En light ening Geometry

Transcription

1 En light ening Geometry for Middle School Students by Julie LaConte Many science topics can naturally be integrated with a variety of mathematical concepts, including the study of light and optics. Working collaboratively with the math teacher on my team, we integrated the concepts of light, optics, and geometry to create a set of handson activities where students can explore the properties of light energy while building their understanding of geometric concepts. One of the main concepts included in the National Science Education Standards, Content Standard B, focuses on the transmission of light, involving both reflection and refraction (NRC 1996). The following activities were designed to help students understand the concepts of refraction and reflection, and can be conducted over a one- to two-week period. These activities were completed while the math teacher on our team was simultaneously teaching a variety of geometry concepts. Reflection We begin with a study of reflection, a topic with which students should already have practical experience. We introduce an activity that has been modified from an AIMS Pieces and Patterns activity titled Mirrors That Multiply (Hillen 1986). I provide two small, square mirrors of the same size to pairs of students. I use D e c e m b e r

2 Diagram courtesy of the author unbreakable plastic mirrors that are approximately 10 cm 10 cm. These are available through a wide variety of science supply catalogues and teacher supply stores. Any small, square mirror will work for this activity. After donning safety goggles and listening to reminders about sharp edges, students begin their exploration of reflection by carefully touching one edge of each mirror together, creating a hinged effect. Students then place a small object (a coin, game piece, etc.) in between the two mirrors. Students move the mirrors closer together and then spread them further apart on the hinge, examining the resulting effect on the image in the mirror. Specifically, students are looking for the relationship between the angle of the mirrors and the number of images created. I have students experiment with this technique for a few minutes and then place a piece of paper underneath their mirrors. They use their pencil to draw and label the angles created as they shift the mirrors and then measure these angles with a protractor or angle ruler. Students create a chart with the measurement of the angle in relation to the number of images produced in the mirrors. Over time, students see that as the angle measurement decreases, the number of images produced in the mirrors increases. This activity coincides with their study of types of angles in math class, so they are able to name the angles created FIGURE 1 Mirror images by the mirrors as obtuse, right, or acute. Students also have experience naming, measuring, and estimating angle degrees from math class. After experimenting with the relationship between the angles and resulting images, students use a flat, or plane mirror to explore the law of reflection. For this experiment, pairs of students get a plane mirror (I use the same mirrors from the last activity), a small block of clay (one small block of clay per pair, stiff enough to support the mirror), a piece of graph paper, and two small toothpicks. Students position the mirror on the graph paper so it runs along the x-axis. They place the block of clay behind the mirror to prop it in an upright position along the x-axis, trying to get the mirror to stand as straight as possible. If the mirror leans, it will distort the image slightly. The mirror should be centered on the graph paper so the y-axis runs through the center point of the mirror. Students then place the end of one toothpick on the origin and position it so it runs diagonally across the lower right-hand quadrant of the graph paper. They make a mark with their pencil at the end of the toothpick and label it point A. Students observe the virtual image created in the mirror and position the second toothpick so it is in a straight line with the virtual image of the first toothpick in the mirror. Thus, the second toothpick has one end at the origin and it runs diagonally across the lower left-hand quadrant of the graph paper. Students make a mark at the end of this toothpick and label it point B (see Figure 1). Moving the toothpicks off the paper, students connect points A and B to the origin with straight lines. They use an angle ruler or protractor to measure the angles created by point A and the x-axis, as well as point B and the x-axis. Students should notice that the angles are the same, or very close to the same. From this quick experiment, students are able to see the principle behind the law of reflection, that the angle of light approaching the mirror (angle of incidence) is equal to the angle of light reflecting off the mirror (angle of reflection). Students can continue to experiment with this law by slightly shifting the position of the toothpicks, drawing new points, and measuring again. The law should hold true with the toothpicks in any position in front of the mirror. After the hands-on portion of this experiment, I assess by showing students a diagram of a plane mirror with a beam of light coming toward it. Students have to label this as the incident beam and then measure the angle of incidence. Then, they have to draw in the reflected beam at the appropriate angle and label the angle of reflection and the reflected beam. I give them two or three of these as an assessment. 2 4 SCIENCE SCOPE

