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Activity Instructions:
1. Prominently write these correspondences for MAB on the
board:
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large cube = one
flat = tenth
long = hundredth
mini cube = thousandth |
2. Each student is given a card with a decimal number on
it and asked to make the number out of blocks. Ask them not to show
their card to others. Use the numbers in the tables below so that
not too many blocks are needed.
3. Students put their set of blocks on a piece of A4 paper
or card (simply to keep the set together) and arrange their blocks
(on their paper) in a long line across the floor/bench with the
smallest TOTAL VOLUME on the left and largest on the right. (The
card with the decimal number can be placed face down on the paper.)
Discussion should arise about what to do when 2 students have the
same blocks (e.g. 0.2 and 0.20).
4. When the ordering is complete, teacher and class decide
what the decimal number on each card could be and then turn the
card face up. Discuss the prevalent decimal misconceptions e.g.
"longer decimals are larger" and "shorter decimals are larger" using
examples from the line to disprove both statements.
5. Collect all materials and then redistribute the decimal
number cards to different students. Ask them to arrange in order
as before without using the blocks.
Variations:
Each student could choose a set of up to three blocks from the
class MAB sets. Students then place their set on a piece of A4 paper,
with their name. These are then ordered ACCORDING TO THE VOLUME
OF THE BLOCKS (smallest on left and largest on right) before
students assign a decimal number to their own blocks using the above
definitions. Discussion should arise on the multiple names possible
for the same block (e.g. 0.2, 0.20, 0.200).
Moving Closer (summary): Five different
decimal numbers are produced by the teacher using the MAB and labelled
from A to E. Students stand at a distance e.g. 10m and look
at the blocks briefly. They then make a decision as
to the largest and the smallest number as well as an estimate
of what the numbers may be. This is recorded in a table. The
students then step closer e.g. 5m and see if would like to change
their predictions. Finally, as the students come closer still e.g.
2m, they order all of the blocks in their correct order. The
decimal numbers are then revealed and compared to the blocks.
Comments:
Whichever way the activity is run (teacher hands out cards OR students
choose their own blocks to make a number) the ordering is firstly
created using the volume of the blocks and NOT the written decimal
number. This should help to eliminate rules which students construct
about ordering decimals, based on length of the decimal numeral.
Numbers using very few blocks:
The table below indicates the different numbers (and various representations)
that students could make using exactly 3 blocks, 2 blocks or 1 block
(assuming that there are sufficient blocks available). So, for example,
there are 34 different numbers that can be made using at most 3
blocks (including 0 as a possible choice makes 35) with a further
31 different representations. If you have 20 students, they could
all have a different numeral on their card, if you allow only 2
blocks each. |