Optimal velocity
This is a level 3 statistics activity from the Figure It Out series. It is focused on showing data on a graph and making a conclusion from the data. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Show data on a graph.
- Make a conclusion from the data.
Optimal velocity
Achievement objectives
S3-1: Conduct investigations using the statistical enquiry cycle: gathering, sorting, and displaying multivariate category and wholenumber data and simple time-series data to answer questions; identifying patterns and trends in context, within and between data sets;communicating findings, using data displays.
S3-2: Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.
Description of mathematics
This diagram shows the areas of statistics involved in this activity.
Statistical investigation |
Statistical literacy |
Probability |
||||
P |
P |
D |
A |
C |
||
The bottom half of the diagram represents the 5 stages of the statistics investigation cycle, PPDAC (problem, plan, data, analysis, conclusion).
Statistical ideas
"Optimal velocity" involves the following statistical ideas: interpreting bar graphs, using graphs such as scatter plots for analysis, and using statistics to make decisions.
Required materials
- Figure It Out, Levels 3+ -4, Statistics in the Media, "Optimal Velocity", page 16
- game results (see Optimal velocity CM)
- a computer spreadsheet/graphing program (optional)
- a classmate
See Materials that come with this resource to download:
- Optimal velocity activity (.pdf)
- Optimal velocity CM (.pdf)
Activity
Discuss with your students popular computer games that they play. Statistics for the games they play may be available online. The students may find it interesting to analyse these after they have looked at the comparatively simple context in the students’ book.
For question 1, you may need to discuss with the students what is meant by handling and what effects good handling, acceleration, or speed have on the ability to race well.
For question 2, it is diffi cult to analyse the race times if they are considered just as a string of numbers. Encourage the students to use graphs to help paint a picture. Scatter plots like those in the Answers work well for this activity. The students will need to separate the times for the three different track types to see any pattern, either with separate graphs (as in the Answers) or by using different colours or symbols.
Extension
Students who have access to and/or interest in a game that gives times or points for performance may be interested in investigating how environmental distractions affect their performance.
You could challenge the students to design an experiment or a “fair test”. Suggest that they limit themselves to two variables (for example, silence or loud music while playing the game). They will also need to repeat the experiment under the same conditions a number of times for results to be more reliable.
The students may like to look at some statistics of real cars and discuss what features are important in a decision to buy a car, for example: cost, comfort, reliability, safety, and appearance. A good starting point for this is the free advice available on Consumer NZ (look under cars, car buying guide). The students could also discuss which features are important for a family car as opposed to a racing car.
Activity 1
1.
a. Drag strip: car 4 because it accelerates fast and has top equal speed.
b. Hill climb: car 2 because it handles well and accelerates well.
c. Circuit: car 1 because it handles well and has top equal speed.
2.
a. Graphs will vary. For example (with times converted to seconds):
b. Your graphs should show that Nick’s times improve for the fi rst few races on each track and then remain relatively constant. The times stay low after 10 races, which suggests that he had reached a plateau in terms of his ability to operate the cars.
c. Variables that you might take into account could include time of day, whether anyone is watching Nick, or the noise level around him. These could all affect his progress.
"Optimal velocity" can be used to develop these key competencies:
- thinking: interpreting, exploring, and using patterns and relationships in data, making decisions
- using language, symbols, and texts: interpreting visual representations such as graphs.
The quality of the images on this page may vary depending on the device you are using.