Funny Numbers
Goals: |
To promote discussion on the importance of zero in decimal notation. |
Year level: |
Year 5 to 8 |
Group size: |
Groups of 3-4 students |
Equipment: |
One pen per group and a recording page.
About 20 cards per group of one colour (say white) and five small
cards of another colour (say blue).
At least one physical model (e.g. LAB) available in classroom for
reference. |
Time: |
20-30 minutes |
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.
|