Funny Numbers

1. Using the blue cards, every group writes a decimal point on one card, a zero on two of the cards and a non-zero digit on each of the other cards (eg 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 (MAB or linear arithmetic blocks) 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 discussion, consolidate the conclusions by formulating some rules about the columns where zeros change the size of numbers. (For example: 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 students may be overwhelmed by the number of decimals to compare and do better if encouraged to compare two at a time.

Students enjoy this game primarily because of the discussion it generates. The best discussion occurs in mixed ability groups and when it is 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 later.

The value of this game lies not just in the ordering but in the writing and reading of the decimal numbers.

Teaching Tales:

After a student wrote 3001., he asked 'Does that make sense?' This led to a fruitful discussion about whether this was a whole number or a decimal number. He had not previously realised that whole numbers are decimal numbers with zeros after the decimal point.

Two students were discussing whether 0.301 or 0.103 is larger, when one comments "But 0.301 has 3 tenths and 0.103 only has 1 tenth so 0.301 is bigger". This dispute was finally resolved by referring to a physical model for decimal numbers (in this case, linear arithmetic blocks).

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These activities are published with permission from Steinle, V., Stacey, K. & Chambers, D. (2006) Teaching and Learning about Decimals. (Version 3.1 ) Faculty of Education, University of Melbourne . (CD-ROM). See also http://extranet.edfac.unimelb.edu.au/DSME/decimals