Halves and quarters (age 8+)

Activities to try

1. 1

   Measure to the nearest quarter and build the fractional scale

   Why it works: The subdivision on the ruler and the subdivision on the plot's axis are the same partition of one unit into equal quarters; a measured length maps to a position on an equal-interval scale, and ½ = 2/4 is one position, not two.

   1. Measure a set of ribbons or objects (about 5–6) against a ruler whose quarter-inch ticks are clearly marked and, at first, labelled with their fraction values (¼, ½, ¾).
   2. For each object, name the quarter inch it rounds to out loud or in writing — e.g. 'this one is 2¾ inches', not 'the third line'; for one or two objects, also name the nearest half inch and notice that the two answers can be different.
   3. Using the ruler to mark it, draw a number line at true scale (1 inch per whole number) that covers every measured length, and partition it into equal quarters between the whole numbers, so the marks run e.g. 2, 2¼, 2½, 2¾, 3 in correct order and with equal spacing.
   4. Place one X per object at its fractional value on the line.
   5. Align the ruler directly under the true-scale plot, with the ruler's whole-inch marks under the matching whole numbers on the axis, so each ¼ tick on the ruler sits beneath the matching ¼ mark on the axis.
2. 2

   Separate frequency from length

   Why it works: On a line plot the horizontal axis position is the measured value, while the height of a stack of Xs is how many objects share that value — these are two different quantities.

   1. On a completed fractional line plot, point to the axis position that gives an object's LENGTH and separately count the stacked Xs that give the FREQUENCY at that length.
   2. Answer paired questions: 'How long is this object?' (read axis) versus 'How many objects were this long?' (count the stack).
   3. Explain in your own words why a taller stack does not mean a longer object.
3. 3

   Interpret and order a given fractional plot

   Why it works: A correctly built fractional scale can be read for order, counts, and comparisons, and equivalent fractions occupy the same position.

   1. Given a finished fractional line plot, order the marked values 2¼, 2½, 2¾ from least to greatest.
   2. Count how many objects fall at a given value (e.g. 'how many were 2½?').
   3. Compare: how many objects were shorter than 2½, and how many were longer.
   4. Confirm that 2½ and 2 2/4 name the same position on the scale (because ½ = 2/4).