Activity Instructions:
1. Every group write a decimal point on one blue card,
a zero on two of the blue cards and a non-zero digit on each
of the other blue cards (e.g. blue cards may be 1, 3, 0, 0
and decimal point)
2. Groups write down on white cards as many numbers
as they can using all 4 digits and the decimal point, including
unusual representations (for example: 1.300, 001.3,
0.130, 3.001, 100.3, 3100. etc.).
3. Together, they arrange the numbers on the white
cards in order from smallest (on the left) to largest (on
the right).
Students could be encouraged to settle disputes by using
one of the physical models (LAB or MAB) with which they are
familiar. This activity uses the physical size of the model
to show the effect of zeros in a decimal number.
Issues that may be discussed include:
Is 1300. =1300?
Is 00.13 = 0.130?
Is .3100 = 0.310?
4. In a class discussion formulate some rules about
the columns where zeros change the size of numbers. (Answer:
the decimal point MARKS THE ONES COLUMN, so the zeros that
matter are those that are needed to see which digit is in
the ones column)
Comments:
Some children may be overwhelmed by the number of decimals
to compare and do better if encouraged to compare two at a
time.
Children thoroughly enjoyed this game primarily because of
the discussion it generated. The best discussion occurred
in mixed ability groups and when it was emphasised that everyone
must feel satisfied in their own mind about the order and
could be the one asked to justify it to the larger group.
The value of this game lies not just in the ordering but
in the writing and pronunciation of the decimal numbers.
Teaching Tales:
These excerpts were recorded during our research:
Observing a student writing 3001. he comments 'Does that
make sense?' He had not previously realised that whole
numbers are decimal numbers with zeros after the decimal point.
Watching a reciprocal thinker with a task expert, discussing
whether 0.301 or 0.103 is larger the reciprocal thinker
comments "Well you're chopping it up into 301 pieces
so they're going to be a lot smaller pieces " so he
was thinking that 0.301 is larger. "But 0.301 has 3
tenths and 0.103 only has 1 tenth so 0.301 is bigger,"
rebuts the expert thinker. This dispute was finally resolved
by referring to the LAB model.
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