Tenths (age 9+)

Activities to try

1. 1

   Zoom the number line to place 0.345

   Why it works: A thousandth is a tenth of the gap between two hundredths; the number line never 'runs out' — you can always subdivide one more time by ten to locate a finer value (a tenth of a thousandth is a ten-thousandth).

   1. Start with a number line showing just 0.34 and 0.35, with nothing marked between them, and predict aloud roughly where 0.345 should go.
   2. Zoom into the gap between 0.34 and 0.35 and divide it into ten equal steps; name what each single step is worth (one thousandth, a tenth of the gap between two hundredths).
   3. Count the steps and place 0.345 exactly on the fifth mark (the midpoint of the gap), then state why: it is 5 thousandths past 0.34.
   4. Repeat the zoom-and-split for another thousandth, e.g. place 0.347, so the subdivision becomes a repeatable action, not a one-off.
   5. Extend the action one level further: split a single thousandth into ten equal parts and name each tinier piece a ten-thousandth, illustrating that the ÷10 subdivision can always be repeated again.
2. 2

   Split a hundredth and compare sizes to break whole-number bias

   Why it works: More, smaller parts means each part is smaller: a thousandth is smaller than a hundredth despite 1000 > 100, overturning 'bigger denominator, bigger part'.

   1. Before comparing, predict which is bigger, one hundredth or one thousandth, and say WHY in words.
   2. Take one hundredth and split it into ten equal parts; identify each part as one thousandth.
   3. Lay a single thousandth beside a whole hundredth and describe what you see — the thousandth is tiny next to the hundredth.
   4. Reconcile this with your prediction: even though 1000 is a bigger number than 100, a thousandth is a smaller amount because it comes from cutting into more, smaller parts.
   5. Compare 0.05 and 0.005 directly and state which is bigger and why, when both use the digit 5.
3. 3

   Write thousandths and justify the placeholder zero

   Why it works: The place a value occupies, not just the digits, fixes the written decimal; the placeholder zero in 0.025 holds the empty tenths position so the 2 lands in hundredths and the 5 in thousandths.

   1. Using a place-value chart with columns ones | tenths | hundredths | thousandths, write 25 thousandths: place the 2 in hundredths and the 5 in thousandths.
   2. Fill the empty tenths column with a 0 and write the decimal 0.025, then explain that the zero holds the empty tenths place.
   3. Contrast the set 25/10 = 2.5, 25/100 = 0.25, 25/1000 = 0.025, and describe how the place of the value decides where the digits land and how many leading places are filled.
   4. Write a second example, e.g. 35 thousandths = 35/1000 = 0.035, and say why there is one placeholder zero straight after the decimal point (in the tenths place).