This activity combines drawing
techniques and mathematical concepts. Students need to be aware
of what they are doing and the results they are getting. Students
will be producing squares by bisecting lines and marking the point
with difference between the two on either side.
Students use paper and pencil.
Start by using Clairswork MacPaint to produce Figure 1.
Mark the point with the difference between the two on either side. Then by joining the figures with diagonals, Figure 2 is produced.
Extend further by again dividing
lines and marking each difference. It may be clear by now what
will happen if the process is repeated and a fourth square is
inserted between the 2's
and 3's. All 1's will
result and the next square will produce O's. Thus producing
1. Start with other numbers: Which will work satisfactorily/ Do not work? Is there any way of knowing
2. Try same with pentagons, hexagons, heptagons, and octagons.
3. Use all odd or even numbers to start
4. Use fractions or decimals
5. Start with mathematical description of this activity; For example-- Ask students why this activity would not work if they add, instead of subtract, the pairs of numbers.
6. Are students achieving a
balance of mathematical thought and software manipulations?
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