Mathematics K–6 · Years 5–6
Thousandths: decimals on a metre and a zooming number line
Number and algebra
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The idea
A millimetre is one thousandth of a metre, so decimals with three places are lengths on a metre rule and are ordered by looking at each place in turn.
Safety card
Hazards
- jumping and landing
- tape measure on the ground
Controls
- jump onto sand or a mat; keep the tape flat and out of the landing area
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.
What you need
- a metre rule marked in millimetres and a tape measure
- a set of decimal cards: 0.3, 0.25, 0.205, 1.2, 1.02, 1.002, 2.345
- a long-jump pit or a gym mat to land on, a masking-tape take-off line and a marker
- a recording sheet
How to do it
- Find 0.3 m, 0.25 m and 0.205 m on the metre rule and mark each with a sticky note. Read them as centimetres and millimetres.
- Order the decimal cards from smallest to largest, then check each against the rule or the tape.
- Each child does three standing long jumps and measures each to the nearest centimetre, recording in metres with two decimal places. Then measure the width of a desk on the metre rule to the nearest millimetre and record it in metres with three decimal places.
- Order the class jumps and find the longest and the shortest. Work out the difference between them in metres and in millimetres.
- Show 2.345 m on the tape as 2 m, 34 cm and 5 mm, then write it as 2345 mm.
What you should see
0.3 m is 300 mm, 0.25 m is 250 mm and 0.205 m is 205 mm, so the order is 0.205, 0.25, 0.3, which corrects the claim that 0.205 is largest because it has the most digits. The card order is 0.205, 0.25, 0.3, 1.002, 1.02, 1.2, 2.345. Jumps recorded as 1.37 m and 1.40 m differ by 0.03 m, which is 30 mm, and two jumps recorded as 1.4 and 1.40 m are the same length. A landing mark in sand or on a mat cannot be read to the millimetre, so jumps are recorded to the centimetre, while a desk edge against the metre rule can be read to the millimetre and recorded with three decimal places. 2.345 m is 2345 mm.
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.
- A decimal with more digits is a bigger number.
- 1.40 is ten times 1.4.
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.