ACARA v9 CONTENT DESCRIPTION “construct and use appropriate representations, including tables, graphs and visual or physical models, to organise and process data and information and describe patterns, trends and relationships”
Builds on putting readings into a table and drawing a simple graph. Here the work is to choose the right representation for the question: a table, a graph and a visual or physical model each hold the same data, but a good choice lets a trend describe itself while a poor one buries it. The dataset is one day of shadow measurements with a clear rise-fall-rise trend.
One shadow, measured all day
You push a straight stick into the ground in an open, sunny spot and measure the length of its shadow every two hours from 8 am to 4 pm. The Sun climbs high near midday and sinks toward each end of the day, so the shadow is long in the early morning, short near midday, and long again in the late afternoon. By themselves the five numbers are easy to lose, so your first job is to organise them. A table does that: each time of day sits beside the length you measured. From that one tidy table you can build a graph and a model that make the trend easy to describe.
Put the shadow lengths in a table, then draw the graph
Here is the shadow length at each time of day. Read the table, then switch to the line graph to see the same centimetres as a shape across the day.
Same data, two representations. The table keeps each time of day beside its own shadow length. The line graph joins those readings in order, and the shape dips to a low near midday and rises at both ends, so the rise-fall-rise trend is easy to describe at a glance.
Reading the trend in the line
A line graph is more than a tidy picture. Because the readings are taken in time order, the line shows how the shadow changes through the day. It starts high at 8 am, falls to its lowest point near midday, then climbs again to 4 pm. Naming that movement is describing a trend, and the trend points to a relationship: the higher the Sun climbs, the shorter the shadow. A bar chart would show the same five numbers, but the line is the better choice here because it makes the smooth rise and fall over time stand out.
Build a physical model of the shadow, step by step
A visual or physical model shows the same data in a form you can see and act out. Add each time of day in turn and watch the picture of the trend build up.
New evidence (1 of 4)
Stand a short dowel on a board and shine a torch low from the side, like the early Sun. The shadow stretches long across the board, marked 64 cm.
Accepted model: Early in the day the Sun is low and the shadow is long, the largest reading on the board.
Add the next piece of evidence and watch whether the accepted model holds or has to change.
Find the reading that breaks the trend
When a representation is built well, a value that does not belong stands out. Suppose on a second day you measure the shadow each hour and one reading sits far above the smooth rise and fall. On the graph that point juts away from the line of its neighbours. A reading that breaks the trend is not proof the whole day is ruined; it is a signal to check that measurement, perhaps the stick was knocked, before you describe the trend.
Find the shadow length that does not fit
Shadow lengths were measured hour by hour through one day and should fall to a midday low then rise again. One reading does not fit the smooth trend. Click the point that breaks it.
Click the point that does not fit the pattern of the others.
Which descriptions read the trend correctly?
Choosing a good representation is only half the skill; you also have to read it honestly. A correct description names the trend the data really shows, the long-short-long shape and the relationship between Sun height and shadow length. A careless one misreads the graph, claims a flat line, or invents a pattern that is not there. Telling a true reading of the trend apart from a misreading is how you make the representation do its job.
Which statements describe the shadow trend correctly?
The table, graph and model all show the same day of shadow lengths. Decide which statements describe the pattern, trend and relationship correctly, and which misread the data.
Claim: The shadow is long in the morning and afternoon and shortest near midday, because the higher the Sun climbs, the shorter the shadow.
The graph falls to a low near midday and rises again toward the end of the day.
The shortest shadow lines up with the time the Sun is highest, near midday.
As the Sun gets higher through the morning, the shadow gets shorter.
The shadow length stays flat all day and never really changes.
The shadow is longest at midday and shortest at the start and end of the day.
Decide whether each statement is evidence for the claim, or not.
Why it matters
Tables, graphs and visual or physical models are the tools you reach for whenever you have data to make sense of. A table organises what you measured, a graph lets a trend and a relationship show themselves, and a model makes the same story something you can see and act out. Learning to choose the representation that fits the question, and to describe the pattern it reveals honestly, is how a young scientist turns a column of numbers into understanding.
Quick self-check
1. You measured a stick shadow once every two hours through the day. Which representation organises those readings first?
2. You turn the table of shadow lengths into a line graph. Why is the line graph a good choice here?
3. On the line graph the shadow is long at 8 am, shortest near midday, then long again at 4 pm. This describes a...
4. A physical model places a stick in sunlight and lets you watch its real shadow swing and shrink. What does this model add to the table and graph?
5. One length on the graph sits far above the smooth rise and fall. Before describing the trend you should...