SQUARE PUZZLES

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.

Traditional Method:

Students use paper and pencil.

Technological Method:

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 Figure 3.

FIGURE 1

FIGURE 2

FIGURE 3

Options/Extensions:

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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