Statistics: How far can we jump?
View Sequence overviewVariation is central to statistics. Some sources of variability can be identified and reduced to ensure our data is reliable.
Whole class
How far can we jump? PowerPoint
Open space to jump
Various measurement tools, including metre rulers, tape measures. Also include some unhelpful tools in this context such as protractors, trundle wheels, scales, and measuring jugs.
Each group
Metre rulers and tape measures
Sheet of A3 paper
Sticky notes
Each student
Planning our data collection Student sheet
Task
Revise the problem the class is investigating—How far can students in our class jump? Show students slide 6 of How far can we jump PowerPoint which shows the PPDAC investigation process.
Explain: We now need to plan how we will find this out.
Explain to students that they will work in groups, and that each group will collect data from three jumps each.
Ask students to get into their groups of 3-4 students and provide each student with Planning our data collection Student sheet and ask them to plan to collect the required data. This sheet provides the following list of prompts to help groups plan their investigation:
- What data do we need to collect?
- How will we collect our data?
- What equipment do we need?
- How will we record our data?
Students use these prompts to plan their data collection.
Explain to the students that they will pilot their data collection plan—this means doing a small test run to see if the plan works, and noticing problems and opportunities. Provide students with access to a selection of measuring tools. Allow students to select the tool/s that they plan to use.
Convene the whole class in an open space with enough room for all students to jump, such as the playground or the school hall.
Allow students time to pilot their data collection plan.
Take note of some of the inconsistencies that you notice across the groups in how students are taking their jumps and how they are measuring them. The following Checkpoint focuses on the need to agree on some measurement protocols for all students to use.
Checkpoint: Fair test
Ask: Did you notice any problems or inconsistencies as you tested your data collection plan?
Allow students to share their noticings, and discuss why they think these inconsistencies might impact the data collected. Add any of your own noticings that are not raised by students. Two possible sources of variability that should be discussed include how students are taking their jumps and how they are measuring them. You might also suggest one that doesn’t matter (for example, shoelaces vs Velcro on shoes) to highlight that some differences aren’t an issue, so they have to consider what matters “enough”.
Discuss the differences and how they may impact the outcome. Ask students if they noticed other inconsistencies. They may also bring up inconsequential factors, such as breezes.
Checkpoint
We use a checkpoint here to pause students in the middle of their activity. Everyone pauses and the teacher selects examples of students’ data collection to discuss. This is an opportunity to highlight some common sources of variability to students, where the jump conditions or measuring are inconsistent or done well, as it’s important for the teacher to acknowledge ideas in the right direction. This is an opportunity to maintain momentum, for students to take notice and to refocus to incorporate some of the data collection and recording ideas discussed.
We use a checkpoint here to pause students in the middle of their activity. Everyone pauses and the teacher selects examples of students’ data collection to discuss. This is an opportunity to highlight some common sources of variability to students, where the jump conditions or measuring are inconsistent or done well, as it’s important for the teacher to acknowledge ideas in the right direction. This is an opportunity to maintain momentum, for students to take notice and to refocus to incorporate some of the data collection and recording ideas discussed.
Ask: How should we jump and measure, so we are consistent?
Develop class jumping and measuring protocols. For example:
All jumps must be standing jumps, taking off and landing with two feet together. Jumps will be taken from a jumping line. People must start with their feet behind the line. We will use a measuring tape to measure jumps and we will measure from the jumping line to the back of the foot where the jumper lands.
Record the class jumping and measuring protocols on slide 7 of How far can we jump PowerPoint for later reference.
Sources of variability
Variation sits at the heart of all statistical investigations. In this sequence, the students investigate the question How far can we jump?. The answer to this question is that the distance that students can jump varies. We use this variation to make predictions about what is likely, or what is unlikely.
But what sort of jump are we measuring? It is unlikely that a student who jumps from a standing position with two feet together will jump as far as a student who takes a running leap.
And how are we measuring these jumps? The length of a jump measured from the starting point to the back of the foot at the landing point will be different to measuring the length of the same jump from the starting point to the front of the foot.
These are also sources of variability, and they impact the data we collect in an unhelpful way. These are sources of variability which we can and should control. The point of establishing jump and measurement protocols in this sequence is to emphasise the need to and strategies for effectively controlling unhelpful sources of variability. By doing so, students improve the reliability of their data.
Variation sits at the heart of all statistical investigations. In this sequence, the students investigate the question How far can we jump?. The answer to this question is that the distance that students can jump varies. We use this variation to make predictions about what is likely, or what is unlikely.
But what sort of jump are we measuring? It is unlikely that a student who jumps from a standing position with two feet together will jump as far as a student who takes a running leap.
And how are we measuring these jumps? The length of a jump measured from the starting point to the back of the foot at the landing point will be different to measuring the length of the same jump from the starting point to the front of the foot.
These are also sources of variability, and they impact the data we collect in an unhelpful way. These are sources of variability which we can and should control. The point of establishing jump and measurement protocols in this sequence is to emphasise the need to and strategies for effectively controlling unhelpful sources of variability. By doing so, students improve the reliability of their data.