Educational Blog Roll

Here are links to five educational blogs that I had found that are truly resourceful and I have found great ideas and have come to a better understanding of how big and wonderful the world of education is!

Blog #1: http://coolcatteacher.blogspot.com/
Blog #2: http://www.learningismessy.com/
Blog #3: http://thankyoubrain.blogspot.com/
Blog #4: https://organizedclassroom.com/classroom-management/
Blog #5: http://www.teachjunkie.com/blog/

Word Problems got you down? Well, Poyla is here to save the day!

Word problems for lots of students can be frustrating and hard to understand. Some word problems have lots of information that is being thrown at you and you want to know what you actually need to use to solve it and what formulas and steps you need to take to get the answer without too much crying. George Poyla helped shed some bright and amazing light on this terrible dilemma with his effective four-step formula.

Step 1: Understanding the problem:
Givens: (What do you know in the problem?)
Goal: (What are you trying to find in the problem?)
Conjecture: Prediction (This should be numerical and in words. Give an estimate you know is too low and an estimate that you know is too high.)

After you first read the word problem you go back to the word problem and highlight and write down the answers to all of those questions to get you started.

Step 2: Devise a Plan:
Strategy: Toolbox (You can choose from the ones listed or write in your own.)
- Draw model/visual
- Make use of structure
- Look for repeated reasoning
- Create an equation/expression
- Guess & check
- Work backward
-  Formula

This is just a short list of many strategies that you could work with and this is where students can feel the most comfortable because they can choose and use multiple strategies to figure out the problem.

Step 3: Carry out the plan: 
Solution: (show all work, label, be precise)
Final answer (written in a complete sentence with units)

I really like the final answer being written in a complete sentence because that gives you time to look back at the original problem and make sure you did everything correctly.

Step 4: Looking Back: 
Verification- Check that your answer is mathematically correct. Is your answer reasonable? (This should be written in words and mathematically calculated.)

Looking back can give you the extra emphasis you need to feel confident and truly make sure that everything makes sense and it completes the original problem and answers what it precisely asked.

I would definitely use this in my future classroom because it gives the foundation and the exact format you need to solve an easy and a hard word problem!!

Helpful Link: http://www.mathgametime.com/subject/problem-solving
(This link is here for students to practice problem-solving with fun games and videos and worksheets for grades K-7.)

Here is the Polya formula used in action! (Link to the example on this website: http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut8_probsol.htm)

A math class has 30 students.  Approximately 70% passed their last math test.  How many students passed the last math test?

 

Step 1: Understand the problem.

 

Make sure that you read the question carefully several times.  We are looking for how many students passed the last math test,  we will let x = number of students

 

Step 2:  Devise a plan (translate).

 

 

Step 3:  Carry out the plan (solve).

 

*Multiply

 

Step 4:  Look back (check and interpret).

 

21 is 70% of 30.   FINAL ANSWER: 21 students passed the last math test.

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)