GIZMOS
Explore Learning: Rotations, Reflections, Translations, Dilations
Explore learning is a site that offers lots of applets to explore many different subjects. Gizmos offer a great way to explore and learn about rigid transformations: reflections, translations and rotations. Because the students can visually see what is going on with the gizmo, they can follow what happens when a point, a line, a polygon is transformed. Adding a similar figures applet allows them to explore dilations.
The website has many different gizmos that are linked by common core standards, state standards, subject and grade. Along with the gizmo is a project sheet that gives several pre-activities as well as activities with the gizmo. An assessment is also offered to test students' understanding.
The website has many different gizmos that are linked by common core standards, state standards, subject and grade. Along with the gizmo is a project sheet that gives several pre-activities as well as activities with the gizmo. An assessment is also offered to test students' understanding.
Standards:Common Core:
MCC8.G.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
MCC8.G.2 Understand that a two‐dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
MCC8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two‐ dimensional figures using coordinates.
MCC8.G.4 Understand that a two‐dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two‐dimensional figures, describe a sequence that exhibits the similarity between them.
STANDARDS FOR MATHEMATICAL PRACTICE: This task uses all of the practices with emphasis on:
1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning
Introduction to Transformations: Reflections and Tranalsations
Students can use the above gizmos to explore translations and
MCC8.G.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
MCC8.G.2 Understand that a two‐dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
MCC8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two‐ dimensional figures using coordinates.
MCC8.G.4 Understand that a two‐dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two‐dimensional figures, describe a sequence that exhibits the similarity between them.
STANDARDS FOR MATHEMATICAL PRACTICE: This task uses all of the practices with emphasis on:
1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning
Introduction to Transformations: Reflections and Tranalsations
Students can use the above gizmos to explore translations and
Dilations (Similar Figures)
Critique of the Reflections, Reflections and Translations Applet:
How well does it work?The gizmo works well if you have Firefox. I was unable to get it to work in Internet Explorer. According to the site, the gizmos have issues with Chrome. Once I downloaded Firefox, the gizmo worked beautifully. The different functions were easy to manipulate. The gizmo aligns nicely with the standardMCC8.G.1, showing that the angles are taken to angles of the same measure and parallel lines are taken to parallel lines. The applet is probably more useful than paper and pencil for simple transformations, as it can be easy to second guess lines and angles when they are hand drawn.
Are the written materials well organized and useful?
The written materials are a great adjunct to this particular applet. There is a pre activity in which the students learn the basics of transformations by using their desk and cut outs to emulate what is going on in the applet. The teaching notes also give lots of input as to how to use the gizmos to teach.
The first activities involve using a single point and moving the y translation to see what happens to the point. (see above). The activities intensify in difficulty and can be tweaked to be a bit easier or more difficult.
What are the purposes and goals for using this technology? Does the technology
reach this goal?
The purposes of this technology is to help students see how transformations effect lines, points and figures in the plane. This gizmo is pretty similar to using paper and pencil, but easier. The only drawbacks are that you can't do sequences of transformations or dilations, which mean the last two standards are not completely covered. However, I did find another gizmo that performs rotations and dilations to add to the transformations. This could be used for standards 3 and 4.
The biggest issue with this gizmo is that you are unable to do multiple transformations. The dilation gizmo allows you to rotate and dilate, but not other transformations.
Is the technology relatively easy to use?
The gizmo is very easy to use. The instructions are clear and it seems pretty intuitive. There is an angle measurement and segment measurement tool that is pretty cumbersome to use, but it is helpful to show that the angles stay the same through the transformations. The dilation widget is easy to use but only offers a reflection option.The reflection, rotation, translation gizmo offers a camera option that is great to have to create worksheets or illustrations. However, it does show that the lengths of the sides of the figure change, while angles stay the same (although not at the same time).
Does this technology enhance or extend the teaching and learning process for the
intended mathematics concepts? How and why?
