Fractals Project

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Start by drawing an equilateral triangle as big as will fit on the page (20cm sides). Find the midpoint of each side with your ruler, and connect the midpoints to form an upside-down triangle. Color this new triangle in with your pencil or a marker; think of it as being removed or cut out from the whole triangle. Repeat for the three smaller triangles that remain, then for the nine even-smaller triangles that remain after that, and so on! Draw through stage 4, completing the chart as you go, then try to predict the numbers for stage 5! Stage 0 1 2 3 4 5

# Triangles Left 1 3 9

Area of a triangle = ½*b*h Area of equilateral triangle = s2 * √(3) ÷ 4

Area of each triangle

Total Area

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Start by drawing a square as big as will fit on the page (20cm sides). Split each side into three equal segments (i.e. measure and divide by three). This will split your large square into nine smaller squares. Color in the center square with your pencil or a marker; think of it as being removed or cut out from the whole square. Repeat for each of the eight smaller squares (surrounding the middle) that remain, then for the 64 even-smaller squares that remain after that, and so on. Draw through stage 3, completing the chart as you go, then try to predict the numbers for stage 4! Stage 0 1 2 3 4

Area of a square = b*h = s2

# Squares Left 1 8 64

Area of each square

Total Area

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Start with an upside-down equilateral triangle (with about 15cm length sides), as Stage 0. Cut up each side into three congruent segments, then draw an equilateral triangle on the middle segment of each side. Erase the original middle segment, so that your Stage 1 design looks like:  Repeat the steps to create Stage 2 (start by dividing all twelve sides from Stage 1 into three equal segments). Stage 2 is not pictured on this page. Stage 3 looks like this: A few questions: 1. At each stage, is the snowflake equilateral? 2. Measure the length of your sides at each stage, and complete the table below. 3. Can you predict the number of sides, length, and perimeter at Stages 3 and 4? 4. Will there be a stage with perimeter over 100cm? Explain why you do or do not think this will occur. Stage 0 1 2 3 4

Number of Sides 3 48

Length of a side

Perimeter