Proportion Graphs

Activities to try

1. 1

   Linked board: one rate, three views that move together

   Why it works: All three representations encode the SAME constant multiplier, and the origin — not mere straightness — is the test of proportionality.

   1. Enter or accept a rate such as 3 kg → £6 and watch a ratio table, a double number line, and a coordinate graph populate for the SAME example.
   2. Plot the proportional pairs on the graph and draw the line; confirm it passes through the origin.
   3. Drag a point to 5 kg and read £10 simultaneously on the table, the number line, and the graph.
   4. Point to where the constant '×2' appears in each view: the gradient of the line (£2 per kg), the multiplier from each kg entry to its £ entry in the table (3 → 6, 5 → 10), and the factor linking each pair of matching marks on the double number line (1 kg ↔ £2, 3 kg ↔ £6).
   5. Flip a 'fixed charge' toggle (e.g. add a standing £2) and observe the whole line lift OFF the origin while staying perfectly straight; state whether it is still proportional and why not.
2. 2

   Annotated proportion graph: reveal the origin, the rate, and a read-off

   Why it works: The recognition cues of a proportional graph are the origin crossing and a single constant rate; a straight line that misses the origin is a direct counterexample to 'straight means proportional'.

   1. Examine a proportion graph and reveal, at the origin, that 'at 0 kg, cost is £0'.
   2. Reveal along the line the constant multiplier (the rate, e.g. £2/kg).
   3. Reveal at a chosen point its read-off (e.g. 5 kg → £10).
   4. Compare a companion line that is straight but does NOT pass through the origin (a fixed £2 charge plus £2/kg) and decide, with reasons, that it is not proportional.
3. 3

   Identify, read, and produce proportional lines

   Why it works: Interpreting a point, interpolating an unknown, and independently producing an origin-anchored line together show whether the learner sees the graph as a constant-multiplier relationship rather than a picture.

   1. Choose which of several graphs shows direct proportion, where a straight not-through-origin line is a deliberate trap.
   2. Given a ratio table, plot the points and draw the matching line through the origin.
   3. Read an unknown off a line through (3,6) (e.g. find the cost of 5 kg → £10), stating which axis you read up from and which you read across to.
   4. On the same axes, DRAW a line for a DIFFERENT fruit's price: note that a £2/kg fruit would COINCIDE with the given £2/kg line through (3,6), whereas a shallower £1/kg line passes through (3,3) — and check your line is anchored at the origin.