This gizmo can enhance learning about transformations. Because the students can quickly see what is happening, they can understand more clearly how flips, turns and slides effect the image. The coordinate buttons can pave the way for thinking about functions as the primage maps to the image. The standards state the students should understand that a figure is congruent to another that has been manipulated by flips, turns or slides. It would be nice to have a dilation button, in order to show similarity. However, I think this app is a great app to supplement teaching MC8GG1 thorugh 4. This is a great add-on, but the limitations are that it can't show more than single transformations. These gizmos are a great applet for students to use to get the hang of transformations, before moving on to more complicated machinations. Along with the activity following, students can use the gizmo as they explore more complicated compositions/sequences of translations. The gizmo is helpful, in particular, for showing that transformations preserve angle measure and length.
Would you recommend this product for purchase to a school? Why or why not?
Explore Learning has so many gizmos and I think this is a worthwhile cost for a school. There seem to be gizmos for any type of application. This applet was one of the most user friendly of the Transformation Applets. The ability to find the points after translation ( or leave these blank) and play with what different transformations do was effective. Seeing what happens rapidly when figures, points and lines are transformed could be a drawback. In actually using graph paper to plot out the points of the transformed image from the pre-image, the students see that they count over a certain amount. However, if done with enough repetition, I think this is a wonderful applet to aid understanding.
Provide an activity that makes use of this technology in an effective manner. You should include enough information such that a teacher could successfully use the activity with students.
Ready the gizmo by selecting point and translation. The move the x and y coordinates using the slider bar.
If x is translated a units horizontally and b units vertically then our translation will have the what coordinates?
I am trying to get the students to come to the conclusion that the image coordinates will be:(x+a),(y+b)
Ready the gizmo by selecting segment and translation. Move the slider bars for x translation to see what happens, then move the y translation slider. What do you think happens to the x coordinates? The y coordinates?
Ready the gizmo by selecting triangle and reflect over the x axis. Have the students drag the pre-image around to see what happens to the reflection . What are the coordinates of the point of reflection?
Repeat using rotations.
This can be expanded to use segments and then polygons.
Using the dilation gizmo:
Change the scale factor to 2, 4, 6, what happens to the side lengths? The angles? What changes, what doesn't?
What if you want to scale a triangle by 1/2? What would this do to the x and y coordinates?
After finishing, check the table to see if your answers are correct. Then discuss a general rule for what happens with each translation.
Have students draw a figure on paper, then reflect, rotate or translate. Then have the students recreate the figure on the gizmo and rotate, reflect , translate and dilate to see what occurs. After discussion have the students work in groups with "Transformation Challenge,"
Optional pre activity:
Make cutouts of shapes or letters and flip, turn and slide with the class to show how the angles and lines stay the same.
How well does it work?The gizmo works well if you have Firefox. I was unable to get it to work in Internet Explorer. According to the site, the gizmos have issues with Chrome. Once I downloaded Firefox, the gizmo worked beautifully. The different functions were easy to manipulate. The gizmo aligns nicely with the standardMCC8.G.1, showing that the angles are taken to angles of the same measure and parallel lines are taken to parallel lines. The applet is probably more useful than paper and pencil for simple transformations, as it can be easy to second guess lines and angles when they are hand drawn.
Are the written materials well organized and useful?
The written materials are a great adjunct to this particular applet. There is a pre activity in which the students learn the basics of transformations by using their desk and cut outs to emulate what is going on in the applet. The teaching notes also give lots of input as to how to use the gizmos to teach.
The first activities involve using a single point and moving the y translation to see what happens to the point. (see above). The activities intensify in difficulty and can be tweaked to be a bit easier or more difficult.
What are the purposes and goals for using this technology? Does the technology
reach this goal?
The purposes of this technology is to help students see how transformations effect lines, points and figures in the plane. This gizmo is pretty similar to using paper and pencil, but easier. The only drawbacks are that you can't do sequences of transformations or dilations, which mean the last two standards are not completely covered. However, I did find another gizmo that performs rotations and dilations to add to the transformations. This could be used for standards 3 and 4.
