Geometry Activity. LESSON: Fractal Snowflakes Formation GRADE: 4 OBJECTIVES:

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Cassandra Goodwin
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1 LESSON: Fractal Snowflakes Formation OBJECTIVES: GRADE: 4 Mathematics Geometry- Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Science Energy 4-PS3-2 Make observations to provide evidence that energy can be transferred from place to place by sound, light, heat, and electric currents. Geometry Activity MATERIALS & RESOURCES: Large sheet of paper (at least 11 x14 ) PRESENTATION: Fractals are repeating patterns of varying scale. In this activity, kids create a two-dimensional snowflake to learn about fractals and geometry. Then learn how energy relates to snowflakes and snowstorms 1

2 DIRECTIONS: 1. Before beginning, the class should have the definitions for the following terms and concepts o points, lines, line segments, rays, angles, right angle, acute angle, obtuse angle, and perpendicular and parallel lines. Classification of two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. 2. As a class, preview the directions and illustrations found below. Help the students find examples of the terms listed in the step # 1. o Draw an equilateral triangle o Divide each side into three equal parts o Remove the middle segment (= 1/3 of the original line segment) replace the middle segment with two segments of the same length (= 1/3 the original line segment) such that they all connect (i.e. 3 connecting segments of length 1/3 become 4 connecting segments of length 1/3.) o To complete the shape, the above procedure is repeated indefinitely on each line segment on the side of a triangle. 2

3 3. In small groups the kids can begin drawing the snowflake. While they are drawing, discuss whether the triangles in the Koch snowflake is a right angle or not. Using different colors of markers or pencils might be fun. Students could decorate their snowflakes, cut out and hang. More examples can be found at the end of this lesson or on the internet. (search Koch s snowflake images ) 4. Afterward, students can experiment with what happens if a right triangle is used to make a snowflake. 5. Fractals are found everywhere. Once you know what it is, you will notice them more often. If time allows, continue to experiment with fractals by showing more examples and allowing the kids to create their own. TIME: min Science Activity MAKE DEW & FROST (From Weather Wiz Kids website: MATERIALS & RESOURCES: 2 tin cans without a lid (condensed soup cans work well, but peel the labels off) rock salt or table salt crushed ice DIRECTIONS: 1. In one tin can put a mixture of crushed ice about half full and about 4 tablespoons of salt. 2. Mix it well for about 30 seconds and then let sit. 3. In the other can put only crushed ice and cool tap water. Fill the can about half way full of ice and then put just enough tap water in the can to cover the ice. 4. Note the frost forming on the outside of the can with the ice and salt mixture. Compare this with the liquid moisture on the outside of the can which contains ice only. 5. Is there evidence that energy is being transferred? How is it transferred? 6. Do you see fractals? Are there similarities between the Koch Snowflake and the frost or is it different? How would you draw the frost? What geometric shapes do you see? Do they repeat? Are the repeating on different scales? 3

4 EXPLANATION: Why does this happen? The salt wants to absorb water to make a salt solution. To do that, the salt has to melt the ice into water. The heat required to melt the ice comes from the ice itself. The strange effect is caused by the chemical reaction between the salt and the ice. Strange as it seems, melting the ice actually makes the mixture cooler. The salt water mixture inside the can gets below freezing, so the moisture from the air that collects on the outside of the can will freeze. This is why frost forms! On the other can, dew forms because the mixture of the melting ice and water is just at freezing and the temperature outside the can is warmer causing the dew to form. Great place to find out about Snowflakes and Frost : Snow Crystals.com TIME: min 4

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Georgia Department of Education Common Core Georgia Performance Standards Framework Fourth Grade Mathematics Unit 6

Georgia Department of Education Common Core Georgia Performance Standards Framework Fourth Grade Mathematics Unit 6 PRACTICE TASK: My Many Triangles Adapted from Van De Walle, J.A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and Middle School Mathematics: Teaching Developmentally 7 th Ed. Boston: Pearson