Statistics: How far can we jump?
View Sequence overviewRepresenting data allows us to make sense of the data, and to use the data as evidence for predictions.
Whole class
How far can we jump PowerPoint
Sticky notes to create a class data display
Each student
Making predictions Student sheet
Lesson
Show students slide 11 of How far can we jump PowerPoint.
Revise: We have a problem to investigate: How far can our class jump? We have a plan of how to find this out. We have collected our data and now we need to represent our data.
Provide the students with a sticky note and ask them to record the length of their longest jump on the sticky note. Ask students to put their sticky notes randomly on the board.
Discuss: We have collected so much data! But it is hard to see what the data is telling us. How could we organise the data to make sense of what the data is telling us?
Allow students to offer suggestions on how the data could be organised.
As a class, reach a consensus and select a way to represent the whole class’s jump data on the board. For example, you might decide to order the sticky notes along a number line to indicate how far students jumped.
Show students slide 11 of How far can we jump PowerPoint.
Explain: We have collected and represented our data and now we need to analyse our data.
Discuss:
- Typically, how far did most students jump?
- The term ‘typically’ introduces the idea of central tendency. To do this, students need to look at the whole dataset, not just the individual data points. Encourage students to think about what is ‘typical’ as a range, rather than a single measurement. Make sure students use evidence from the data.
- Which jumps were not typical?
- Those jumps that lie outside of the ‘typical’ range. There may be some distinct outliers as well.
- If a new student came into our class, how far do you think they might jump?
- Students can think about what is typical to predict how far someone else might jump. Conditional language is important as we do not know how far this hypothetical student will jump. Make sure students use evidence from the data.
Pose the question: How far do you predict a different class might jump?
What is typical?
The questions we ask in this discussion ask students to consider the distribution of the data. Distribution refers to patterns in how data is similar and different from each other. Measures of centre are an important characteristic of distribution. While calculations are used to determine centre in secondary mathematics, the notion of centre informally should be introduced informally in the primary years. Young students can usually visually identify where most of the data sits. As they go through school, children learn other more precise forms of average to compare to what they see visually.
In this discussion, we ask students to reflect on which jumps are “typical”, that is, those jumps that sit in the middle of the data. Representing data allows students to visually see the clumps of data that sit towards the middle, which indicates what is “typical”. The data that lies outside of these clumps at the extremes indicates jumps that were not typical for this dataset. Recognising which jumps are typical and which ones are not typical provide evidence to inform predictions about future jumps.
The questions we ask in this discussion ask students to consider the distribution of the data. Distribution refers to patterns in how data is similar and different from each other. Measures of centre are an important characteristic of distribution. While calculations are used to determine centre in secondary mathematics, the notion of centre informally should be introduced informally in the primary years. Young students can usually visually identify where most of the data sits. As they go through school, children learn other more precise forms of average to compare to what they see visually.
In this discussion, we ask students to reflect on which jumps are “typical”, that is, those jumps that sit in the middle of the data. Representing data allows students to visually see the clumps of data that sit towards the middle, which indicates what is “typical”. The data that lies outside of these clumps at the extremes indicates jumps that were not typical for this dataset. Recognising which jumps are typical and which ones are not typical provide evidence to inform predictions about future jumps.
Provide each student with a copy of Making predictions Student sheet. This sheet poses the following questions:
- How far do you predict another Year 3 class might jump? What makes you say that?
- How far do you predict a Year 1 class might jump? What makes you say that?
- How far do you predict a Year 5 class might jump? What makes you say that?
- How far do you predict the teachers might jump? What makes you say that?
Ask students to get into their groups of 3-4 students. In these groups students need to discuss the questions on the sheet and record their predictions.
Conduct a whole class discussion.
Invite students to share their predictions; they may have made inferences about a number of different classes. They should share the reasoning they used in making these, express them through language of uncertainty, and use evidence to support them.
Save the class data display or take a photo for use in the following lesson.
Can we know for certain?
Making predictions is a natural experience of everyday life, so when students are asked to predict ‘how far might another class jump’ they consider what is likely based on their previous experience of how their own jump data.
Students’ predictions are not expected to be exactly right. A prediction is based on what students think is most likely using their prior experience (e.g., a friend in another class that is the school long jump champion) and the data of the class as evidence.
When students make predictions, encourage the use of conditional language, such as “might”, “possibly” or “likely”. It is important to express uncertainty, as they do not know for certain what will happen. They can only consider what is likely in light of their experience and the evidence of the data on their jumps.
Making predictions is a natural experience of everyday life, so when students are asked to predict ‘how far might another class jump’ they consider what is likely based on their previous experience of how their own jump data.
Students’ predictions are not expected to be exactly right. A prediction is based on what students think is most likely using their prior experience (e.g., a friend in another class that is the school long jump champion) and the data of the class as evidence.
When students make predictions, encourage the use of conditional language, such as “might”, “possibly” or “likely”. It is important to express uncertainty, as they do not know for certain what will happen. They can only consider what is likely in light of their experience and the evidence of the data on their jumps.