The biggest issue with this gizmo is that you are unable to do multiple transformations. The dilation gizmo allows you to rotate and dilate, but not other transformations.
Is the technology relatively easy to use?
The gizmo is very easy to use. The instructions are clear and it seems pretty intuitive. There is an angle measurement and segment measurement tool that is pretty cumbersome to use, but it is helpful to show that the angles stay the same through the transformations. The dilation widget is easy to use but only offers a reflection option.The reflection, rotation, translation gizmo offers a camera option that is great to have to create worksheets or illustrations. However, it does show that the lengths of the sides of the figure change, while angles stay the same (although not at the same time).
Does this technology enhance or extend the teaching and learning process for the
intended mathematics concepts? How and why?
This gizmo can enhance learning about transformations. Because the students can quickly see what is happening, they can understand more clearly how flips, turns and slides effect the image. The coordinate buttons can pave the way for thinking about functions as the primage maps to the image. The standards state the students should understand that a figure is congruent to another that has been manipulated by flips, turns or slides. It would be nice to have a dilation button, in order to show similarity. However, I think this app is a great app to supplement teaching MC8GG1 thorugh 4. This is a great add-on, but the limitations are that it can't show more than single transformations. These gizmos are a great applet for students to use to get the hang of transformations, before moving on to more complicated machinations. Along with the activity following, students can use the gizmo as they explore more complicated compositions/sequences of translations. The gizmo is helpful, in particular, for showing that transformations preserve angle measure and length.
Would you recommend this product for purchase to a school? Why or why not?
Explore Learning has so many gizmos and I think this is a worthwhile cost for a school. There seem to be gizmos for any type of application. This applet was one of the most user friendly of the Transformation Applets. The ability to find the points after translation ( or leave these blank) and play with what different transformations do was effective. Seeing what happens rapidly when figures, points and lines are transformed could be a drawback. In actually using graph paper to plot out the points of the transformed image from the pre-image, the students see that they count over a certain amount. However, if done with enough repetition, I think this is a wonderful applet to aid understanding.
Provide an activity that makes use of this technology in an effective manner. You should include enough information such that a teacher could successfully use the activity with students.
Ready the gizmo by selecting point and translation. The move the x and y coordinates using the slider bar.
If x is translated a units horizontally and b units vertically then our translation will have the what coordinates?
I am trying to get the students to come to the conclusion that the image coordinates will be:(x+a),(y+b)
Ready the gizmo by selecting segment and translation. Move the slider bars for x translation to see what happens, then move the y translation slider. What do you think happens to the x coordinates? The y coordinates?
Ready the gizmo by selecting triangle and reflect over the x axis. Have the students drag the pre-image around to see what happens to the reflection . What are the coordinates of the point of reflection?
Repeat using rotations.
This can be expanded to use segments and then polygons.
Using the dilation gizmo:
Change the scale factor to 2, 4, 6, what happens to the side lengths? The angles? What changes, what doesn't?
What if you want to scale a triangle by 1/2? What would this do to the x and y coordinates?
After finishing, check the table to see if your answers are correct. Then discuss a general rule for what happens with each translation.
Have students draw a figure on paper, then reflect, rotate or translate. Then have the students recreate the figure on the gizmo and rotate, reflect , translate and dilate to see what occurs. After discussion have the students work in groups with "Transformation Challenge,"
Optional pre activity:
Make cutouts of shapes or letters and flip, turn and slide with the class to show how the angles and lines stay the same.
Questions for Discussion: Suppose you reflect a figure over the x axis and then over the y axis. What single transformation is this the same as? [A rotation of 180° about the origin.] When a figure is rotated, reflected, or translated, is the image congruent to the preimage ? [Yes.] Explain. [The only thing that changes about the figure is its location its size and shape do not change.] Is it possible to reproduce the effects of a reflection with a combination of translations and rotations? [Yes.] Explain. [This is only possible when the preimage is symmetrical about the line of reflection) |
Video games are loaded with Transformations!