# Running styles

**This task is about reading information off a graph.**

Y8 (05/2008) |
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a) b) c) d) |
1. Hemi started slowly, and then sped up (increased speed) near the end. 2. Miro ran at a constant speed throughout the race. 3. James started quickly, and then slowed (reduced speed) toward the end. 4. Pania ran fast at the start, stopped for a bit, then ran a bit slower to finish |
easy moderate moderate moderate |

Based on a representative sample of 222 Y8 students.

NOTE: A correct answer involves students identifying the movement toward a point (finish line) and the variation (or not) of speed.

**Graphs and the Curriculum**

- Both algebra and statistics produce graphs similar to the one in this resource. The fundamental difference between the two is that an algebraic graph is based on a rule which gives exact values, whereas statistical graphs are based on data which is intrinsically variable in nature. In real life, most relationships are statistical, but some have such a small amount of variation that they can be used as algebraic for practical purposes.
- Science investigations produce data for statistical graphs, many of which are very close to algebraic in the sense that a smooth curve almost exactly fits through them (for example, see The stretch of a rubber band, Beneath the surface, Light and photosynthesis and Boiling meths).

**Key competencies**

This resource could be useful for exploring the key competency Using language, symbols, and text by:

- Exploring the axes (distance and time) and how they affect the line used to represent the runner.
- Looking at start of graph, breaking into smaller parts to interpret what the change in slope actually mean.

See * Next steps* for further details.

In part d), nearly 20% of students did not recognise that Pania had stopped for part of the time. Interestingly, the context of running a race appeared to help students' understanding of what the graph represented. For example, Pania's run which involved interpreting a flat horizontal line ("stop") paralleled a similar resource of a distance-time graph of a motion of a car. In the latter resource Y8 students found the questions difficult, and considerably higher proportion did not recognise the "stop".

**Interpreting the graph symbolically**

For students who interpret the graph symbolically, it may be helpful to also talk about the difference between these line graphs and the locus (actual paths of motion) with some examples. Simply put, this is a graphic representation with distance and time, whereas a locus would be a simple motion pathway that only shows motion, not speed. They may also need experiences of interpreting the slope of the graph (see below).

**Difficulty explaining what the graphs were representing**

For students who could not explain what the graphs were representing, it may be helpful to step through points on the graph referring to the meaning of the axis labels. Asking about distance, and the change of distance over time may help them build an understanding. For example, using James's running in Graph 1 you could divide the graph into 3 even parts (vertical lines) and identify how much distance was covered for each part, then ask the students to explain the difference. Further scaffolding could be given by explaining what it means to cover more distance in the same period of time (go faster). This should help students identify that the graphs are about speed (distance over time), and that the varying slopes of the line indicates variation of speed.

For resources that look at interpreting different points along graphs of this sort see Hare's progress, Hemi's bike trip, and Climbing the wall).

**Exploring plots on a graph**

- Plot some graphs of how far people have travelled from a table of values (see Crawling spider, Foreign currency exchange, Bike repairs, and Hare's progress) and then discuss the meaning of the slope of the graph.
- Get the students to physically "act out" the journeys in an open space such as a hall or a playground.

**Other resources**

For similar ARB resources see Jonathan's journey to school, Crawling spider, Hare's progress and Getting to school.

Read more about graphs (and tables) across the curriculum in this article.