Mathematics K–6 · Years 3–4
Tenths and hundredths: a flat as one whole
Number and algebra
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The idea
When a flat is one whole, a rod is one tenth and a unit cube is one hundredth, so decimals name parts of a whole in the same base-10 pattern as whole numbers.
What you need
- base-10 materials: 5 flats, 30 rods, 100 unit cubes
- a place-value mat with columns ones, tenths, hundredths and a decimal point card
- 10 by 10 grid squares printed on paper and coloured pencils
- a metre rule marked in centimetres and a 10 cm strip
How to do it
- Agree that one flat is 1. Show that 10 rods cover it exactly and 100 unit cubes cover it exactly, and name a rod one tenth and a unit one hundredth.
- Build 0.35 on the mat with 3 rods and 5 units. Write it as 0.35 and as 35 hundredths. Then build 0.3 and lay it beside 0.35 to compare.
- Colour 0.35 on a grid square, then 0.5 on another, then 0.05 on a third. Order the three by the area coloured.
- On the metre rule, show that 1.5 m is one whole metre and 5 tenths of a metre, and that 1 cm is one hundredth of a metre. Measure a desk and write it in metres to two decimal places.
- Build 1.2 and 1.20 on the mat and say whether they are the same amount.
What you should see
0.35 covers 35 of the 100 small squares and 0.3 covers 30, so 0.35 is larger, which corrects the idea that 0.3 is bigger because it has fewer digits. The coloured grids order 0.05, then 0.35, then 0.5. A desk 1.2 m long reads 1.20 m to two decimal places, and 1.2 and 1.20 are shown by 1 flat and 2 rods both times, the same amount. A 10 cm strip is 0.1 of the metre rule and 1 cm is 0.01 of it.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- 0.3 is larger than 0.35 because a shorter decimal is a bigger piece.
- Adding a zero to the end of a decimal makes it ten times bigger, as it does with whole numbers.
Safety card
Hazards
- none beyond ordinary classroom materials
Controls
- none needed
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.