Today we did an activity sheet in group-projects called "Circumference versus Diameter." It was about circumference, radius, and diameter formulas. We measured some of the stuff Mrs. Roxanne brought over including some lids, containers, and even an easy-button using a yard/metric-stick. We measured the items by centimeters. We determined the radius, the circumference, and the distance of each of the objects. We also went over formulas including how the circumference, radius, and diameter are related. We recorded the data on a table and then we answered the questions using the formulas.
We did another activity called "Right or Not?" It was a group activity and we used a bunch of square-tiles to determine the areas of angles. We use three different-shaped square tiles to form a triangle. We would then determine if the triangle was obtuse, right, or an acute angle.We then filled in another table. We add the area of the smallest square and third squares to find the areas of the two smaller squares. We then make up the numbers for the areas of the smallest squares and the areas of the third squares. In the next page we have to determine the angles based on the descriptions of the length of the sides. I thought it was very interesting how three squared tiles of different lengths can form different sized-triangles.
Here is a website that further explains the formulas of a circle:
This is my last entry for this semester. We were given
study-guides for the test. I have to admit that I’m pretty scared. This test
requires us to memorize a bunch of formulas. I could easily get some of the
formulas mixed up. But nevertheless, I still have my study-guides. With
practice and motivation I’ll have no problem acing the test. The professor
showed us some really cool geometric origami. They were made using the methods
of tessellation and formed different geometric-patterns. It’s amazing how creative
children’s minds can be. They can perceive certain aspects that teachers would otherwise not have noticed.
We also had some very unusual class-room
presentations. One presentation involved candies which covered the topics of
geometry and building a ginger-bread house.
Every child loves to make ginger-bread houses. Although it’s a shame we
never really got to make one. But at least we still got some candies. Then
there was another presentation where the student brought in a pet iguana (or is
it a lizard?). She covered the topics of measurements and measured the lizard’s
lengths. This is an excellent teaching-method because children love it when
there are animals around.
Here is another ginger-bread house activity:
Gingerbread Houses
Gingerbread Geometry: challenge students to find the footprint, perimeter,
surface area and volume of their proposed gingerbread houses before actual
construction begins. If students are covering milk cartons, small groups could
use empty cartons to find the measurements and describe the tools they used for
each item. Have students use customary (in.) or metric (cm.) measurements,
depending on teacher choice. Volume will be a challenge to younger students
but they might fill the carton with water, rice or sand and then calculate how
many cm-cubes or inch-cubes would fill the same number of cups to get an
estimated volume. They could also fill the house with cm-cubes if a good
supply is available. Students could leave the measurement in cups, if they are
studying liquid measurements.
Decorating on a budget: Price candy decorations and allow students a certain
budget to purchase decorating supplies. Allow students to plan out their house
before actually constructing it.
Patterns: encourage students to use patterns for the roof and for walkways.
Students should classify the patterns as AB, AAB, etc.
Tessellations: which candies tessellate the house surfaces by covering the
entire surface without gaps or overlaps?
Today we did some Geogebra activities. Following the
procedures on work-sheets, we traced the angles along the x and y-axis and
created a triangle. We then drew a second triangle using this weird method by
clicking a button that enables us to make a copy of the triangle that
originates from a certain point. We then did the same thing for the second
activity only this time we had to make a reflection of the angle across the
x-axis. The last work-sheet was the most confusing. Following the procedures,
we had to draw a new triangle and then find the pre-images and reflections of
each of the x and y-axis. On another table we had to find the x and
y-coordinates using the horizontal line-slider and the vertical line-slider. I
was really stumped because it was also confusing. I had to keep track of which
triangles were the original and second triangles.
The professor showed us some art-works about tessellation.
There were images made up of similar patterns that it was almost like an
optical illusion. She also showed us a math video from “Cyberchase.” The topic
was about tessellation. In this video an artist finds how he can move around
similar objects to create a large object. But they all must be the same shape
and they cannot over-lap or form gaps. Tessellation is a pattern made by
repeating a regular polygon. They can be moved around using translation,
rotation, and reflection.