3 Students are encouraged to create their own patterns and challenge their classmates to complete the flip of their image. We compare the reflections created to other geometric transformations they are learning about in math class, including translations and rotations, looking for similarities and differences. Symmetry After building on students math skills of naming, estimating, and measuring angles, we continue to use mirrors to reinforce the geometric transformations they are learning about in math class. I give students a paper with a variety of large letters and simple shapes on it (a heart, smiley face, polygon, etc.) modified from an AIMS Pieces and Patterns activity titled Halves and Halve-nots (Hillen 1986). Students use small square mirrors to find the lines of symmetry in the shapes and letters, and then mark them using dotted lines. Students are challenged to find all lines of symmetry and draw an object of their own that they can trade with a friend to find the lines of symmetry. Upon completion of the symmetry activity, students use their mirrors to demonstrate the geometric transformation of a reflection, or flip. I provide students with small grids that have been divided in half, with one side showing a shaded pattern. Students then hold their mirrors on the dividing line and observe the reflection of the pattern in the mirror. They shade the reflection, or flip, of the pattern on the opposite side of the dividing line. Again, students are encouraged to create their own patterns and challenge their classmates to complete the flip of their image (see student samples in Figure 2). We compare the reflections created to other geometric transformations they are learning about in math class, including translations and rotations, looking for similarities and differences. In the past, I have assessed their understanding of the concept of reflection by observing their grid patterns to ensure that they are shading correctly to show the reflection and accurately flipping the image across the axis. flat, rather than sloped or curved, sides. Plastic shoebox containers work well, are available at a wide variety of stores, and are not expensive. The group also needs water (enough to fill the container halfway), a few drops of milk, a large piece of graph paper (11 17 or larger), an angle ruler or protractor, and red, blue, and green colored pencils. A laser pointer will also be used by the teacher for the group (see Scope on Safety on page 60 in the Summer 2007 issue of Science Scope). FIGURE 2 Student samples Refraction The final, and most extensive, light and geometry activity is adapted from an AIMS activity called Bent on It (Mitchell 1998). This activity focuses on the concept of refraction, or the bending of light as it passes through different media (see Light Refraction Activities Sheet, Part A ). For this activity, students work in groups of four. Each group will need a large, clear container with D e c e m b e r

4 Light Refraction Activities In these experiments, you will be examining how light refracts through different media. But first, you will need to prepare the path that light will travel. Answer all questions on another sheet of paper. Part A: Light Refraction Lab Procedure 1. Plot the following points on your graph paper. Label each point with the designated letter. (0, 0) = O (-9, 9) = A (-9, 3) = B (-9, 0) = C (9, -8) = D (9, -3) = E (0, 9) = F (0, -9) = G (9, 0) = H 2. Connect the points Connect points A, O, and D with a blue line Connect points B, O, and E with a red line Connect points F, O, and G with a green line 3. Name the angles. Remember, acute angles measure, right angles measure, and obtuse angles measure. 4. What type of angle is angle AOC angle AOH 5. Estimate the angle measurement of the given angle. angle aoc angle aoh 6. Measure the angles. Use your angle ruler to find the actual measure of each angle. angle AOC angle AOH 7. Test the path of light. (Make your observations looking down onto the paper, as your teacher shines the light for you.) place the laser pointer on point D and shine it along DA. place the laser pointer on point E and shine it along EB. place the laser pointer on point G and shine it along GF. What medium is the light traveling through? How does light travel? 8. Take the clear container and place the long side of it along the x-axis of your graph. (Make your observations looking down onto the paper, as your teacher shines the light for you.) place the laser pointer on point D and shine it along DA. place the laser pointer on point E and shine it along EB. place the laser pointer on point G and shine it along GF. What medium is the light traveling through? how does light travel? 19. Add water to the container so it is half full. Starting at point G, have your teacher shine the light along GF. Look down into the water. Can you see the beam of light? 10. add a few drops of milk to the water and swirl it around. Again, start at point G and have your teacher shine the light along GF. Look down into the water. Can you see the beam of light now? Why? Place the laser pointer on point D and shine it along DA. Place the laser pointer on point E and shine it along EB. What do you observe about the path of light when the water is added to the container? Why does that happen to the light? 11. observe as the teacher places the laser pointer on point G and shines it along GF through the water. Does the light bend? Why or why not? Part B: Light Refraction Challenge Procedure 1. Have your teacher place the laser pointer on point D and shine it along DA through the water. 2. Make a new point on the graph paper where the light is refracted to and label it point X. What kind of angle is XOC? What is the measure of angle XOC? 3. Compare angle AOC to XOC. What is the difference between the two angles? (This is called the angle of refraction.) 4. Have your teacher place the laser pointer on point E and shine it along EB through the water. Make a new point on the graph paper where the light is refracted to and label it point Y. What kind of angle is YOC? What is the measure of angle YOC? 5. Compare angle YOC to BOC. What is the angle of refraction? 2 6 SCIENCE SCOPE

