CCSS.Math.Content.8.G.A.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Personal Opinion: This is a useful simulation tool to gain understanding of the properties of geometric transformations. Therefore, this activity is easy to incorporate into a math lesson to support the procedural practice of translating points, segments, triangles and quadrilaterals
Ease of Use: This activity did not have any supporting directions yet it was easy to use. In rotations, students may not see a square rotate since it will map back onto equivalent sides. It would be beneficial to have students understand why they can't "see" the rotation.
Educational Value: What I liked about this simulation was that it aligned to the CA CCSS to understand the effects of translations, rotation, and reflections. I also like that it provides an option to generate a table of values. This is helpful for students to be able to communicate verbally, graphically, and through tables.
Age/Developmentally Appropriate: This simulation aligns directly with the CA CCSS math standards and would be appropriate lesson for 8th grade math students.
Applicability to Theme: This simulation (and many others on the website) directly apply to 8th grade mathematics. The use of these simulations help provide a concrete example to abstract concepts.
Reflections
8.G.1.a: Lines are taken to lines, and line segments to line segments of the same length.
Personal Opinion: One of the most difficult transformations is the abstract idea of a flip (mirror) over a line. This simulation enforces the line of reflection and that the two points are equidistant from that line.
Ease of Use: This was easy and fun to manipulate both the segment length and the line of reflection. By checking the "Show Connecting Line" it made it clear how the two segments are mirrored.
Educational Value: This simulation is useful to help students understand two ideas on the line of reflection and equidistance.
Age/Developmentally Appropriate: This simulation aligns directly with the CA CCSS math standards and would be appropriate lesson for 8th grade math students.
Applicability to Theme: This simulation directly relates to finding the mirror image or reflection of points, line segments and shapes across a line.
Composition of Transformation
Personal Opinion: This was a unique lesson to teach that transformation can be made of two of more movements to determine the final location of the object.
Ease of Use: The use of flash severely limited the use of all the virtual manipulatives on this site. For $29.95, you can download an offline version to run on both window and Mac. on both individual computers and servers.
Educational Value: I like the simplicity of only having two transformations in the practice of composition of transformations. However, it would limit students that want to explore having more than two transformations.
Age/Developmentally Appropriate: This simulation aligns directly with the CA CCSS math standards and would be appropriate lesson for 8th grade math students.
Applicability to Theme: This simulation helps to extend the idea of transformations and the idea that the order they are applied matters. This could be used for both procedural practice and for exploring the effects of order.
Dilations (Non-Rigid Transformations)
8.G.1.b: Angles are taken to angles of the same measure.
Personal Opinion: I found that this simulation is a great entry point to go from discussing rigid transformations to non-rigid transformations (dilation and scale-factor). I would appreciate if both the original and transformed figure could be shown on the same screen with a choice of colors. The green and pink are the standard colors.
Ease of Use: This was easy to understand and use. There were a variety of shapes to choose to dilate.
Educational Value: This is a good starting point to begin to describe dilations and both enlarging and shrinking. I would point out to notice that the shape only changes size, not shape. It would be helpful if both the green (pre-image) and pink (image) had the same rigid transformations to compare side to side. But this application provides a table for comparison. In this case, I would point out that line segment AB in the preimage is line segment EF in the image (it has undergone a 90 degree counter-clockwise rotation.
Age/Developmentally Appropriate: This simulation aligns directly with the CA CCSS math standards and would be appropriate lesson for 8th grade math students.
Applicability to Theme: It is important for students to understand that there are non-rigid transformations called dilations that are used to determine similarity of two objects.
1. Dice Reflections In this activity, a dice is reflected in two mirrors. The question asked is "What numbers would be on the reflected faces". This lesson is intended to be a teacher led activity or can written extension of reflections onto plane surfaces. The teacher can specify vertical, horizontal or a diagonal mirror lines. There is also a choice of four different comic faces intended to motivate pupils to make a good job of the task.
2. Tessalations In this activity, students can drag fun shapes (like dogs/aliens) onto the canvas using reflections or rotations to create tessellating patterns.
3. Math Planet Is a basic introduction to the different types of transformations including Translation, Reflection, Rotation including supporting video. This would be a great activity as a starter or to help re-teach concepts.
4. Geogebra (Applet). This group of applets help simulation a series of basic transformations including translation, rotation and reflection across intersecting lines.
5. Spoked Wheel (Applet). A torus and some spheres and cylinders are put together to form a wheel. You can use the controls to vary the sizes of the tire, hub, spokes, and axle. Helps to visualize the symmetry of rotations.
6. Mirror Flip Transpose This is a flash game intended for students to use a series of steps to transform the given grid of colors at the top into the target grid at the bottom. Students use critical thinking to combine the three available operations: mirror, reverse and transpose to solve the puzzle.
7. TranStar Game Reflections, rotations, dilations and translations are use to guide your spaceship. The games begins with identifying the line of reflection and then gradually increases to incorporate more than 1 line of reflection. When you loose a game, unfortunately you have to return to the first level and instructions which may cause some students to loose interest.
8. Transformation Golf Game This "golf" game works through 9 holes or opportunities to combine transformations to get the ball (a point) into the hole (to coincide with image). Translation gives the option to move up,down,left, or right one unit. Rotation gives the option to rotate clockwise or counterclockwise, 90 or 180 degrees. Reflection gives the option to reflect over x-axis, y-axis, y=x, or y=-x. Dilation gives the scale factor option of multiplying the radius by 2 or 3, or by 1/2 or 1/3. This game increases in difficulty and require students to consider units of movement in addition to general transformations. 9. Shapes in Motion Game Uses a flash game to practice translations, reflections and rotations. A general game with images instead of shapes (like flags). This may be more appealing to some students. This is a basic game that is short and affords a beginning learner or struggling learner a chance to learn to recognize basic transformations. 10. Shapes Mod Game by Math Playground 18 levels to flip, slide and turn shapes into matching puzzles. I like this game because of the challenging nature. Not only does it ask you to translate up/down or left/right, it makes you specify "by how much". This is a key attribute in learning transformations and is often confusing to students to learn.