Here is a very helpful link that further explains the
methods of tessellation. There are different shapes and patterns. Notice how
they are allowed to have more than one shape.
Today in class we went over the concepts of reflections,
translations, and rotations. We did activity sheets and drew out the shapes and
lines on grid-sheets. The translation part was easy. All we had to do was
follow along the x and y-axis to form the new shapes. We then did the
reflection activity. The center-points were based on wherever the problems said
they were located along the x and y-axis. For instance, if the problem says to
reflect along the x-axis then we draw the center line vertically. If the
problem states to reflect along the y-axis then we draw the center line
horizontally.
The rotation activity was pretty tricky. We had to figure
out where the shapes would be located along the x or y-axis based on whether
they are rotated 90 or 180 degrees clockwise or counterclockwise. The trick is
we have to turn the paper in whatever rotation the problem indicates to see the
new image. We then have to use a patty paper. I’m still stumped on this part
but I will eventually figure it out. The professor also showed us some videos
that are related to the assignment. One video is called “Transformation”
involving a guy being rotated, translated, and reflected (although you may need
to create an account to watch this video): http://www.brainpop.com/math/geometryandmeasurement/transformation/preview.weml
Here is another video from the Denise Carter’s website
(Smarty Bunch) called “Geometry Transformations.”
I recommend teachers use these videos because they are very
helpful and even fun to learn about geometry.
I found a very helpful math website and I regularly use it
for this class. It goes over the three main transformations of the shapes:
rotation, reflection, and translation. Here it is:
Today we did some activities involving the surface areas of
different shapes. Some of the shapes included prisms, spheres, cylinders, and
cones. We went over the formulas and then solved them based on the information
given for each shape. Many of the formulas included Pythagorean theorems so
find the missing sides of each shape. Some of the answers were solved in base
squares. Others had the pie symbols or were solved by incorporating the pie
formula with the answers. We also went over the formulas for the volume of the
shapes.
We did a class-group activity about the volumes of pyramids
and cones. We had to find the relationship between the volume of a pyramid and
a prism and then we had to find the relationship between a cone and a cylinder.
We used scissors and tapes to cut out and put together the shapes. We then
filled the pyramid-shape with rice and compared its volume with the
square-prism. We did the same thing with the cone and cylinder. The results
were mostly the same. The pyramid and the cone were both 1/3 the volume of the
square-prism and the cylinder. Students will enjoy this activity and find it
easier to understand the concepts of different volumes.
Here is a very helpful video on evaluating formulas of
volume of different shapes:
On Wednesday we went over the concepts of measurement and
area. We did an activity sheet that showed pictures of pins and lines forming
geometric patterns. We had to count the number of squares and outer pins that
formed the geometric shapes. We used the number of squares to find the area and
the number of outer pins to find the perimeter of the geometric shapes. We also
did a classroom activity involving rubber bands and pins. By stretching around
the rubber bands we were able to form geometric shapes. We then applied the
same method from the activity sheet to count the number of squares and outer
pins. We also went over the concept of Pick’s Theorem.
Pick’s Theorem is A = 1/2 x P – 1
Example:
If a geometric figure has a perimeter of 8 pins, what is the
area of the geometric figure?
A = ½ x 8 + 2 – 1
A = (1/2 x 8) + 2 – 1
A = 4 + 2 – 1
A = 6 – 1
A = 5
The area is 5 or I have 5 squares in the geometric figure.
Another method is A = ½ P + I – 1
The I stand for
the interior pins that are inside of the geometric figures.
I found a website that further explains Pick’s Theorem.
Notice that some of the letters have been changed around but they still apply
the same concepts:
From this lesson I learned a different method on how to find
the areas and perimeters of geometric figures. The activities taught me how the
figures can be broken up into squares, triangles, and trapezoids. I really
enjoyed doing the rubber-band activity. It helped me get a better grasp of the
concepts. Children will also find this activity fun and because they are more
actively involved. This is an excellent activity for students who are visually
disoriented, visual, or hands-on-learners.