5 Upon completion of these light activities, students have grasped not only the scientific concepts of reflection and refraction, but strengthened their understanding of often abstract geometric topics with frequent practice and handson experimentation. Although the materials and setup of some of these experiments can be unwieldy, the resulting authentic experience it provides students is worth the effort. This activity begins with students plotting nine different points on their graph paper. Students then connect three points with a blue line, three points with a red line, and three points with a green line (see Light Refraction Activities Sheet). Students then name the angles as acute, right, or obtuse, estimate their measure, and then find their actual measurement. Then, the teacher operates the laser pointer and students observe the path of light as it travels along different lines they have created. They place the clear container over the graph paper along the x-axis and shine the laser along different lines, observing the path of light by looking down into the empty container. Students add water and a few drops of milk and repeat their observations. When the water and milk are added, students can see the beam bend as it passes through the water/milk mixture in the container, resulting in a new line created by the laser. As an extension, students can plot this new line and measure the resulting angle of refraction (see Light Refraction Activities Sheet, Part B). Conclusion Upon completion of these light activities, students have grasped not only the scientific concepts of reflection and refraction, but strengthened their understanding of often abstract geometric topics with frequent practice and hands-on experimentation. Although the materials and setup of some of these experiments can be unwieldy, the resulting authentic experience it provides students is worth the effort. By taking a little extra time to coordinate our light and geometry units, the math teacher and I have been able to provide students with a practical application of geometry and the visual representation of the transmission of light in an engaging context. These activities are just a few selected ones that I do during an entire light/optics unit. Throughout the unit, students receive hands-on experience with geometric concepts. As they are learning about angles and angle measurements, they are able to see the application of these geometric concepts in the real world in how they relate to reflected images. Students notice that as angles change, the appearance of the reflected image changes as well. They see how the light is refracted at an angle as it passes through different media and we again discuss this in terms of the real world and relate it to our previous study of the atmosphere. We discuss how the refraction, reflection, and scattering of light as it passes through the atmosphere affects the colors and visual effects we see in our sky. We extend these activities with simulations modeling mirrors in the real world where students have to set a mirror at a certain angle so a driver in a car has optimal vision from their side mirrors. Understanding the law of reflection allows them to set the mirrors at the best position based on the angle created between the driver and the mirror. Students are also challenged to use mirrors to see around barriers and find a pathway using the appropriate angles to position the mirrors for a clear view around the model objects. n References Hillen, J Pieces and patterns: A patchwork in math and science. Fresno, CA: AIMS Education Foundation. Mitchell, D Bent on it. AIMS Education Foundation Magazine 13 (5): National Research Council (NRC) National science education standards. Washington, DC: National Academy Press. Julie LaConte (lacontej@ritenour.k12.mo.us) is a classroom teacher at Hoech Middle School in St. Ann, Missouri. D e c e m b e r