Line graph problems

Activities to try

1. 1

   Read values and estimate between temperature observations

   Why it works: On this temperature graph, plotted points are observations and the connecting segments provide straight-line estimates between them. Compare rises over equal daily intervals to distinguish change from the temperature at a point.

   1. Use a temperature-over-a-week line graph with observations at the same time each day and equal daily spacing. Slide a ruler, crosshair or finger along a segment to read a straight-line estimate between observations.
   2. Slide between Monday and Tuesday and say aloud the values the line passes through — e.g. 14, 15, 16 degrees — noticing that the line gives estimated in-between values, not only the measured values at the plotted dots.
   3. For each point, trace it back to BOTH axes: finger on the point, drop straight down to the time axis to read the day, then go back to the point and slide horizontally across to the value axis to read the temperature; say the paired coordinate.
   4. Use a 'find the difference' move: mark two points and read the vertical gap between them (e.g. the rise from Tuesday to Wednesday).
   5. Take on the challenge 'Which day did it warm up the MOST?' — then check whether the warmest day (tallest point) is the same as, or different from, the day of the steepest climb.
2. 2

   Separate HEIGHT from CHANGE on one graph

   Why it works: A higher observed temperature is not the same as a bigger increase. Over these equal one-day intervals, the largest rise has the steepest rising segment; with unequal intervals, compare changes and rates separately.

   1. On a single temperature line graph, answer 'Which day was warmest?' (height) and 'Which day did it warm up the most?' (steepest rise) — treat them as two different questions.
   2. Draw a small vertical arrow for the change between each pair of consecutive days, pointing up for a rise and down for a fall, then compare the lengths of the upward arrows to find the biggest rise.
   3. Justify your 'warmed up the most' answer by saying how far the line climbed across that one day, not by which point is highest.
   4. Try a tricky case: a graph where a huge jump happens early in the week and the highest point is reached later by only a small rise, so the tallest point and the steepest segment are clearly on different days — identify each.
3. 3

   Read the data, between the data, and beyond the data

   Why it works: Graph comprehension has a progression — you must read a value before you can compare, combine or find differences between values, and only then predict or infer — and naming which you are doing clarifies the task.

   1. Read the data: lift a single value straight off a marked point (e.g. the warmest day's temperature).
   2. Read between the data: compare two observed values, find their difference, and combine values only where the quantity makes a meaningful total, such as rainfall totals for March and May. Do not add daily temperatures as if they were a total temperature. On a temperature line graph, separately estimate an intermediate value under the straight-line assumption.
   3. Read beyond the data: hide the final plotted day (e.g. Friday on a Monday-to-Friday graph), predict and place it from the earlier trend, then reveal the real value and compare — discuss why the prediction may differ.
   4. Each time, name which kind of reading you are doing: reading a value, reading between, or predicting.