Gum Drops, and Toothpicks, and Polyhedra OH MY!

In class this past week we learned of what geometric solids and polyhedra are by going through 6 different stations that included hands-on activities electronically (I-pads) and on paper. With each individual activity, the overall common goal was to find and look for the relationship between vertices, faces, and edges. One of the stations that was in the rotation was the Gumdrop Polyhedra. I will explain what and how to do the activity in a lesson plan type format to be able to use in my future class.

Materials needed: 
-Bags of gumdrops
-Toothpicks
-Colored paper of instructions (picture below)

-Blue fact cards (picture below)

Instructions: 
- Using gumdrops and toothpicks and the picture below, create and build different models of polyhedra.
- While you are building the polyhedra be sure to fill out the fact cards.
-Fact cards: blue pieces of paper, fill out the shapes name, draw a picture of the shape, count the number of vertices, faces, and edges and record each and also draw the shape of the faces.
- The gumdrops as the representing a vertice and the toothpicks are representing an edge.
- Construct each polyhedron on the piece of paper which include: Cube, triangular pyramid (tetrahedron), square pyramid, triangular prism, pentagonal prism
- After you create each polyhedron fill out the fact cards using those models to get a better visual and also try to look for a relationship between vertices, faces, and edges.
- Discuss the relationship between vertices, faces, and edges

The finished product

This activity and the rest of the activities were so hands-on and truly helped me understand and truly visual polyhedra and how they connect to each other and the real world. I think that this gumdrop activity is perfect for any age because it can be easily manipulated into something less complex or even more difficult. I truly enjoyed this activity and I know that I will be able to use it in my future classroom.

Helpful link: https://illuminations.nctm.org/activity.aspx?id=3521
This link takes you to a website that students can interact virtually with geometric solids and polyhedrons.

Symmetry, Symmetry, Symmetry!!

Yesterday in class, we learned about shapes and the how symmetry is in the vocabulary bank for defining every shape. So, there are two definitions one is line symmetry and the other is rotational symmetry. Line symmetry is when a figure divides a figure into two congruent halves. To help truly illustrate this definition in class we each got a strip of white paper with a triangle, a square, a pentagon and a hexagon on it. With a ruler, we were supposed to draw all of the possibilities of a line of symmetry in each shape. (picture at the bottom of the post) I discovered after checking my work with everyone else's and the sample I forgot so many different lines! Then I learned that each line of symmetry can be drawn from every possible vertice within a shape and that changed my whole perspective and understanding of symmetry.

Next was rotational symmetry. A figure has rotational symmetry when it is rotated 0° and 360° the resulting figure coincides with the original. The number of times you get an identical figure is called the order. So to truly understand this concept we were given a colored piece of paper with three yellow shapes (square, parallelogram, and trapezoid) and three brads. (finished product below) As we cut out each shape we were instructed to poke a hole through the shape and then poke the brad and the shape through the colored paper and close it so we could glue it in our notebooks. Because of the brads, we were able to see the rotations that each shape could do. The square has rotational symmetry and can be turned in the order of 4. The parallelogram also has rotational symmetry and can be turned in the order of 2. And then the trapezoid has no rational symmetry as you could physically tell when you tried to move it, it would not rotate.

This activity truly helped me get a solid foundation and start to understanding symmetry which is also a foundation for understanding each individual shape we use in geometry. Also being able to physically touch and move things around helped me and also could help my future kinesthetic learners truly understand this concept on a whole other level.

Helpful link: https://www.topmarks.co.uk/symmetry/symmetry-matching
This is an interactive website geared towards 4-8-year-olds and learning about symmetry with colorful pictures and games.

(Line symmetry activity)

(Rotational Symmetry Activity)

The Mystery of the Nameless Triangle

In class on Tuesday this week we got to explore the complex but fascinating world of triangles. The first activity consisted of us all getting a colored piece of paper and ruler and could draw any big triangle we wanted to and then we needed to classify what kind of triangle it was. But we had no words or even their definitions of what to classify the triangle we couldn't just leave it nameless! So, with the mystery needing to be solved, we needed clues and definitions so next came the foldable that was going to solve our dilemma of the nameless triangle.

The "classifying triangles" foldable (picture at the bottom) consisted of the categories angles and sides. First, we addressed the angles side which is put into three separate categories the first being acute, then right, then obtuse. Acute triangles are defined as having all angles measure to less than 90°. Right triangles are defined as having exactly 1 90° angle within the triangle. And lastly, obtuse triangles are defined as having one angle greater than 90° and less than 180°. So with these definitions, we could now define what kind of triangle it was by its angles! But, we still needed the sides to get the full picture and completely define what kind of triangle we had next to us laying on the table waiting to be labeled and to be solved. The sides were put into three categories just like the angles and the categories were equilateral, isosceles, and scalene. An equilateral triangle is defined as all of the sides having the same length. An isosceles triangle is defined as at least 2 sides having the same length. And a scalene triangle is defined as all of the sides have different lengths. After sides and angles were defined, there were extra boxes within the foldable that we were able to draw close to accurate pictures of what each triangle would look like to get a visual aspect and understanding of classifying triangles.

Now we could FINALLY solve the mystery of what we could name our different triangles. Using our newly gained knowledge, and angle finders and protractors, we were able to solve it and name our triangles! My official name for my triangle was an acute scalene triangle.

This lesson was interactive and I could truly apply what I learned automatically and if I still didn't understand I could ask for clarification in class from my fellow peers and professor. I would definitely use a hands-on activity like this in my future classroom because it truly helps you visually see what types of triangles there are and finding the way that works for you to understand and remember the definitions of each classification of a triangle.

Helpful link: 
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/triangles_shoot.htm
-This link gets you to an interactive math game called triangles shoot which will give students a better understanding of triangles and their angles and sides.

 (The foldable in its full glory.)

 (What the foldable looks on the outside)









(The triangle that was finally named!)