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# Activity: 100m sprint times

## Purpose

Students will investigate the progression of 100m sprint world record times since the start of the 20th century.

## Achievement objectives

• NA6-7 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
• NA6-8 Relate rate of change to the gradient of a graph.
• S6-1 Plan and conduct investigations using the statistical enquiry cycle:
• Identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays.
• Justifying findings, using displays and measures.

## Indicators

• Makes connections between representations such as number patterns, spatial patterns, tables, equations and graphs.
• Identifies and uses key features including gradient, intercepts, vertex, and symmetry.
• Calculates average rate of change for the given data.
• Relates average rates of change to the gradient of lines joining two points on the graph of linear, quadratic, or exponential functions.

## Specific learning outcomes

Students will be able to:

• plot points and spot trends in the progression of 100m sprint times
• question, validate and critique the data they are using
• describe what is happening in particular time segments to the 100m sprint times, for example, statements like 'the world record time is reducing by x seconds per y time period'.

## Diagnostic snapshot(s)

Students plot (x,y) coordinates using suitable linear scale:

 X2561525 Y1519223055

## Planned learning experiences

Source 100m world record times and provide these for students (or get the students to source them from the Internet).

• Students plot the 100m times and join the points and then a ‘best fit’ curve.
• Students investigate the data by asking questions such as:
• What’s the overall trend?
• What could happen eventually with the 100m sprint times?
• What is more likely to happen? How can we ‘prove’ this?
• What are the differences between men’s and women’s ‘curves’?
• Using decade long periods, by how much do the times reduce on average?

Other investigations include:

• Students plotting the differences to see the non-linearity of the progression.
• Equation of line of best fit (linear) and using this to interpolate and extrapolate by using substitution.

• There is scope to introduce non linear curves.
• Use of difference scales and investigate the non-changing gradient but perhaps different conclusions ('the eyes have it').
• Investigate other sports whose progression is characterised by other ‘decreases’ over time (skiing, marathon etc) or increases (long jump, highest cricket test score etc).
• Students could run 100m and compare their times with the early 20th century times.

There is a strong link to history (for example, Jesse Owens, 1936) and physical education (the anatomical reasons behind the progression of 100m sprint times).

## Planned assessment

This teaching and learning activity could lead towards assessment in the following achievement standards:

## Spotlight on

### Pedagogy

• Encouraging reflective thought and action:
• Supporting students to explain and articulate their thinking.
• Making connections to prior learning and experience:
• Checking prior knowledge using a variety of diagnostic strategies.
• Teaching as inquiry:
• What are next steps for learning?

### Key competencies

• Thinking:
• Students explore and use patterns and relationships in data and they predict and envision outcomes.
• Using language, symbols and text:
• Students interpret visual representations such as graphs.
• Managing self:
• Students develop skills of independent learning.

### Values and principles

• Students will be encouraged to value innovation, inquiry, and curiosity, by thinking critically, creatively, and reflectively.