students opportunities to count the class using multiple strategies helps them to see that, no matter how members of the class are arranged or counted, the final number is the same each time. This idea is known as conservation of number, which is powerful idea in counting.
In Foundation, most students are still learning to “trust the count”. Siemon and colleagues (2021) explain that trusting the count involves:
- counting to find “how many”.
- access to a range of mental objects for numbers to 10.
- recognising that counting the same collection again will produce the same result.
Giving students opportunities to count the class using multiple strategies helps them to see that, no matter how members of the class are arranged or counted, the final number is the same each time. This idea is known as conservation of number, which is powerful idea in counting.