Tables, charts, and graphs

For ages 12–13, learners work both directions on paired continuous data: they interpret what a line shows (a straight line indicates a constant-rate/linear relationship, and one through the origin — as in this spring data — is additionally proportional) AND construct the representation — a headed data table with ratio-form SI units, a graph type chosen from the data structure, accurately plotted points on evenly-scaled labelled axes, a single line of best fit, and a gradient read from two points on that line with its compound unit. The load-bearing work is construction with feedback at each step; recognition and value-reading tasks test the skill but do not themselves have the learner construct a table and graph from scratch. A spring extension vs load dataset makes the gradient a meaningful physical quantity (extension per unit load, in cm/N; this is the inverse of the spring's stiffness, which is load ÷ extension in N/cm).

• Joining data points dot-to-dot and calling it a line graph, instead of drawing a single best-fit line.
• Believing the line of best fit must pass through every point or always through the origin.
• Reading the gradient from raw data points rather than from two points on the drawn line.
• Choosing a bar chart when both variables are continuous (so the trend/relationship is lost).
• Omitting units from table headings and axis labels, or writing them inside every cell instead of in the heading.
• Using a non-uniform, cramped or origin-forced scale that distorts or hides the pattern.
• Quoting a gradient as a bare number with no unit, treating it as dimensionless.

• Headed data table with ratio-form units, e.g. column 'Mass / g' | 'Extension / mm'
• The graph-type decision tree: categoric IV → bar chart; continuous IV → line graph; two continuous measures → scatter graph
• Labelled, evenly-scaled x–y axes (IV on x, DV on y) with a 'sensible scale' fraction-of-grid heuristic
• Line of best fit balancing points above and below, with a right-angled 'rise/run' triangle drawn on it
• Gradient as rise ÷ run carrying compound units (e.g. mm/g), read from two points on the line

• Teach the data structure first, then the display: decide whether the independent variable is categoric (→ bar chart) or continuous (→ line/scatter) BEFORE drawing anything, so graph choice is a reasoned decision not a habit.
• Require the ratio-form unit in every heading and on every axis (e.g. 'Mass / g'), so the numbers in cells and on axes are pure and unambiguous — model it explicitly and mark it every time.
• Explicitly teach scale choice as a design decision: axes should use at least half the available grid with a sensible interval (1, 2, 5, 10), and demonstrate side-by-side how a squashed or awkward scale hides a trend.
• Contrast a line of best fit with a dot-to-dot join: show that best fit summarises the trend and averages out scatter, deliberately need NOT pass through every point (or the origin), and enables reading between data.
• Read the gradient from two widely-separated points ON the line, not from raw data, and always attach the compound unit — practise the rise÷run with the units carried through the calculation.
• Use real experimental data the child has a stake in (e.g. spring extension vs mass, cooling curves) so the gradient means something physical rather than being an abstract exercise.