Well, I teach middle schoolers, but I would say that a great place to start is nature. You can use animals, plants and people to demonstrate reflective symmetry and rotational symmetry (from antlers to butterfly wings, to human bodies; flowers, shells, pine cones, bottle caps, and kaleidescopes). Maybe even have a scavenger hunt for them to find things with symmetry, then make drawings of symmetrical things where they have to draw in lines of symmetry. They could make their own kaleidescopes as well.
What do they need to know about transformations in 4th grade? You could do a game of Simon Says to start. Simon says move two steps to the right, Simon says turn halfway around, etc. Then he could explain the terms and what they mean, using pictures or diagrams, then do a repeat game. This time, each time you tell a move, the kids have to shout out what it is: translation! rotation! etc. If you need more depth on each one, he could then have a follow-up lesson on each later in the week. These subjects are perfect for acting out and doing artwork. Centers would work, too, for reinforcement: they could build something with a certain kind of symmetry out of blocks, identify the translation on a worksheet, draw symmetrical objects, etc.
Why is he banned from using the textbook? It this something his college requires? The textbook is a good tool for beginning teachers to use until they become "sure footed." Then they will branch out and use many other resources.
With that being said, do you have an overhead or document camera? This would be a good way to show these concepts. He could have the students come up and demonstrate the move as well.
The reason I "banned" him from the textbook for this particular unit is that he was struggling to come up with ways to TEACH....he was simply reading every lesson without regard to student understanding.
I showed him how to pull all the key objectives from the unit and wanted him to find alternative ways to teach them--he had just done a full unit from the math book--and not super successfully.
I laid out the unit for him....1-2 lessons on symmetry, 1-2 lessons on slides, etc. It was just a matter of finding ways to present the information--and the internet is full of them. I have kids who learn in many different ways and large group, lecture from the text isn't always best. That's why I asked him to try something different. I even gave him several ideas. There is way more to the story....but I won't go there!
I understand now. I can see there is more to this story than meets the eye.
Maybe he could make a power point lesson to present the differences between these concepts then do a hands on lesson where the kids actually have to move the shapes etc...
There are two things that I've used to teach these - tessellations and quilts.
I love Escher, so I use his tessellations and we talk about how he tessellated the plane - did he flip the figures, did he rotate them around a point, etc. Then my students create their own tessellation - they can do the "easy" way - just slide over each time.. or they can make it more complicated. I've used this with every grade from third to sixth. The variations are basically how complicated the tessellations get.
The quilts - I found TONS of quilt patterns(squares) online and made a powerpoint of JUST the squares. We go through the PPT as a class and discuss the geometric shapes, the symmetry, is it reflectional or rotational symmetry. Did they make a pattern by reflecting, rotating or translating. Then students use grid paper and each create their own quilt square design.
I teach 4th grade math to third graders. I taught geometry a while ago, but I will see what I can remember at the moment.
The first thing that comes to mind is the slide, flip, turn with geometric objects.
A great activity to do with this is to give the students manipulative's and graph paper. Take the graph paper ( i like to use the stuff that has the big boxes) and draw a line down the middle. Place the object (triangle, diamond/just not circle or square) on the left side of the line and trace the shape. Then flip, slide, or turn over the line and retrace the shape. On each of these I have the students label what they did (flip, slide, turn).
Another great idea is to create designs using flips, slides, and turns on graph paper. Simply keep flipping sliding and turning and tracing the shapes each time. The students can then color their designs. ADVICE: do only one action per graph paper to limit confusion!
one thing i did help my 4th graders GRASP the concept of the flip, translate, slide, etc.....
get out pattern block manipulatives, such as a trapezoid.....i then had students fold a paper in half, and draw a line on the crease, then they would physically move the shape(such as the trapezoid) certain ways, including rotating, etc...they might flip it across the line....or slide it...etc....and they physically see the movement with their own eyes..this also helped to introduce the concept and get them to see what i was about to ask them do........
Alphabet City...geometry in nature and symmetry
The Greedy Triangle...polygons
Sir Circumference and the First Round Table...circles
Shape Up: Fun with Triangles and Other Polygons...triangles, lines, angles
Mummy Math...solid geometry
Grandfather Tang...tangrams, polygons, problem solving
Sir Circumference and th eSword in the Cone...solid geometry
Sam Johnson and the Blue ribbon Quilt...geometry
Elmer...tessellations
The kids love them and there are so many activities to do.
I try to incorporate all multiple intelligences within my lessons so we dance! Everyone gets into a large circle and slides to the right as I yell out translate! Then we rotate by doing a marching pivot with our feet-four point turn as I call out rotate for each turn. Then when I say reflect the kids do a 180 turn to "look" at themselves in the mirror. We do this several times and have a blast doing it!
Perhaps they could try teaching students about tessellations. If you do a search online you can find some wonderful Powerpoints. Escher is a good example of tessellations. Have students create their own tessellation art (it will teach them slides, rotations, etc.) They can describe what focus they used or have the teacher select a minimum of focui for them (ex: Your project needs at least 2 slides, one rotation, etc.)
After they have created their project set 'em loose in the school yard or nature ato find more of the concepts.
I have done this project with my 4th graders for the past two years and they really enjoy it and don't reralize they are learning math concepts :-)
04-17-2008, 09:28 AM
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