Scaled picture and bar graphs

Activities to try

1. 1

   Flip the scale: watch the same bars change value

   Why it works: A bar's or symbol's size maps to a value only via the scale; changing the scale re-maps every value, and a sensible scale (e.g. 2, 5 or 10) makes the largest value fit with equal intervals.

   1. Draw bars for a small data set on squared paper where 'each square = 1'.
   2. Then change the key to 'each square = 5' and re-read every bar: say what each bar now means (e.g. a 4-square bar is now 20, not 4).
   3. State out loud: 'The height on its own doesn't tell me the value — I only know the value once I read it through the scale.'
   4. Optional with an interactive scaled-graph builder: use a scale selector (each square = 2/5/10) that re-labels the axis live, so the same drawn bars instantly re-map to new values.
   5. Choose a sensible scale (e.g. 2, 5 or 10) for a given data set so the largest value fits, mark the axis in equally spaced intervals, and explain why that scale works.
2. 2

   Reading values between the marks

   Why it works: Part-symbols and bar tops between gridlines carry real values: a half-symbol is half the key, and you read between gridlines by counting the scale's sub-intervals rather than rounding to the nearest line.

   1. Read a scaled pictogram with a stated key (e.g. one symbol = 10 children) that includes half-symbols, and give the value of a row ending in a half-symbol: a half-symbol is half the key (with a key of 10 that is 5). Note that with a key of 5 a half-symbol is 2½, which is why pictograms are usually built with an even key so half-symbols land on whole numbers.
   2. Read a scaled bar whose top reaches a specific sub-interval mark between two gridlines — e.g. a bar reaching the 13 mark between the 10 and 15 lines — and state its value by counting the scale's sub-intervals. Separately, note that a bar sitting exactly at the midpoint of 10 and 15 reads as 12½, not a whole number.
   3. Optional with draggable part-symbols or a draggable bar top: hit an exact intermediate value and check it against the key by counting sub-intervals.
3. 3

   Two-step problems as two reads then combine

   Why it works: The two-step data problems here are two reads followed by one combine (sum or difference); naming both steps helps prevent collapsing it to a single glance or using the wrong operation.

   1. From a scaled graph, answer a 'how many more' comparison (e.g. how many more chose football than tennis?) by reading each value through the key and finding the difference.
   2. Solve a two-step problem such as 'how many altogether for the top two choices?' by first reading each of the two values separately, then deciding whether to add or subtract, then doing it.
   3. Say the two steps aloud before answering: 'First I read these two values; then I [add/subtract] them.'
   4. Optional with a question panel that shades each bar as it is read before combining, so the two reads are visible as two distinct actions rather than one glance.